T i - V I C"' K - >■■ ' ■ 1 ■"■•If «■t tj I-- • ■»■■• t..-'-hV- * i' ^ ^ ! > .■t it?' - K' : s pO rt ^ , — ^ 1 v • . - -i p t-' ^ »t-J.-* , t srl? A JcKiirnal of Computing anđ Iiiforinatks iP f- V The Slovene Society INFORMATIKA LJubyana Informatica A Journal of Computing and Informatics Subscription Information Informatica (ISSN 0350-5596) is published four times a year in Winter, Spring, Summer and Autumn (4 issues). The subscription price for 1992 (Volume 16) is US$ 30 for companies and US$ 15 for individuals. Claims for missing issues will be honoured free of charge within six months after the publication date of the issue. Printed by Tiskarna Tomi Pretnar, Bratov Komel 52, Ljubljana. Informacija za naročnike Informatica (ISSN 0350 - 5596) izide štirikrat na leto, in sicer v začetku marca, junija, avgusta in novembra. Letna naročnina v letu 1992 (letnik 16) se oblikuje z upoštevanjem tečaja domače valute in znaSa okvirno za podjetja DEM 30, za zasebnike DEM 15, za študente DEM 8, za posamezno številko pa DEM 10. Številka žiro računa: 50101-678-5184L Zahteva za izgubljeno številko časopisa se upošteva v roku šestih mesecev od izida in je brezplačna. Tisk: Tiskarna Tomi Pretnar, Bratov Komel 52, Ljubljana. Na podlagi mnenja Ministrstva za informiranje št. 23/216 - 92, z dne 27.3.1992, šteje znanstveni časopis Informatica med proizvode informativnega značaja iz točke 13 tarifne številke 3, za katere se plačuje davek od prometa proizvodov po stopnji 5%. Pri financiranju časopisa Informatica sodeluje Ministrstvo za znanost in tehnologijo, Slovenska 50, 61000 Ljubljana, Slovenija Informatica A Journal of Computing and Informatics EDITOR-IN-CHIEF Anton P. Železnikar Volaričeva ulica 8, 61111 Ljubljana ASSOCIATE EDITOR Rudolf Murn Jožef Stefan Institute, Ljubljana The Slovene Society INFORMATIKA Ljubl[jana Letnik 16 Številka 4 December 1992 ISSN 0350-5596 Informatica Časopis za računalništvo in informatiko VSEBINA Into the New Perspective An Essay on Epistemology and AI An Introduction to Informational Machine Learning Qualitative Models with Inductive Logic Programming Explanation of Neural Network Classification Implemetacija TEX-a na računalu Atari - ST Vpliv časovne razvrstitve izvajanja modulov algoritma na pospešitev porazdeljenega SPV Genetski Algoritmi Metodologija načrtovanja namenskih RT sistemov Computers in Mathematics in Slovenia A.P. Zeleznikar O.B. Popov A.P. Zeleznikar S. Džeroski M. Drobnič B. Korenjak M. Varga V. Jovan B. Filipič P. Kolbezen Nika Gams M. Gams O.B. Popov Prologue to the Soul of a New Science Informatica v letu 1993 (navodila) Avtorsko stvarno kazalo časopisa Informatica, letnik 16 (1992) 1 .2 8 30 42 48 53 59 69 86 91 94 96 Into the New Perspective In its seventeenth year of publishing (Volume 17, 1993), the journal Informatica is entering in the following conceptual breakdown concerning its contents, typographical standards, and organization. The new image of Informatica will offer a heterogeneous international editing board with globally recognized personalities. On the other hand, several information-significant fields will be considered ranging from the technological field of computing to the philosophical realm of the extended notion of information. In this way, the boundary areas of contemporary philosophy, science, and technology will be conjoined representing the perplexed and disciplinarily interweaved realm of live and artificial informational entities. As pointed out, in its contents. Informatica will follow several diversely oriented scientific fields in which informatics is placed into the focus of human investigation all over the world. In this sense, also the postmodemis-tic view of scientific mind pertaining to informatics, cybernetics, robotics, intelligence, informational theories, new formal symbolism—to stress only the most remarkable items—will be treated. Thus, Informatica will prepare a place of possibilities for a spontaneous and, simultaneously, variously open exchange of the informational-scientific thought and its researching within new landscapes of technological development. In its typographical shape. Informatica will follow the so-called TEX standards which are, more or less, familiar to the scientific communities in the developed as well as developing countries. An internationally dispersed net of editors and referees will guarantee not only the highest possible professional (that is, objective and neutral) standards for submitted paper evaluation, but also the necessary objectivity to the possible diversity, significance, and contents innovation. Further, communication between editors and authors will be enhanced by using regular e-mail channels. In this way, the editorial service of Informatica will perform friendly and fluently for authors over the globe. The new perspective of Informatica will contribute to the scientific alloy of global theoretical thought in the field of informatics, cybernetics, and artificial intelligence. It will become the friendly abroad for many authors, for Slovenia is a small, poor, and hospitable European developing country. This position of Informatica will offer a rhythmic and harmonic background for author' and editors' improving initiative and a loosened satisfaction to all involved parties. Anton P. Železnikar The Editor-in-Chief AN ESSAY ON EPISTEMOLOGY AND ARTIFICIAL INTELLIGENCE Keywords: cognition, mentalism, complexity, ratiocination, artifact, doxastic and epistemic notions, formalization, formal system, logic Oliver B. Popov Institute of Informatics Faculty of Natural Sciences and Mathematics University of Skopje, Skopje In the selective constellation of pure philosophy epistemology or the study of knowledge has a long and distinguished tradition. However, in the last half of the twentieth century many epistemologica! concepts and paradigms have entered in a number of diverse disciplines such as linguistics, economics, computer science and artificial intelligence. Indeed, the study of knowledge has become a major area of research in the field of artificial intelligence. The interplay between epistemology and artificial intelligence and its reflections is in the focus of this essay. The essay is comprised of a series of articles. The first one deals with the origin of relations between AI and epistemology by identifying some of the fundamental questions and problems in AI and the possibility for their solution through epistemology. The second one attempts to find a mode for modality or non-standard logical systems, as well as explores the classical theory of knowledge. The series proceeds with the study of the semantic and syntactic approach, and is finally exploring the hybrid paradigm. At the end, an extensive bibliography is provided for the concerned reader. part I: the Origins of the relationship "All men by nature desire to know... .• Aristoteles 1. Genesis The contemporary echo of the idea of an intelligent machine originates with the invention of the stored program computer and the reflections by Alan Turing and Claude Shannon. Those reflections are certainly behind the emergence of Artificial Intelligence as a valid scientific discourse in the second half of the 20th century. The possibility that an artifact could perform cognitive functions, ones exclusively in the domain of human competence, is intriguing in its implications. It appears that human nature has been deprived of the last marvels of existential uniqueness: the ability to reason and create knowledge which are intrinsic components of the phenomena termed as intelligence. Indeed, a respectable number of researchers in Artificial intelligence have explicitly equated the cogitative potential of humans with the one of artifacts. There are two plausible sources for the equivalence drawn between artifacts and humans: the first one is the complexity of artifacts and the second one is the rationalist tradition in the analysis of human cognitive behavior. Complexity is reflected in the essential attributes of each artifact: relative independence, flexibility and multi-usefulness. All of the attributes are present both on a structural level (or hardware) and on a functional (or software) level. The effect of unpredictability is a direct consequence of complexity. Regardless of the intended level of determinism that might be possibly achieved through simulation, the presence of unpredictability is inevitable. This might be due to the empirical notion that results of a process are at least one level higher in their complexity than the process that has produced them. Hence, there is a possibility for unequivocal opposition to the rationalist tradition which demands a closer examinations. Intellectual disciplines usually evolve over many centuries. The 'success' of any intellectual discipline is often measured in how well its fundamental principles have been encapsulated within a formal system. The mathematical method that attempts to coincide with pure formality and rationality has been accepted as a metric of how 'serious' and 'hard' scientific endeavor is. Rationality requires clearly defined problems. However, most AI problems defy stable formulations which raises the second argument against the rationalist approach. The rationalist method has also been adopted in the identification of the phenomena that create knowledge: experience and ratiocination. The notion of experience is reduced to that of a modification of a knowledge base. In this case, the initial set of facts represents an apriori knowledge built into a system which upon the application of valid inference becomes an experience for a reasoning agent. Informally, an argument as a result of inference is valid if and only if its premises could not be true and a conclusion false. Ratiocination is to be understood as a form of analysis entirely dependent on the inherent power of the 'mind' to reason. The identification of processes of reasoning and computing leads to general (although not universal) acceptance of brute force capabilities by an artifacts as a form of ratiocination. The characterization of experience and ratiocination is consistent with the axiomatic acceptance in AI of the dictum "cognition is a resolute computation". Pragmatics makes this quite necessary. After all, there will always be a difference between a form and a context. One must recognize that form is a prerequisite for computation. By adopting some of the principles of mathematical logic, the present body of work in epistemology and AI follows the rationalist tradition. The diviation from rationalism is the requirement that epistemic reasoning is done within the system. It is acknowledged that cognition demands inner presence, or as Heidegger argues "being-in-the world". The intention of an epistemic system is to capture a part of the world by empowering an artifact with its own mechanism for reasoning about the state of knowledge that encompasses it. Thus, it is important to distinguish between the method which is rationalistic and the intention which is mentalistic. The mentalism induced by the intention should not be confused with the phenomenon of anthropomorphic fallacy whose ramifications are addressed later. 2. The Limits of Formality The word formal, as commonly understood, is synonymous with the word mechanical.The definition of Hilbert's Programme and the seminal works of Godei and Church put to rest the speculative arguments of unlimited expressive power of formal systems, hence on mechanization or automation [Chu56,God31]. These results are a vindication in the resolution of mentalistic problems with formal methods. Instead of confining, the results simply state that formality might prove to be a reasonable first step due to structural and functional constrains of an artifact and the incomplete knowledge of ourselves. The nature of discipline such as AI where Man is an object and a model of studying is inevitably a source of problems. An adequate simulation of bona fide human properties subject to self-reflected interference which mislead some researchers to look for and recognize purely anthropomorphic features in artifacts. For example, Searle distinguishes between a weak AI that "can build a powerful tools to mimic and study the mind", and strong AI where "something can think in virtue of instantiating a computer program"[Tor84]. Accordingly, Searle claims that the former problem is solvable while the answer to the later One is a definitive no. Others have asserted that on an abstract level there is no difference between the mind and the computer. These arguments are 50 strong that can be easily dismissed on the grounds that the understanding of human cognitive properties and functions is still in its inception. A prima facia value is the affirmation of the symbiotic relationship between AI and Man. Although there is "still to be learn more about machines form the study of man" as Von Neumann put it, hopefully there is something to be learned about man from the way some artifacts work. The artifacts are actually a possibility for an extension of human potential and never its replacement. At this point, it might be prudent to propose a principle of 'rational commitment'. It is an informal recognition of the fact that the question of intellectual equality between Man and Machine is an exercise in impuissance and a statement against the reduction of intelligence to a single phenomenon. The principle does not imply either the acceptance of rationalist tradition or the exclusion of mentalism. As stated earlier, formalizations are based on abstractions. Abstractions, occasionally create deviant images of reality as it is reflected in efforts to capture the essence of common sense reasoning. By necessity models in AI start ad hominem, by desire they end up ad machinum. Whether they coincide in extension is yet to be seen. Both should be acknowledged whenever a question is raised of how comprehensive, compelling and complete a certain theory is that leads to better understanding of human mental abilities. The principle is asserted since the emphases is on factual and positive rather then on speculative and negative. 3.Fundamental Concepts Any serious intent by an artifact to encompass a level of cognitive generality postulates an integral ability on its part to reason with deductive, inductive and evidential rules [Chi66]. The evaluation of evidence is also subject to inductive and deductive criteria. A distinction is made in order to stress the meta-system significance of evidence. In essence, the rules of evidence govern the epistemic environment of an intelligent agent. They determine the course of proper reasoning since in extension the true evidence coincides with knowledge. The assessment of knowledge within a reasoning system is usually a result of an internal or external query. The nature of the request might be either to revise the current knowledge of the system (in view of some new situation) or to answer whether some proposition is known or not. It is the later type of response that epistemic models are trying to capture. Inter alia, the solution of reasoning about what is known may also prove necessary to address the problem of knowledge revision. The AI community shares the controversy concerning the ontological difference between declarative and procedural knowledge with so many paradigms in epistemology. Declarative knowledge is expressible through the mode 'knowing that' while procedural knowledge through the mode 'knowing how'. An addition^ mode, often used in the process of explanation, is expressed through 'knowing why'. There are authors who take the position that both procedural and explanatory modes are reducible to declarative mode. In the case of causal ordering (an instance of which is the notion of plan) the nature of ordering and its condition can also be expressed through a set of declarations (or propositions). If propositions are treated as objects of knowledge then the notion of knowing is examined as an empirical relation between a reasoning agent and an object. Doxastic and epistemic inclinations such as knowing and believing are expressed through the verbs of propositional attitudes, know and believe [Rus61]. Propositional attitudes usually define or appear in an intensional context. A context is intensional if its co-referential expressions such as singular terms, predicates or sentences that have the same denotation are not substitutable^ without changing the truth value of the contexts as a whole. Otherwise the context is termed as extensional. One can find the metaphysical difference between knowledge and belief rather interesting in understanding the nature of knowledge. Knowledge is a correct interpretation of reality; the imposition of correctness is distinguish knowledge from mere ideas, opinions, perceptions, and beliefs. As defined, the notion of knowledge is identical with the notion of truth. De facto one of these notions would be redundant in the presence of the other. Knowledge is intrinsically committed to representation and identification, The representation deals with the ontological properties of knowledge; the identification addresses the metaphysical properties. It is commonly understood that: an agent 'a' knows n if and only if (1) The Truth conditions is satisfied: 11 is true (2) The Belief condition is satisfied: an agent 'a' believes n . The term 'agent' denotes an entity capable of reasoning while 11 stands for an arbitrary proposition. The first condition is the least controversial one, since it is a matter of intuitive sanction and linguistic necessity. Contrasting views exist with respect to the Belief condition. One view accepts the condition either in a strong form such as 'knowledge entails certainty' or in a weak form such as 'it is not the case that knowledge entails certainty'. The other view denies the Belief condition either in a weak form 'is not the case that knowledge entails not belief or in a strong form 'knowledge entails not belief. In summary, the study of an epistemic context requires that both conditions (1) and (2) are satisfied. Whence, in a doxastic context the Truth condition is neither necessary nor adequate. Various paradigms for knowledge representation in AI such as semantic networks, frames and units, reach for mathematical logic whenever a need for justification and rigor arises. This is done by transformation of the object formal system into a modified system of logic. It is not surprising that the need for formalization has been plagued with empirical adventures under the name of heuristic adequacy. One might agree with Ryle who posits that formal logic is a regimentation of the relevant sectors of the ordinary discourse. An extreme care should be taken in order not to defeat the aim and intent of logic which" is the discrimination of invalid form valid argument arid provision of rigorous but simple standards for the expression and evaluation of arguments. The nature of extension is to be understood as follows: the basic system and the extend one share the same vocabulary, and have the same theorems and rules of inference a propo the shared vocabulary. The extension is done to enrich the expressive power of the underlying system via some extended vocabulary, additional axioms and rules of inference. It is implicit that the arguments are subject to the criteria of rationality, material adequateness and intuitive admissibility. In the absence of consensus with respect to the standards for inclusion of arbitrary formal systems to the family of logics, the question would be ignored because it can lead to an unnecessary metaphysical digression. The use of a logical system follows from the intention to put forward an explanatory model for understanding the use of epistemic notions in an ordinary discourse. Clearly the laws of logic and the laws of thought are not isomorphic [Hin62]. The former are consider to be an expression of ability rather then obligation. Thus given an intellect and sufficient time (effort), logical and material information, inferences could be made about some state of affairs. It is in the nature of logic to induce new knowledge in an environment where the information content is restricted to the initial one. Hence, the intuitive understanding of logic that we have is probably best expressed by Witgenstain who wrote"...logic is not a theory of the word, but its reflection". It is this reflection, particularly in epistemology and AI, that is in the focus of our interest. Bibliography [Arm73] Armstrong, D. Belief. Truth. and Knowledge. Cambridge University Press, 1973. [Chi66] Chisolm, M. J. Theory of Knowledge. Prentice Hall, 1966. [Chu56] Church, A. An Introduction to Mathematical Logic. Princeton University Press, 1956. [God31] Godei, K. "Uber Formal Unentscheidbare Satze der Principia Methematica und Verwandter Systeme", Mathematische Physik. Vol. 38, 1931. [Hin62] Hintikka, J. Knowledge and Belief. Cornell University Press, 1962. [Rus61] Russell, B. Basic Writings. A Clarion Book, 1961. [Tor84] Torance, S.B. The Mind and the Machine. Ellis Horwood Ltd, 1984. AN INTRODUCTION TO INFORMATIONAL MACHINE* Keywords: architecture, cybernetical perquisites, data machine, foundations, informational machine, informational program, informational theory, intelligent machine, operating system, technological perquisites Anton R Železnikar Volaričeva ulica 8 61111 Ljubljana Slovenia This essay is an introduction to informational machine (IM) as it might be implemented in the coming decades. IM is an informational phenomenon and informs in itself and to the user in an informationally phenomenal way (IM extemalism, intemalism, metaphysicalism, and phenomenalism). For this purpose it needs: a massively parallel structured interconnection net of high- performance microprocessors (e.g., 64-bit, three-dimensional RISC); specifically (informationally) designed processor interconnection network; an operating system offering informational, counterinformational, and embedding support to informing entities (operands and operators) and translating informational language; an informational dictionary of entities; and lastly, a powerful peripheral equipment capable to accept (memorize) and transmit all kinds of information (picmre, sound, data, signal, control, linguistic information, etc.). The goal of IM design is to achieve the state of »intelligence«, by which IM is an understanding device operating (behaving) within the surrounding world. Uvod V informacijski stroj.* Ta spis je uvod v informacijski stroj (IS), ki bi ga bilo mogoče uresničiti v naslednjih desetletjih. IS je informacijski fenomen in informira v sebi in k uporabniku na informacijsko fenomenalen način (ekstemalizem, intemalizem, metafizikalizem in fenomenalizem IS). V ta namen potrebuje: masivno paralelno strukturirano povezovalno mrežo visokozmogljivih mikroprocesorjev (npr. 64-bitni, trirazsežnostni RISC); operacijski sistem z informacijsko, protiinformacijsko in umeščevalno podporo informacijskim entitetam (operandom in operatorjem) in s prevajanjem informacijskega jezika; informacijski slovar entitet; in nazadnje zmogljive periferne naprave, ki spejemajo (pomnijo) in oddajajo vse vrste informacije (sliko, zvok, podatek, signalno, kontrohio, lingvistično informacijo itd.). Cilj načrtovanja IS je doseganje stanja »inteligence«, s katero postane IS razumevajoča naprava, ki deluje (se obnaša) v obdajajočem svetu. *This essay is a private author's work and no part of it may be used, reproduced or translated in any manner whatsoever without written permission except in the case of brief quotations embodied in critical articles. 0. Introduction The phenomenological account of how scientific facts are arrived at by leaving out significance shows why, once we have stripped away all meaningful context to get the elements of theory, theory cannot give back meaning. Science cannot reconstruct what has been left out in arriving at theory; it cannot explain significance. For this reason, even though natural science can explain the causal basis of the referential whole, »'Nature' ... can never make wordliness intelligible«. - Hubert L. Dreyfus [BIW] 121 One of the aims of informational theory [TIL, FIP, BIA] is to lay the foundations of the informational machine (IM). These foundations pertain greatly to the concept of an intelligent informational machine (IIM) and their laying is a process in which several new components have to be settled in theoretical, symbolic, cognitive, technological, architectural and other, yet not completely recognized, informational ways. IM is a consequence of that what one understands as the computer, computing system, or data processing device. The computer is a data machine (DM) where data is a particular, informationally specific entity, a bounded form of information, which concerns facts, factical information, which as a fact does not change during an informational process. DM is an informationally reduced device within the concept of the arising IM and, as such, can never reach the level of, for instance, an intelligent informational machine. Data intelligence remains within the scope of the artificial, modeled, simulated intelligence which, in comparison to namral intelligence, roots in the structure and organization of the algorithmic and data programming on (and by means oQ a computer system. Along these lines, the result is a data-stable, algorithmic, well-determined system designed by both mathematical and programming philosophy and conceptual means. The difference between data and informational processing lies in algorithm vs. informational program, determined foreseeability vs. possibilities of spontaneous informational arising, strict splitting between data and programs vs. operand and operator duality of informational entities, recursively determined program and processing cycles vs. metaphysical informational circularity, the determined closeness of data and programs vs. the phenomenal informational openness of informational operands and operators. IM is an essential extension of DM, from the rigid, algorithmic, mathematical machining to the circularly spontaneous possibilities of informing within the goal-directness, intention, orientation, significance and, not lastly, possible intelligence of arising informational entities in the world. Only in case of an informational machine it becomes possible to speak about the informational understanding, which is a synonym for the intelligent informational behavior of entities within an informational realm, that is, informational entities' surrounding world. Intelligent entities have to behave informationally (in this case understanding^) in the real world, which concerns them in an essential, intentional, developmental, and significant way. By this essay, the author communicates the concept of an informational machine in the form of a foundational, researching, and technological discourse. Is it already possible to presume and pre- view the architecture and operating system of the future IM? Both informational theory and philosophy offer concepts and mechanisms which could dramatically impact not only the strucmre and organization of the IM involving components in the field of electronic, photonic, and biological technology, but also the realms of sufficiently clear comprehension, conceptualism, design, and implementation of machines. 1. The Informational Theory and Informational Machine Das Miteinandersein ist — ihm selbst verborgen — von der Sorge um diesen Abstand beunruhigt. Existenzial ausgedrückt, es hat den Charakter der Abständigkeit. Je unauffälliger diese Seinsart dem alltäglichen Dasein selbst ist, um so hartnäckiger und ursprünglicher wirkt sie sich aus. Martin Heidegger [SZ] 126 Informational theory (IT) offers formalized means which pertain to informing and informedness of entities (things, phenomena, processes). Informational operands, informational operators, parentheses, commas, and semicolons constitute the syntactic background of formulas and informational formula systems of the theory. In IT, operands and operators are united entities which can be distinguished from each other in instantaneous situations of a formula or formula system. Thus, it is possible to determine informational theories for different purposes. The most remarkable theories of this sort concern understanding, computing, inference, cognition, etc. and also signal processing on a physical level, process control, living phenomenality in biological systems, informational üieories of societies, informational mathematical theories, scientific languages, and system theories. IT's enable new approaches to various theoretical and practical problems using specific, informationally conceptualized languages, in which formulas by themselves inform and are informed, that is, arise and are arisen information-ally, These formalisms (informational programs) are on the way to be implemented by the use of informational machines. An IM will perform on the basis of informational formulas, which are programs, expressed in informational language and behave as logically arising entities, possessing their own extemalism, intemalism, metaphysics, and phenomenalism. In this point, informational programs differ essentially from computer programs, which can be comprehended as texts which contents (semantics) does not change in any way. IP's (informational programs) surpass the computer programming structure and philosophy, programming bounds, and strict, mathematically conceptualized notions. The way to the proposed informational machine goes back to the basic axiomatic concepts of informational theory. In a concrete case, IT by itself is a texmal informational entity, possessing informational phenomenality, which in accordance with its intention, significance, understanding, etc, informs and is informed by means, mechanisms, and informational support of an informational machine. Thus, the informing of a theory's text can be achieved, realized, or implemented by an IM, In a similar way as computer programs are executed by computers, IP's will govern the informing of an IM. So, the question arises, how an IM has to be conceptualized and constructed to come close to the requirements of informational phenomenality of entities in general and in each particular (thinkable) case. It is to understand that IT and IM support each other. First, a concept and realization of IM becomes possible by the (strict) application of IT's principles, derivation of theorems, and machining informational systems. Then, the IM is supported by the so-called system informational programs, which constimte an informational operating system. When an IM functions as a machining informational entity, the machine can take an IT and let it arise informationally within a given informational realm. Thus, an IT can develop the IM in an informational way and vice versa, simultaneously, in parallel, intentionally, significantly, and intelligently, To bring this possibility of informing to the foreground, we have to develop the sufficiently clear and straightforward detailed concept of informational machine. And this way of development will be shown stepwise in the sections which follow. 2. The Computer as a Data Machine What is the difference between a data entity and an informational entity? What is the difference between a data machine (= computer) and an informational machine? A DM has to follow the data phenomenality in an architectural and programming construction, while an IM follows the informational phenomenality which broadens the conceptualism of its architecture and programming in an informationally arising manner. The difference between these phenomenalities is essential: data is well-defined information in a particular way; it is specifically bounded by an algorithmic structure and in this way not flexible as information at all. As a fact or factical information, data informs externally in an unbounded way; it simply informs external observers as any oüier informational entity. Regardless of the nature of its factic-ity, the informing of data is spread (broadcasted) in space and time, where different observing entities can become sensitive for informing of data, that is, informed by data. Intelligent entities can, for instance, observe the steadiness of data informing, its facticity, and its informational unchangeable-ness, non-arising in contrary to a regularly informing entity. Thus, data appears to the observer as a steady, reliable, and predictable information, which can vary only in some known value, degree, truth, etc., but not in its, for instance, semantic character, mood, property, relation, intention, and significance. Data possesses a firm characteristics (property, relation) of something which it concerns, for instance, number, value, degree, structure, facticity of something. In this respect, its characteristics must never change and its changeable components are only factical parts of its characteristics. The first question relating computers is how does data inform? As a specific informational phenomenon, data informs, but it is informed merely in the sense to preserve (memorize) its facticity, characteristics, or well-determined meaning. The meaning of a certain data, its semantic scope, must never change. It means that the informedness of data is a steady phenomenon, meaningly stable, and semantically unchangeable. How can this phenomenality of data be expressed abstractly, on a formal and symbolic level? Let 5 mark a data entity as an operand and let [= be the symbol for the most general operator of informing. Informing of data is a data property (its own predicate) and the proposition Data Informs is the most primitive phenomenological fact of data itself. It belongs to data as an entity, is a part of data possible (entire) informational phenomenality. It means that data as an entity implies the informing of data. Thus the informatio prima pertaining to data is postulated by (1) The sense of this implication (symbol is to show how the informing of data, that is, 51=, is an integral part of data itself and not a separate entity. The consequence of axiom (1) is (2) (Ò1=)CÒ where C is the operator of informational inclusion which says that process 51= is a part of 5 itself. It is to say that formulas (I) and (2) do not differ for any general case when data entity ò is replaced by an informational entity. Where does the essential difference between data and information occur? Data has to keep its identity, which is the facticity of its phenomenality. With other words, it has to memorize its informational identity by preventing its informational structure to be changed. What does the keeping or memorizing of data identity mean at all? Data informs factitiously, which has the meaning of non-spontaneously and artificially. Thus, formula (1) can be particularized into (1 ') 5 (Ò ^factitious) where operator ^=factitious is a general informational operator of factitious informing, probably constructed (imagined) by the data observer in an artificial and informationally not spontaneous way. The question is: can data, in the described sense, exist as a natural situation (entity) at all or is it the consequence of an observer's attitude? The next basic question is how data is informed? As a fact, data must keep its identity. So, the possible answer to the question is The sense of this implication is to show how the informedness of data, that is, =5, is an integral part (property) of data itself or (4) (=5)CS and that this informedness is identical. Instead of operator = operators |=identic. Nsteady or |=facti-tious could be used. The consequence of identical informing of data 5 is the so-called metaphysical identity which presupposes the steadiness of data, that is (5) = and, certainly, (6) (5 = 5) C 5 Formula (5) is an axiomatic consequence of both axioms (1) and (3). Thus, also the last fundamental axiom of informing of data can be given by (7) where (8) (5N=5)C5 is the logical consequence. We can unite the four basic axioms into the following logical scheme of informational formulas: (9) S ^ (51=); [data extemalism] (5NC5; 5 (= 5); [data intemalism] (=5)C5; 5 (Ö = 5); [data metaphysicalism] (5 = 5) C 5; Ö (5 [=; = Ò); [data phenomenalism] (5N=5)C5 Data extemalism, intemalism, metaphysicalism, and phenomenalism are basic properties of data 8 where operators of informing |= and = are integral parts of data 5 itself. This axiomatic introduction of the nature of data was necessary to get the possibility for characterizing the components of data machine S) (computer). The straightforward formula of informing of a data machine 3) is (10) (òinput Hreceive Nsend ^output where data input 5input pertains to computer system programs ^gys (operating system), computer user programs ?Puse (applications, tools), and user data 5yse (user data bases). Informational operator Hreceive says that Sj^put is received by machine 2). Informational operators of the reversed type, that is, =|, express the passive (participle) mode of informing when read from the left side to the right of informational formula. Implicitly, data machine S) as an data informing entity (device) operates and is operated by means of the received programs and data in an open, however, normally, well-determined way, that is, (11) S) =» (S) =; = Formula (11) shows another bounded situation of data machine S), where machine phenomenalism roots in an identically structured (architectural) machine extemalism (informing S) =) as well as in an identically structured (architectural) machine intemalism (informedness = S). In this sense, machine S) receives (=|receive) "iP^t data and sends (t=send) results presult of ^^ action to its peripherals peripheral- Data machine S) is informationally open (S) =; = S)) only for programs, data, and results which fit its architecture, and system described by formula (11) implies the machine openness of the form (12) S) |=arc; Krc ^ where |=arc is the architectoral (computer hardware) defined property of DM functioning. Certainly, the informing (® [=arc ^s extemalism or output) and informedness (|=arc ® ^ intemalism or input) case can be particularized in different possible ways. What is a more detailed structure of data machine (computer)? We already Usted (marked) some components in the previous paragraph. That which is, in fact, called a machine is the data machine architecture (structure of machine's hardware), marked by ilare- What does the machine architecture produce and what does it sense? The general answer is (13) 21; arc (^arc Narc_prod'> Narc_sense ^arc)'» ISC' ^use Narc_ ^arc Narc_prod Presult ^sys' ^sc' ^use Narc_sense ^arc The last system constimtes the informationally open phenomenal and metaphysical stmcture of machine architecture, where Sl^rc is a well-defined and informationally non-arising physical stmcture, operator |=arc_prod means produce (s) architecturally and operator |=arc_sense i^^s the meaning sense(s) architecturally. Thus, the phenomenalism of DM is data-informational. Functioning of a DM S) can be described by the formula (14) %se. 5use ^ ^peripheral) Hreceive (ölarc Nexecute ^sys' ^use> ^use)) Nsend (Presult ^ ^peripheral) It is to stress that all occurring operands in the last formula belong to data entities which are well-determined, algorithmic, mathematical, and data stmctured items (alphabetically, Sugg, Presult' ^aro ^peripheral, ^sys- and 5Puse)- A data machine ® functions according to formula (14), where the architectural bounds of formula (13) have to be considered. If by 9(^4) formula (14) is marked, the data machine open informing can be expressed by (15) ® (9(14) =; = 9(14)) or (16) S) (9(14) [=; = 9(14)) in case where S) is not necessarily recognized by its observers (users) as a data device, so, they may believe that S) informs informationally (for instance, in situations and attitudes of artificial intelligence). 3. Architecture of IM We recognized in which sense the architecture of a data machine is merely data-informational (in-formationally non-arising). What is the architecture of an informational machine and what could it be in the present technological circumstances? The first request would be that the architecture of an IM, marked by 9Iarc_iM. niust be informational without any limits in advance. The request is (17) 2I„c_IM (aiarc.IM N'. N ^tarcJM) How could such a machine architecture be implemented conceptually and then technologically? Let us examine some general architectural criteria for an IM in the following manner: (1) SlarcjM is a massive parallel processor system where the number of processors is not limited in advance. (2) Massive parallelism of ülarcjM means an extremely flexible, changeable, and arising processor network in which sufficiently complex processors and their interconnections arise in an informational sense. (3) At the present state of technology, processors Ttj, 1^2, ... of ^arcJM ^^ta processors (e.g., 64-bit RISC) capable to fit into the massively parallel network by three (and not only two) dimensions. (4) Informational entities (operands, formulas of operands and operators) represented by processors in the massively parallel network are supported by mechanisms for sensing relevant (entities concerning) information in the interconnection network. (5) The architectural interconnection network (Snetwork ^ 2Iarc_iM) possesses methods for the building-up of connections between processors representing operands and formulas (also sub-formulas) which interact informationally according to particular informational formulas. (6) Each informational operand has its own processing informational system (basic informational determination of the entity by the basic entity formula in an informational dictionary of entities) to which processors are allocated. Processors are allocated not only to operands but also to informational formulas in which operands occur. Thus, to a complex formula, processors are allocated to each operand, sub formula and to the formula itself. The last two behave as additional operands with additional processors allocated. (7) An informational arising of IM architecture can be simulated by a dynamically changing interconnection network (interconnection distributed processing device), Snetwork' m which a sufficient number of operable processor components is available. On the other side, the functional power (operational complexity, speed) of processors and their interconnection can reach performances necessary for informational systems for the most pretentious applications. (8) The listed performances of IM architecture can grow by the advancing of computer and telecommunication technology. For instance, the number of microelectronic components may reach several billions per chip. The next frontier may be based on single-electron devices and ballistic transistors where the philosophy and perspective of quantum physics is coming into scientific and technological game. Photonics will take over many electronic functions in transmission of information, logic functions, communication switching (interconnection networks), etc. [FOT]. Let us determine üie IM architectore Sla^cjM in more detail by the informational architecture system. The following operands and operators are introduced: 7Ti, 712, ••• are high-performance microprocessors inserted in the nodes of massive parallel interconnection network Snetwork» costate represents the state of architectural informing Si (where i marks processors' subscripts) of processors within the interconnection network Snetwork'» c^state(^arc_IM) is the state of architecture, expressed as informational function pertaining to the IM architecture itself; ^arcJM is the IM architecture as informational entity; Si, S2. ••• are the so-called informings belonging to particular processors ttj, 7t2, ..; Sl(7tl), S2(^2).- are informational functions, where particular informing Si depends on - the state of processor Ttj; Snetwork is informational entity representing the processor interconnection network in all imaginable complexity which can be decomposed to the arbitrary details; t=by means inform(s)_by or inform(s)_by_means_of; Nconnect means connect(s); means implies/imply; and C means inform(s)_in or simply is/are_in. The initial formula system (prior to the detailed informational decomposition) is (18) (Tti, 7r2, ... C Snetwork) ^ SlarcjM! TTj, 7T2, ... (Ttj =; = Tti; 7t2 =; = 712;...); (Snetwork Nconnect (^1» ^state(^arc_IM)); Estate (Sl(^l). ^2(7^2). •■■ C Snetwork) The first formula is an outset of the position of (the arising) IM architecture which functions as an array of dynamically connected high-performance microprocessors (RISC). In this sense, the IM architecture remains informationally open on the level of its intercoimection network and, so, is informationally phenomenal. In the second formula the data namre of processors is explicated as a consequence of nowadays electronic and fumre photonic technology. The only request is that processors have a unique and »sufficiently« complex and effective strucmre (e.g., high-performance RISC with at least 64-bit). The third formula expresses the informational nature of processor connection in a particular situation by means of the present functional state of IM architecture. The last formula says that the functional state of IM architecture implies the informing of particular (active) processors within the interconnection network. Formula (18) is an initial architectural position. This formula may now be decomposed in more and more details according to the concepts of the IM architecture designers. It may happen that a future microprocessor generation, at least in some respects, will reach the step of informational phenomenalism. 4. Informational Programs So far, informational programs belong to the most promising concepts of informational phenomenal-ity [IBU]. In a massively parallel IM SJl, the role of informational programs (in short, IP) becomes informational in all imaginable entirety. An IP, marked by is a regular informational entity in the IM environment. What could this property under machine circumstances mean at all? An informational program ^ has its extemal-ism, intemalism, metaphysicalism, and phenomenalism, that is, in a symbolic summarizing form, (19) q3^(qif=;|=fp;Jpf=q5) Then, IP sp is informationally open to the IM environment in several ways. Firstly, it informs the IM system and is informed by it or, symbolically, (20) (sp C 5K) (£p 1= OR 1= 5p) and, secondly, it is informationally open to other active, that is, informing informational programs ?P2, ... within the informational machine 9R, thus, (21) (q5,ipi,5p2. •••ca)i)=> Thirdly, within IM ÜJl, informational program informs IM architecture SUarcjM IM operating system ^PsysjM ^^ is informed by them. This fact yields (22) (qìN^IarcJM-^sysJM); (2Iarc_IM» ^sysJM) N ^ Machine architecture and machine operating system support the informing of IP ^ in an informational way, enabling its informing, counterinforming, and embedding of information and communicating in an informing way with other programmed informational entities. To an IP ^ pertaining informational entities may be variously distributed through the interconnection network Snetwork of machine architecture SlarcjM- System mechanisms for sensing certain IP involving and concerning information must be available for ac- ti ve informational programs. On the other side, IM system must enable the arising of informational programs through suitable counterinforming and information embedding mechanisms. In the first step of development, these mechanisms could be algorithmic, using methods of deterministic chaos, fuzziness, probability, randomness, etc., but in the second step, they may become creative, unforeseeable, spontaneous, natural, etc. in the sense of Being-in-the-world. In its initial state, an informational program can be comprehended as a text. In Latin, textum or textus (from the verb texo with the meaning to weave, plait; to frame, construct, fabricate, make, compose) means web, texture, stuff, structure, construction, connection, which is a product of artificial weaving, plaiting, composing, etc. A text is not only a connection of words, but also various informational interweavement. The meaning of a text is a result of the text understanding and pertains to the arising semantic interpretation of the in-formationally involved understanding entity. Thus, a text is in no way a torpid (rigid) depiction of information. It would be true only in case of a data form which stays for itself and does not concern informing entities. In this case, a text would not be perceived or even observed by a text understanding entity. Thus, a text is an informational realm of its context and its contents, a landscape of words, word groups and their distributed meaning in which the informational spirit finds its arising dwelling, understanding, informational phenomenality. In a later state, a text develops informationally and this state can be compared to the understanding of text by a text observer (reader, comprèhender). Thus, in this stage of development, a text becomes a parallel structure of its different interpretations, which all form a complex and an arising structure of text where parallel meaning, semantics, contents, intention, significance, etc. are coming to the informational surface. Discussing informational properties of a text expressed in a natural language, we can determine the difference existing between a computer program and a text on one side and between a text and an informational program on the other side. There exists an informational hierarchy concerning the triplet program—text—informational program in the following sense: (1) A computer program or mathematical formula (or formula system) is a rationalistically bounded (artificial, abstract) informational entity with a unique, unambiguous, fixed meaning for programmers, mathematicians, and machines, respectively. Understanding of programs or mathematical formulas is not a subject of these entities themselves; it is a process within human behavior (mathematician or programmer community) or machine's semantic routine. Programs and mathematical formulas belong to executively automatic, semantically unique, logically uncontroversial, or rationally understandable structures, delivering safe, predictable, and anticipated results. The informing among entities (operands, operators, relations, functions) inside a program or formula is well-defined by abstract data declarations, definition equivalences, algorithms, and other unique rules. (2) A text in a natural language is in principle metaphoric, ununiquely structured in the meaning of its components (words and word groups) and in the semantic interconnection possibilities among its components. However, in its initial state, a text is the written, also recorded (stored) or transmitted (broadcasted) entity which as the text does not change its structure. The understanding entity of a text is, for instance, its reader, hearer, or seer who gives the text additional metaphoricalness, ambiguous meaning, oblique discursiveness, that is, arising understanding. Text is a higher informational structure in comparison to a program or informational formula; from the standpoint of the observer, it carries, causes, and informs creative (intelligent) information. This type of informing is not allowed in case of rationalistic information which is artificially bounded, logically and meaningly closed to a certain tautological structure. (3) An informational program (formula or formula system) is simultaneously (in parallel) rationalistically structured in its symbolic expressiveness, keeps the informational metaphoricalness and a degree of informational indefmiteness for its constituting entities, possesses its own possibilities of arising (text changing, text developing) component and its own understanding (consciousness, intelligence). While programs and texts do not change as entities in the sense of informational phenomenality, infor- mational programs arise, develop, change, and vanish through the course of their informing. We may say that programs and texts inform passively, while informational programs inform actively. Within this reality, the informing power of informational programs informing in an IM becomes superior to computer programs and texts because of its own informational arising and, maybe, intelligent development. We are able to give the following additional comparisons: (i) A program or mathematical formula is like a discrete black-white landscape (deserted, unique, once for all determined dot structure), where black dots play the role of logical significance on the white background. (ii) A text is a written piece of paper, a stable picture (photo, depiction, well-known melody, aviso, a fixed sequence of words, sounds, pictures, etc.) which is laid down (written, recorded, fixed) as a foreseeable, predictable, repeatable structure. (iii) An informational program is by itself a dynamic structure which is similar to a view to the live landscape in which entities exist, to an arising program which runs from one into another situation. It has its own understanding, interweavement of its items, and it changes lively, dynamically, but intentionally in the world of information. Within the triplet program—text—informational program, informational program stands at the highest possible place in the hierarchy of informational structure. 5. Operating System of IM Operating system (OS) is a technological synonym for a system interaction of system programs and machine architecture within an IM. One of the basic, global questions pertaining to an IM is: What is the system support to informing entities being represented by informational operands, basic and composed formulas of operands and operators, and informational formula systems? Which are basic features of this kind offered by the OS of an IM? It is clear that some common properties of informing of entities can be »delivered« by OS to satisfy the request of efficient informing (counterinform-ing, embedding) of entities. Otherwise, a sophisticated mechanism of informing, counterinforming and embedding of information would be necessary for each occurring entity. Let us join the OS of an IM in the following principles: (1) OS of IM supports the informing of operands (including sub formulas, formulas, and formula systems) in their own metaphysical nature, by which an entity representing operand informs, counterinforms, and embeds information which concerns it informationally. (2) OS performs the searching of information pertaining to a particular operand. (3) Operands marking original entities (simple or proper operands) have their informational definitions; their initial formulas are stored in the operand dictionary. In this dictionary also those operands which occur in the definition of proper operands are defmed. In this way the operand dictionary is informationally closed (tautological). (4) OS processes informational formulas and formula systems by means of understanding (translating, compiling, interpreting, etc.) informational language. (5) OS enables the modification and the arising of initial informational formulas during the process of their informing and, within this process, supports their understanding after they have been informationally reshaped (arisen, modified, vanished). (6) On the IM level, OS performs as an understanding entity of informational language. In this respect, an IM is the informational language machine (ILM). (7) Of course, OS is adapted to the IM architecture and supports the informational massive processor parallelism together with the specific machine language pertaining to architecture processors (for instance, RISC) and also the specific control language of the IM architecture interconnection network. (8) OS of IM is the informational interface between user's informational language and machine system language (processor and interconnection language). Processor interconnections on the machine level have their origin in operators of informational formulas, which connect particular operands. (9) Formulas of a formula system are treated as parallel processes. This rule is extended to op- erands and subformulas. OS manages the arising parallel situation of processing. Operating system is a synonym for a system of system informational programs of IM, marked by ?Psys_lM. where (23) ^Psys, 1 ' ^sys,2' ^sysJM OS 5Psys_IM performs as an open informational entity possessing its own extemalism, intemalism, metaphysicalism, and phenomenalism. Operating system of an IM, ^PsysjM- performs together with the IM architecmre SlarcjM managing and informing of user informational programs. How do IM architecture SlarcjM ^nd IM operating system ^sysjM support an informing entity a informationsäly within an IM? Operand oc as an informational phenomenon is confronted with the triplet of its informing, counterinforming, and embedding of information. In a narrower sense, informing of an entity embraces, in general, its informational broadening, modification, shortening, etc. which are a consequence of the entity's interpretive scope. On the linguistic level, a typical scope of informing represent the so-called synonyms of words or word groups. However, there are many other informational equivalents to occurring informational items, for instance, of parallel interpretive character. The consequence of this informational possibilities concerning an informing operand is its informational broadening which includes modification, informational shortening, vanishing and of course arising. If by the informing of entity a is marked, the following initial system of IM architecture and operating system support to informing of operand a can be given: (24) System support to informing of operand a: (^arcJM' ^sys. .IM Nsynonymize Nproduce a. (^arcJM. ^sys_IM Ninterpret Nproduce a. (^arcJM. ?sys_IM Nbroaden Nproduce The occurring informational operators have the following meaning: Nbroaden broaden(s)_the_scope_of, inform(s)_in_an_informationally_ _broadened_way_to; Ninterpret interpret(s), inform(s)_interpretatively_to, deliver(s)_interpretation(s)_of; Nproduce produce(s), embed(s)_in; Nsynonymize synonymize(s), give(s)_synonyms_for, inform(s)_synonymously_in_ _respect_to, inform(s)_by_synonyms_of, inform)s)_in_a_synonymous_way_to In formula (24), a possibility for shortening its formal expression arises when operational alternatives come to the surface. We can introduce the so-called alternative operator structure with the meaning operatori or operator2 or operators or.... The Or is marked by symbol |. Thus, (24') (SlarcJM' ^sysJM Nsynonymize 1 Ninterpret I Nbroaden a. Nproduce a. The second mode of system support to an informing entity is counterinformational. We can investigate principles of counterinforming from a characteristically pragmatical point of view. The adverb counter pertaining to conterinformation and counterinforming has several meanings: for instance, in the opposite informational way, contrary the course of information or informing, in the reverse informational direction, contrary in an informational way, in opposition to the ruling information or informing, in the sense to inform counter or against to the informing rules. The adjective counterinformational means informationally opposite, opposed, and contrary. Counterinforma-tion informs opposite or contrary to information from which it arises. Counterinforming means to act in opposition to informing, also to frustrate informing by counterinforming. Thus, counterinforming could mean to produce antonymous information (to »antonymize«) in comparison to informing by which synonymous, meaningly broadened information is produced. If by Y(a) and (£(a) the counterinformation and counterinforming of entity a is marked, respectively, the following initial system of IM architecture and operating system support to counterinforming of operand a can be expressed: (25) System support to counterinforming of operand a.: (^arc_IM> ^sys_IM Nantonymize T(a), SCa)) [=produce T(a). S;(a); (^arcJM. ^sys. JM Fcounterinterpret T(a), SCa)) ^produce T(«). ^(po', (^arc_IM' ^sys_IM Ncounterbroaden y(a), ©(a)) |=produce r(a). ^(a) The occurring counterinformational operators have the following meaning: Nantonymize antonymize(s), give(s)_antonyms_for, inform(s)_antonymously_in_ _respect_to, inform(s)_by_antonyms_of, inform (s)_in_a_antonymous_way_to ; Ncounterbroaden broaden (s)_the_scope_contrary_to, counterinform(s)_in_an_ _informationally_broadened_way_to; —counterinterpret counterinterpret(s), counterinform(s)_interpretatively_to, deliver(s)_counterinterpretation(s)_of; Nproduce produce(s), embed(s)_in In formula (25), the possibility for shortening its formal expression is given: (25') (SlarcJM. ^sysJM Nantonymize I Ncounterinterpret I Ncounterbroaden T(«). called the IM operating system. This system controls the functioning of IM and offers the so-called basic informational support to informational operands, which occur in the formulas of user informational programs, marked by ^se,l> ^se,2' •••' shaping the user informational system of machine 3R. Thus, the system and user informational program systems together with the system of other user information items are (30) ^sys.b ^sys,2. ••• ^^ ^sysJMJ ^use.2 ••• ^ %se_IM "•use,!' ^use,2' ••• ^ "-useJM An essential part of IM is the strucmre of system and user open informational operand dictionary 5d ictionary in which the initial informational defini- tions of system and informational user program operands are stored. This dictionary represents a semantic net of entities for the entire realm of an informational field, discipline, application, science, etc. An arbitrary net for a distinct operand must be informationally circled in a complete way. It means that for each occurring operand a complete or informationally well-circled informational system of formulas exists. If these entity operands of metaphysically structured parallel formulas are marked by «j, the dictionary structure is (31) «1, «2» ••• ^ ^dictionary At last the peripherals have to be considered in which input and output information is stored, that is, system and user informational programs, other informational entities, and results of IM informing. Thus, a general peripheral simation is (32) ^sys_IM' ^use_IM' "-useJM» ^dictionary PresultJM ^ ^peripheralJM Under these conditions tiie metaphysicalism of an IM 9Ji [= SDÌ can be observed as a general informational scheme in the form (33) ^peripheral N ((((^useJM. "-useJMN^sysJM. ^dictionaiy) N ((TTl » ^2> ••• ^ Snetwork) C2Iarc_IM))[= %se_IM. l-useJM) 1= (presultJM ^ ^peripheral)) The last formula can now be decomposed, parallelized, etc. in more details. The outmost cycle is peripheral in which the initial informational programs and information is stored. Results of informing of IM are transferred to peripherals, so they can be observed by the IM user. 7. Informing and Informedness of IM Informing and informedness of an IM constitute its phenomenalism. We say that an observer of IM as its user is impressed by IM informing and concludes what an informational phenomenalism of the machine could be, for instance, informationally efficient, comprehensive and, last but not least, intelligent. The last could be true especially because of the informational character of the machine when significant realms of information are taken into machines informing, that is, informationally arising processing. On the other hand, an IM can be informed by an observer as its user, and this informedness is in no way limited in advance, so the entire user informational creativity comes into the game of the machine informedness. Because IM OR is no more as a machine, the questions concerning its extemalism, intemalism, metaphysicalism, and phenomenalism could be of particular importance. Usually, such questions are not customary for machines as rational, artificial entities which have their unique, determined purpose, functional ability, and applicability. How- ever, this is only a common belief and the question of, for instance, machine's metaphysics remains entirely righteous. The function of an IM hides the machine informing, counterinforming, and embedding of information. This function concerns as well the informing of operands occurring in informational programs which informing is partly supported by the IM system. In this sense, an IM becomes an informational phenomenon by itself. 7.7. IM Extemalism IM informs its exterior. Machine extemalism (iER =) is important for the informedness of machine observers, users, and other machines. How does a machine OJÌ inform according to its architecture, operating system, dictionary, user informational programs and user information? An observer oruseroflMisableto recognize several general machine properties which can be expressed verbally and by informational language. Let us see some of them. (1) External informing ofSR. IM informs in parallel ways. One of the basic implication system of machine extemalism is (34) where operator |j= marks parallel informing. According to formula system (34), extemal parallelism of [Si is circular and the consequence of it is (34-) This implication shows the parallel possibilities of informing of Oil to extemal entities, where 3R's extemal informational openness is manifested as parallel informing. Parallelism of 9Jl belongs to the most powerful, but theoretically unmasterable realm of informing under spontaneous and circular circumstances. For instance, problems of understanding and through it produced meaning of something may remain unmastered in several informational ways, that is, philosophically, theoretically, formally, linguistically, designingly, technologically, communicatively, connectively, etc. But, this is also true for any other informa- tional parallelism. The phenomenon of parallel extemalism belongs to the most unrevealed and simultaneously theoretically pretentious problems. On the other hand, the parallelism of mind con-ceming associative processes at the arising of thought seems to be natural. In case of 5DÌ machine SR can produce intentional, spontaneous, circular, etc. parallelism, possessing its own mechanisms of informing, creating of operand dictionary, user informational programs and user information. This kind of parallelism may look to be unforeseeable and not well-predictable, that is, informationally spontaneous for the IM observer or user. (2) Extemal metaphysicalism of SR. IM SK informs in its own circular way. This kind of circularity is called extemal metaphysicalism (also metaphysics) of 2R. The machine observer or user copes with the metaphysical implication of the form (35) m [=) m [= SDÌ) H concerning not only the general machine extemalism ÜJI |=, but also the machine metaphysical extemalism (TO 1= 3Jl) \=. The phenomenon of observing the machine metaphysicalism by machine users is a parallel informational phenomenon, where (35') ((SIJl^!K)t=)=»((®|=®i)H; (TOj^iK)^;...) In this way, the observed metaphysicalism of is in no way unique and unambiguous since the arising metaphysicalism of SDÌ shows the arisen phenomena to machine observers. Within the machine metaphysicalism, informational formulas are circularly decomposed, parallelized, composed, etc. and through this phenomenality the observing of machine metaphysics Sm [= SKI through (SDÌ |= SDÌ) 1= becomes possible. (3) Extemal resulting o/SDÌ, Machine SDÌ delivers results which may be expected, but also unforeseeable, unpredictable, and arising from a complex informational realm. The question of result PresultjM is senseful because IM informs and produces essential changes of informational entit- ies through their informational arising. Under such circumstances, there are dedicated results in the form of informational meanings concerning various kinds of information, for instance, linguistic, numeric, logical, formula-informational, signaling, controlling, etc. Results can be stored, displayed, or otherwise communicated, but they can also remain unobserved and lost in the process of informing. Thus, the user or observer of IM must determine, at least roughly, for which kind of results there exists an interest in distinct informational programs and how the informing machine SR may transfer its results to the peripherals, that is, (36) (ÜJi 1= presultJM) Nto ^peripheral Because of the possibilities of intelligent informational programs, these programs (informational formula systems) can decide by themselves how to inform results, store them, or present to the exterior of IM. Thus, (37) (5R \=) m N PresultJM) N is conditio sine qua non that the informing of ÜR is (becomes) informationally sensefiil. Otherwise, SDl would perform as a closed system, which does not concern the machine exterior. (4) From the pragmatical point of view, machine extemalism ffll [= is able to explicate not only the discussed forms of parallelism, metaphysical-ism, or informational resulting (productivity, conclusiveness), but other, very specific phenomenal forms, exporting informationally dependent phenomena of understanding, managing, controlling, signaling, modeling, etc. in cooperation with other systems, machines, observers, users, and machine envirormient. In this way, an IM may be informationally embedded in other systems not only via its extemalism, but also intemalism, building up a composed, metaphysically structured informational system. 7.2. IM Intemalism Machine intemalism \= characterizes the machine informational sensibility (informedness) for informing of informational programs, requests, and information coming from machine users, observers, and other informational systems, ma- chines, environment, etc. How is machine 3)1 informed according to its architecture, operating system, dictionary, user informational programs, and user information? Let us show some informational phenomena concerning the IM intemalism. (1) Internal informedness of SIR. IM 5K is informed in parallel ways. One of the basic implication system of machine intemalism (informedness) is (38) (IN ON®); where operator \\= marks parallel informing. According to formula system (38), intemal parallelism of SDÌ is circular and the consequence of it is (38') (|=SK)=>(t=ÜJi;|=aJl; ...) This implication shows the parallel possibilities of informedness of by extemal entities, where 3Ji's intemal informational openness is manifested as parallel informedness. Parallel informedness of 3JÌ belongs to the most powerful, yet theoretically unmasterable realm of informedness under spontaneous and circular conditions. For instance, problems of machine understanding and through it produced meaning of something informational may remain unmastered in several informational ways, that is, philosophically, theoretically, formally, linguistically, designingly, technologically, communicatively, connectively, etc. (2) Intemal metaphysicalism o/QJl. IM 3)1 is informed in its own circular way. This kind of circularity is called intemal metaphysicalism of Tl. The machine as an informing entity is confronted with the metaphysical implication of the form (39) (^g]i)^(^(gjl|=3jl)) concerning not only the general machine intemalism 1= 3Jl, but also the machine metaphysical inter-nalism |= (3)1 (= 3)1). In this case, machine 3)1 becomes the observer of parallel possibilities in the form of its metaphysicalism, where (39') (N: (0)11= 3)1)) ^ dN P N 3R)); dN (3)11=3)1))^ (|=(3)1N:3R);[=(3)1[=3)1);...) As we see, the observing metaphysicalism of 9)1 is in no way unique and unambiguous since machine metaphysicalism is able to observe the the arisen phenomena in its environment and within itself. Within the machine internal metaphysicalism, informational formulas are decomposed, parallelized, composed, etc. and through this phenomenality the observing machine metaphysics OJl t= OR through [= (OJi ilR) becomes possible. (3) Internal resulting (resultedness) of QJl. Machine ÜR creates results internally according to informational programs and by its own informational characteristics (states, processes). Results may be expected, but also unforeseeable, unpredictable, controversial, and arising from a complex informational realm. The question of result pre-sult_lM is senseful because IM informs and produces essential changes of informational entities through their informational arising. How does the IM intemalism, üJi, concern the IM resulting, that is, results PresultjM*? IM informs and is simultaneously informed, the result of machine informedness may be any informational change within occurring informational operands. Various informational meanings may arise pertaining to linguistic, numeric, video, signal, and other information. The arisen potential results PresultJM i^* form OR and within OJi's informedness the decision takes place which information will be considered, transferred, and informed as result significant. One has (40) (PresultJM f= h ^peripheral Within IM processed informational programs can decide by themselves (in an intelligent way) how and when to form interior results. Thus, (41) ([= m) (h- (PresultJM N m The openness of Sffi's informedness guarantees the possibilities of choice, to obtain information which pertains to Presult JM ^^so from machine peripherals, so, (42) %>eripheral N (PresultJM N By this discussion, the mutually reversing processes of machine resulting informing and result- ing informedness can be understood and decomposed informationally to the necessary details. 7.3. IM Metaphysicalism Machine metaphysicalism SR |= SDÌ is a particular case of machine phenomenalism constitoted as machine extemalism and machine intemalism, that is, as a system (9)i [=; |= 2R). In this sense, IM metaphysicalism is hidden in machine phenomenalism or (0)i 1= SK) C (Ifi t=; [= SR). In general, machine metaphysicalism is an unrevealed phenomenon for the machine observer or user w and can be observed only through the machine informing SK \= and the observer's informedness \= w, that is, SDl [= oj. (1) General metaphysicalism of SDl. Let us remind of the informational structure of 3R which marks informationally interweaved entities, that is, (43) where Nmark (^arcJM- ^sysJM. ^dictionary ^peripheral) (44) ••• ' Snetwork C ^arcJM'. ^sys.b ^sys,2' ••• ' "-sys ^ ^sysJM^ Sj, S2, ••• C Sdictionary! ^se,l' ^use,2. ••• ^ ^seJM^ "-use,!' '-use,2' ••• ^ ""usaJM» ^sysJM' ^seJM» use JM^ ^peripheral Within machine metaphysicalism SK t= SIR, all metaphysical cycles of sdì's constituting entities (components) are possible and can be deduced from the basic machine metaphysical cycle, that is, (45) cm [= qjperipheral)) N (^arcJM> ^sysJM> ^dictionary)) (^^useJM' "-usc.IM)) N ^ where SK is represented by the informational structure in formula (43). (2) Metaphysical parallelism of SDÌ. IM SDÌ informs in metaphysically parallel ways. For, instance, machine metaphysicalism SDÌ [= SDÌ is able to inform by keeping and arising of metaphysical (interiorly circular) processes in unforeseeable parallel ways. So, (46) (an ^ gji) => (m my, m IN m N 9Jl); (SDl 1= 0)1); ...) where operator ||= is the shortcut for parallel informing. In this situation, as the consequence of the last formula, machine ÜJI copes with the interior circular parallelism in the form of different metaphysical processes, that is, (46') (OR 1= Oil) ((OK 0)1); (Sm 1= OJÌ); ...) This implication shows how machine metaphysics on 1= OH develops in different (parallel) ways. Within machine 0)1, parallel informational processes arise and inform various, interweaved information simultaneously. (3) Metaphysical extemalism o/QJl. We have to draw a clear distinction between the external metaphysicalism (35) and metaphysical extemalism. The adjective external in external metaphysicalism is understood as a predicate (property) of 0)1 [= OJl, for instance, as (0)11= 0)1) Kxtemal What does the metaphysical extemalism mean after that? We have the following basic implication concerning the machine metaphysics 0)1 ^ (47) (0)i|=0)ì)^(((0)ì|=)N®ì); (0)l[=(0)lt=));((0)ìt=)N(®i|=))) There is a control of 0)1's extemalism by OJ? itself (metaphysical control). The shortcut of this situation would be, for instance, (0)i (=) |=metaphysical where the adjective metaphysical is understood as an interior predicate of machine extemalism 0)11=, (4) Metaphysical intemalism of 0)1. Similarly, one can determine the metaphysical intemalism in contrary to the intemal metaphysicalism discussed in formula (39). The adjective intemal in internal metaphysicalism is understood as a predicate of entity HI [= 0)1, that is, l=mtemal(®iN3R) We have the following implication concerning the metaphysical intemalism: (48) (0)it=0)l)^(((^=0)l)[=0)Q; (0)ll=0=0)l));((^=0)i)[=(|=0)i))) There is a control of 0)1's intemalism by 0)i itself (metaphysical control). The shortcut of this situation would be, for instance, Nmetaphysical (N where the adjective metaphysical is understood as an interior predicate of machine intemalism |= 0)1. (5) Metaphysical metaphysicalism of m. Among other informational phenomenalities, metaphysicalism aims at consciousness as informational entity; and metaphysicalism of metaphysicalism alludes at self-consciousness. An informationally sophisticated IM should possess the informational power which through time would succeed or even essentially surpass the informational power of a living actor because of possibilities to use extensive, informationally unlimited realm of referencing. In the informing and self-observing of metaphysicalism 0)1 ^ 0)i, machine 0)1 decomposes 0)i 1= 0)i in different (parallel) ways. Thus, (49) (0)i N 0)i) ^ (((0)1 N N 3«); (0)i (0)10)i)); ((0)lt=0)i)|=(0)lt=0)i))) In (0)i 0)1) (= 0)i, machine Tl is the observer of its metaphysicalism and, simultaneously, a circularly perplexed, informationally arising mechanism of informing, countprinforming, and embedding of information. This mode of informing may be called conscious self-observing. In case 0)11= (0)11= 0)1), metaphysicalism of 0)1 observes the behavior of machine OR, where M informs 0)1 ^ 0)1 on its informational states (necessities and possibilities). This mode of informing is called conscious self-informing. The last case (OH [= OR) |= (0)1 [= OR) is the case of recursive machine self-consciousness. Each metaphysical machine cycle OR |= OR can be decomposed by OR in different ways, offering a real realm of informational possibilities, unforeseeableness, uncertainty, etc. and, through this, a spontaneous informational arising of entities (operands) within IMSDl. (6) Metaphysical production of results ofW. Few words have to be said in concern about possibilities of metaphysical production of results. Results is always significant information in a certain sense. Metaphysicalism of machine IR or of an informing entity in question decides which dedicated item of an informational phenomenon becomes a result because of its possible meaning, sense, significance, etc. Thus, there is not only the user who decides on the occurrence of a result, but metaphysical judgement of the informing entity (operand, formula) suddenly produces results and put them into a result index where they are available for otiier entities and users. Resulting entities are unforeseeable, unpredictable, informationally arising to a certain extent in their nature, kind, significance, occurrence, value, etc. 7.4. IM Phenomenalism Machine phenomenalism (3)1[= ÜR) is the most general case of machine external informing and internal informedness. It would correspond to the term »machine as such« (in German, »die Maschine an sich«). Informational phenomenalism of machine ÜR says that machine as an informational entity cannot be revealed in its phenomenal entirety: because it is not possible to foresee completely its exteraalism which depends on machine observers; because an essential part of its intemal-ism may be unrevealed to exterior observers and »known« only interiorly to the machine metaphysicalism; because its metaphysicalism or its interior circular informing is not directiy informationally open to the machine exterior; because its phenomenalism is only a resultant phenomenon of machine extemalism, intemalism, and metaphysicalism. Certainly, these informational assumptions hold for any informational entity (operand, formula, phenomenon, thing, formation, etc.). We have to remind the reader that machine phenomenalism is defined formally as a system (aR |=; 1= 3Jl) of informationally parallel, tied, and mutually impacting and impacted formulas, that is, ail's extemalism ail [= and ail's intemalism aH. In this system, machine extemalism and machine intemalism are informationally interweaved. depended, metaphysically supported, etc. in a phenomenal (spontaneous, circular), entirely open way. As a system, machine phenomenalism is more than any of its components (extemalism, intemalism, metaphysicalism) and embraces these components, for instance, in the form (50) (OIl[=)C(g)l^;^ail); (}zzgii)c(aiit=;[=:a]i); (an [= an) C (an [=; an) After this introduction, let us overview some particular phenomenal cases of machine an. (1) Phenomenal extemalism of aJl. Several cases of phenomenal exteraalism of machine Oil can be observed. How does a machine phenomenalism inform the machine exterior? The parallel extemal case is the following: (51) ((an t=; N N m N; N IN); ((an t=; ^ an) ^ (((an an) h ); ((an^:3;[=an)|=);...) where operator marks parallel informing. According to formula system (51), parallel phenomenal extemalism can be expressed as (51 ') ((an N; \=m\=)=^ (((® \=; N N; m\=-,\=m\=y,-) This implication shows the phenomenal parallel possibilities of extemal informing of an. The other methodically parallel case could be (52) ((an |=; h 3n) h) ^ IN; IN N or, in an extremely parallel form, (53) ((an N SK) N ^ m IN; IN ^n) |N) The consequences of these implications can be derived easily. (2) Phenomenal intemalism ofüR. We may now repeat the questions and formulas pertaining to phenomenal extemalism for phenomenal inter-nalism. Thus, according to formulas (51) to (53), there is, (54) (t= (an h; ^ an)) (an |=; 1= an)); (an 1= an)) ((h (an |=; 1= an)); where operator ||= marks parallel informing. According to formula system (54), parallel phenomenal internalism can be expressed as (54') (\=im^-,\=m))^((\=m\=-,i=m); This implication shows the phenomenal parallel possibilities of internal informing of iK. The other methodically parallel case could be (55) (\= (ffli h; N ^ (N P IN; IN m or, in an extremely parallel case, (56) (N N; N (IN IN; IN m) The consequences of these implications can be derived in a systematic way. (3) Phenomenal metaphysicalism o/SK. Machine phenomenal metaphysicalism is at the background of machine's »consciousness« in the form of machine metaphysicalism and its phenomenalism, In this mode of informing, machine W, reaches the most complex, phenomena of its extemalism and internalism interweavement and interconnection, projecting the exterior and interior world into a global informational depiction of a distinguished informational realm. Through this spontaneous and circular phenomenology, machine OJl becomes a part of the worldliness pertaining to its, instantaneously most significant informational realm. In this respect, according to informational terms, machine OJl is able to behave as something in the world, with its own reflection, consciousness, and external and internal openness to the world. One may say that through metaphysically structured phenomenalism, IM W. reaches the state of the profound Being-in-the-World. The metaphysical closing of machine phenomenalism, that is, (57) (!1JI[=;|=0R)=> ((5m[=:;t=an)t=(3Jit=;[=®)) preserves the external and internal openness to the machine exterior and interior, that is, possibilities of machine functioning in the exterior and interior world. (4) Phenomenal phenomenalism ofTl. Phenomenal phenomenalism means formally (58) (((lIR|=;[=(R)^=);(}=(3R^;|=nJi))) which is nothing else than machine phenomenalism of machine phenomenalism. In short, as any other informational phenomenon, phenomenalism is recursive in the sense of phenomenal self-(re)produc-tion. (5) Phenomenal production of results o/ÜJl. Phenomenal production of results depends on machine particular modes of informing (extemalism, internalism, metaphysicalism) and, in the last, the most complex informational consequence, on phenomenalism, which not only unites particular cases, but can also produce results outside of these particularities. Phenomenal production of results concerns the most general phenomenality of information (informing, counterinforming, embedding) in the framework of entities which govern and decide on the nature of results and their arising. This is the realm of IM productiveness as a specific view ('seeing') of the most significant informational entities. 8. Technological Perquisites of IM IM requires a fundamentally new conceptualization and development in functional design and technology. It is essentially different from that what, by nowadays terms, is notionally understood as computer. For instance, processors in its interconnection network are new RISC type, at least 64-bit, high-performance, high-speed, electronic, and/or photonic microprocessors. The processor interconnection network requires informational elements concerning intention, significance, and other properties and predicates of informationally extensive, prompt, and sensitive criteria of information exchange. All this calls for a radically new architecture of IM. Operating system of IM must support the informing, counterinforming and embedding of information of machine and user program operands and its system programs must perform in informationally regular way. It must compile user informational programs written in informational language. As a basic informational operand support a sufficiently extensive dictionary (similar to Japanese term of electronic dictionary, for instance in [OED, JWD, EWD, CD, BD, IMD]) must be available for free informing of informational operand entities, including the possibilities of sentence (formula, program) translation in other natural and formal languages. Japan & Co, may be the best suited background for the future IM development and production. 9. Cybernetic Perquisites of IM Informing is certainly a cybernetic activity in which all kinds of known and arising creativity play their informationally phenomenal roles. The cybernetic is synonymous for the live, emerging, understanding, etc. as well as for the informational. The cybernetic comes from the conceptual-ism of managing and controlling machines, living beings, individuals and societies. In this traditional approach, not a specific accent is given to information as a phenomenon: information is simple data necessary for managing and controlling systems in an optimal, goal-directed, surviving, or other way. Consciousness of the informational is not present at the beginning of the cybernetic epoch, at least not in an informationally arising sense. But, only the consciousness of the informational triggers the request of rethinking of cybernetic phenomenality in a philosophic and symbolic theoretical, informational way. In this point of rethinking, informational and cybernetic phenomenalism come close to each other and can be examined from one direction or the other. Informing and informedness of entities is cybernetic, but not only cybernetic. Cybernetics is a study of human control functions (one might say, more generally, informational or communicational functions) and of mechanical, electrical, and electronic systems designed to replace them. This determination was set at the very beginning of modem cybernetics (N. Wiener). Later on, cybernetics encountered the philosophical discourse as a scientific discipline smdying dynamically self-regulating and self-organizing systems. Its boundary fields are system, control, information, communication, game theory, etc. Already Plato gave the word a general meaning (proceeding from the art of boat steering) in the sense of managing a state. As it has developed over the years, cybernetics has become multidisciplinary, involving engineering, computer science, artificial intelligence, psychology, biology, neural science, sociology, philosophy, etc. 10. Intelligent Informational Machine When I assert my own belief that true intelligence requires consciousness I am implicitly suggesting (since I do not believe the strong-Al contention that the mere enaction of an algorithm would evoke consciousness) that intelligence cannot be properly simulated by algorithmic means, i.e. by a computer, in the sense that we use that term today. ... For I shall shortly argue strongly ... that there must be an essentially non-algorithmic ingredient in the action of consciousness. —Roger Penrose [ENM] 407 In the full sense of the word, IIM is the goal of future machine development. Through times, the meaning of the adjective intelligent will more and more approach to the meaning of the »sufficiently complex and specific in informational way«. The main task of IIM will be the production of specific informational entities like meaning, sense, significance, intention, self-observation, conceiving, perceiving, consciousness, etc. which all can be characterized by the happening of machine understanding in the surrounding world. Understanding as an informational activity will remain on the top of intelligent informing of living beings and machines. Before this happens, the entire phenomenality of the universe has to be understood in informational terms, that is, by the ascent from the arbitrary formational (physical, biologic, chemical, etc.) to the adequate informational, throughout the scientific and everyday thinking and acting of mankind. In general, IIM as a future tool is a parallel understanding informational machine behaving informationally in the surrounding world in which it is informationally embedded. In the very last consequence, the informational (and in this sense, the intelligent) means to be in a formation (the Being of Formation) with itself and with other existing (factical and possible) formations (entities, things, phenomena). Thus, information (Being in Formation) as it is, is always in context with information as formation of some- Table of informational machine axioms with Latin, informational, formal, Kantian, information- ally interpretive, and cognitional terminology Latin terms Informational terms concerning informational machine Basic informational formula Kantian terminology for informational machine Informational interpretation Cognitional terminology informatio prima of informational machine OR informational machine extemalism; external informing of machine ÜR; informing of machine 3JÌ ®i|= Informationsmaschine för die anderen informational machine for others informational machine conceptualism informatio secunda of informational machine m informational machine intemalism; internal informing of machine 3JÌ; informedness of machine Informationsmaschine für sich informational machine for itself informational machine perceptiveness informatio tertia of informational machine m informational machine metaphysicalism; metaphysical informing of machine 9R; circular informing and informedness of machine 3R Informationsmaschine in (bei) sich selbst informational machine in itself informational machine consciousness informatio quarta of informational machine m informational machine phenomenalism; phenomenal informing and informedness of machine OR |=; ^ gji Informationsmaschine an sich informational machine as such informational machine phenomenology Anton P. Zeteznikar, An Introduction to Informational Machine, Informatica 16 (1992) 4, 7-28. thing. Formations as observable phenomena are References impacting and are impacted in formational ways and are in certain formations to themselves and to other formations. In information there is no vacuum in the sense of apartness, of contextless situation in concern to the surrounding system of formations. Information is like a text in a context and in this function it is able to approach something which demonstrates intelligence, consciousness, understanding. 11. Conclusion The clue of IM will lead through formalization (symbolization) of informational phenomenal-ity. A solid axiomatic method, that is, a language has to be found to enable technological implementation of informational concepmalism. In the attached table the reader will find four basic axioms of IM informing and their Latin, informational, formal, Kantian, informationally Kantian, and cognitional interpretation. Informational language (philosophy, theory, design) has to be developed in verbal and symbolic form with the aim to master not only the arising problems of informational machines but also informational problems of the living phenomenality. This article is on the way to symbolization and realization (machine implementation) of the proposed informational concepmalism. IM is on the way to surpass essentially human performance. Imagine a written text and its understanding by man and IM. IM can »understand« all sentences of the text in a parallel manner, that is, simultaneously and, additionally, can inform and [OED] be informed in parallel by all in text occurring informational entities. Man, at least, on the level of consciousness, can never perform such a parallel [JWD] task of text recognition and interpretation. And IM will be able to perform by such method of understanding in any case, for any kind of information [EWD] (picture, sound, data, signal, »phenomenon«, etc.). It seems that informational parallelism will reach its processing and meaning zenith in various [CD] IM applications and, right through parallel operation, will extensively surpass certain possibilities of individual mind. [BD] [BIW] [ACR] [SZ] [FOT] [ENM] [IMD] [TIL] [FIP] [BIA] [IBU] Dreyfus, H.L., Being-in-the-World (A Commentary on Heidegger's Being and Time, Division 7), The MIT Press, Cambridge, MA (1991). de Garis, H., ALife III Conference Report, Email: bingvmb.bitnet, Aug 4, 1992. Heidegger, M., Sein und Zeit, Max Niemeyer Verlag, Tübingen (1986). Mayo, J.S., The Fumre of Telecommunication, AT&T Technology 7 (1992) 1, 2-7. Penrose, R., The Emperor's New Mind (Concerning Computers, Minds, and the Laws of Physics), Punguin Books, New York (1989). Železnikar, A.P., Informational Models of Dictionaries I, Informatica 15 (1991)7, 11-21. Železnikar, A.P., Towards an Informational Language, Cybemetica 35 (1992) 2, 139-158. Železnikar, A.P., Formal Informational Principles, Cybemetica 35 (1992) ?, (in press). Železnikar, A.P., Basic Informational Axioms, Informatica 16 (1992) 3, 1-16. Železnikar, A.P., An Informational Approach of Being-there as Understanding (in three parts), Informatica 16 (1992) 1, 9-26; 2, 29-58; 3, 64-75. An Overview of the EDR Electronic Dictionaries, TR-024, Japan Electronic Research Institute (April 1990). Japanese Word Dictionary, TR-025, Japan Electronic Dictionary Research Institute (April 1990). English Word Dictionary, TR-026, Japan Electronic Dictionary Research Institute (April 1990). Concept Dictionary, TR-027, Japan Electronic Dictionary Research Institute (April 1990). Bilingual Dictionary, TR-029, Japan Electronic Dictionary Research Instimte (April 1990). LEARNING QUALITATIVE MODELS WITH INDUCTIVE LOGIC PROGRAMMING Keywords: machine learning, qualitative modelling, qualitative simulation, inductive logic programming Sašo Džeroski Institut Jožef Stefan Qualitative models can be used instead of traditional numerical models in a wide range of tasks. These tasks include diagnosis, generating explanations of the system's behaviour and designing novel devices from first principles. Also, qualitative models are in some cases sufficient for the synthesis of control rules for dynamic systems. An important task in the theory of dynamic systems is the problem of identification of a model that explains given examples of system behaviour. This task can be formulated as a machine learning task of inducing a hypothesis that explains given examples. As the induced hypothesis (model) has to capture relations among the parameters of the observed system, we have to use an inductive tool for learning relations, i.e., an inductive logic programming system. In this paper we describe the application of the inductive logic programming system mFOIL to the problem of learning a qualitative model of the connected-containers dynamic system. Učenje kvalitativnih modelov z induktivnim logičnim programiranjem Kvalitativne modele lahko uporabimo za reševanje različnih nalog, npr. za diagnostiko, generiranje razlage obnašanja dinamičnega sistema ter načrtovanje naprav iz osnovnih načel delovanja. V nekaterih primerili zadošča kvalitativni model tudi za sintezo pravil vodenja dinamičnega sistema. Pomemben problem v teoriji dinamičnih sistemov je problem identifikacije modela, ki razloži znane primere obnašanja sistema. Omenjeni problem lahko formuliramo kot problem avtomatskega učenja kjer je treba generirati hipotezo, ki razloži podane primere. Glede na to, da sestoji model iz relacij med parametri sistema, uporabimo za reševanje problema sistem za avtomatsko učenje relacij oz. induktivno logično programiraiije. V članku je opisana uporaba sistema za induktivno logično programiranje mFOIL pri problemu učenja kvalitativnega modela sistema povezanih posod. 1 Introduction Qualitative models can be used instead of traditional numerical models in a wide range of tasks [Bratko 1991]. These tasks include diagnosis (e.g., [Bratko et al. 1989]), generating explanations of the system's behaviour (e.g., [Falkenheiner and Forbus 1990]) and designing novel devices from first principles (e.g., [Williams 1990]). Bratko [1991] conjectures that qualitative models are sufficient for the synthesis of control rules for dynamic systems, and supports this conjecture with an example. Among several established formalisms for defining qualitative models of dynamic systems, the most widely known are qualitative differential equations called confluences [De Kleer and Brown 1984], Qualitative Process Theory [Forbus 1984] and QSIM [Kuipers 1986]. In this paper, we wiU adopt the QSIM (Qualitative SIMulation) formalism, as it has been already used for learning qualitative models. A fundamental problem in the theory of dynamic systems is the identification problem, defined as follows [Bratko 1991]: given examples of the behaviour of a dynamic system, find a model that explains these examples. Motivated by the hypothesis that it should be easier to learn qualitative than quantitative models, [Bratko et al. 1992] have recently formulated the identification problem for QSIM models as a machine learning problem. Formulated in this framework, the task of learning QSIM-type qualitative models is as follows: given QSIMtheory and ExamplesO/Behaviour, find a QualitativeModel, such that QSIMtheory and QualitativeModel explain the ExamplesO fBehaviour, or formally, In the paper, we describe the application of the inductive logic programming system mFOIL [Džeroski 1991], which can use nonground background knowledge, to the same task [Džeroski and Bratko 1992]. A brief introduction to inductive logic programming is first given, followed by an outline of the main features of mFOIL. We proceed with an overview of the QSIM formalism and illustrate its use on the connected-containers (U-tube) system. The experiments and results of learning a qualitative model of the U-tube system with mFOIL are next presented, followed by a discussion of related work. Finally, we conclude with some directions for further work. QSIMtheory A QualitativeModel |= 2 Inductive logic programming ExamplesO f Behaviour. The identification task can be formulated as a machine learning task. Namely, the task of inductive machine learning is to find a hypothesis that explains a set of given examples. In some cases the learner can also make use of existing background knowledge about the given examples and the domain at hand. So, the learning task can be formulated as follows: given background knowledge B and examples S, find a hypothesis H, such that ß and 7i explain €, i.e., B A Ti [= £. We can see that ExamplesO f Behaviour correspond to E, QSIMtheory corresponds to B and the target QualitativeM odel to H. As a qualitative model consists of relations among the parameters of the modelled system, we have to use an inductive system for learning relations. Systems that learn relations from examples and relational background knowledge, represented as a logic program, have been recently called inductive logic programming (ILP) systems [Muggleton 1992]. Bratko et al. [1992] describe the application of the inductive logic programming system GOLEM [Muggleton and Feng 1990] to the problem of learning a qualitative model of the dynamic system of connected containers, usually referred to as the U-tube system. There have been, however, several problems with the application of GOLEM, to this task, stemming from the inability of GOLEM to use non-ground and nondeterminate background knowledge. In this section we introduce the field of machine learning of relations, or, as it has been recently called, inductive logic programming (ILP). We first mention some systems for learning relations, define the task of empirical inductive logic programming and illustrate it on a simple example. We then briefly outline some features of the ILP system mFOIL, which was used in our experiments in learning qualitative models. Various logical formalisms have been used in inductive learning systems to represent examples and concept descriptions. These formalisms are similar to the formalisms for representing knowledge in general. Several widely known inductive learning systems, such as ID3 [Quinlan 1986] and AQ [Michalski 1983] use propositional languages to represent examples (objects) and concepts. In both cases objects are represented as tuples of attribute values, i.e, in terms of their global features. To represent concepts, decision trees are used in IDS and if-then rules in AQ. Another class of learning systems induce descriptions of relations (definitions of predicates). In these systems, objects are described structurally, i.e., in terms of their components and the relations between them. Training examples are represented by tuples of their components, while the relations between components belong to background knowledge. The languages used to represent examples, background knowledge and concept descriptions are typically subsets of first-order logic (logic programs). In this case, learning is in fact logic program ^ synthesis and has recently been named inductive logic programming (ILP) [Muggleton 1991, Muggleton 1992], Two different approaches can be distinguished in the ILP paradigm [De Raedt 1992]: the interactive and the empirical ILP approach. Interactive ILP systems include MIS [Shapiro 1983], MARVIN [Sammut and Banerji 1986] and CLINT [De Raedt 1992] as well as CIGOL [Muggleton and Buntine 1988] and other approaches based on inverting resolution [Rouveirol 1991,Wirth 1989]. These systems typically learn definitions of multiple predicates from a small set of examples and queries to the user. Empirical ILP, on the other hand, is typically concerned with learning a definition of a single predicate from a large collection of examples. This class of ILP systems includes FOIL [Quinlan 1990], mFOIL [Džeroski 1991], GOLEM [Muggleton and Feng 1990] and LINUS [Lavrač et al. 1991]. LINUS, FOIL and mFOIL upgrade attribute-value learners from the ID3 and AQ family towards a first-order logic framework. A different approach is used in GOLEM which is based on Plotkin's-notion of relative least general generalization (rlgg) [Plotkin 1969]. Empirical ILP systems are more likely to be applied in practice for two reasons. First, there is more experience with learning single concepts from large collections of data than with deriving knowledge bases from a smaU number of examples. Second, empirical ILP systems are much more efficient because of the use of heuristics, because there is no need to take into account dependencies among different concepts, and because no examples are generated [De Raedt and Bruynooghe 1992]. In fact, they are already efficient enough to be applied to real-life domains [Bratko 1992]. Several applications have been reported, including learning qualitative models from example behaviours [Bratko et al. 1992] [Džeroski and Bratko 1992], inducing temporal rules for satellite fault diagnosis [Feng 1991], learning to predict protein secondary structure [Muggleton et al. 1992] and learning rules for finite element mesh design [Dolšak and Muggleton 1992, Džeroski and Dolšak 1991]. ^ For an introduction to logic programming we refer the reader to [Bratko 1990], A detailed theoretical treatment of the subject is given in [Lloyd 1987]. Empirical ILP The task of empirical ILP, which is concerned with learning a single predicate, can be formulated as follows. Given: • a set of training examples €, consisting of true and false S~ facts of an unknown predicate p, • a description language specifying syntactic restrictions on the definition of predicate p, • background knowledge B, defining predicates qi (other than p) which may be used in the definition of p and which provide additional information about the arguments of the examples of predicate p. Find: • a definition Ti for p, expressed in C, such that Ti is complete, i.e., ^e £ S'^ : B AH \= e, and consistent with respect to the examples, i.e., -.BAH Y-e. The true facts are called positive examples, the false facts £~ are called negative examples diixà the hypothesis H, i.e., the definition of p, is usually called the definition of the target predicate. When learning from noisy examples, the completeness and consistency criteria need to be relaxed in order to avoid overly specific hypotheses. The ILP system mFOIL The ILP system mFOIL [Džeroski 1991] is largely based on the-FOIL [Quinlan 1990] approach. We thus briefly describe FOIL first and then outline some of the key features of mFOIL. FOIL extends some ideas from attribute-value learning algorithms to the ILP paradigm. In particular, it uses a covering approach similar to AQ's [Michalski 1983] and an information based search heuristic similar to ID3's [Quinlan 1986]. The hypothesis language C in FOIL is the language of function-free program clauses, which means that no constants or terms other than variables may appear in the induced clauses. Function-free ground facts (relational tuples) are used to represent both training examples and background knowledge. After the pre-processing of the training set, which consists of generating negative examples if none are given, the outermost loop of the FOIL algorithm repeats the following two steps untili all positive facts are covered: • find a clause that covers some positive and no negative facts, • remove the facts covered by this clause from the training set. Finding a clause consists of a number of refinement steps. The search starts with the clause with empty body. At each step, the clause c built so far is refined by adding a literai to its body. These literals are positive or negative atoms of the form Xi = Xj or qk{Yi,Y2,...,Yn)^), where the X's appear in c, the Y's either appear in c or may be new variables and q^ is a relation (predicate) from the background knowledge or the target predicate p itself. To stop the search for literals to be added to a clause, FOIL employs the encoding length restriction, which limits the number of bits used to encode a clause to the number of bits needed to explicitly indicate the positive examples covered by it. The construction of a clause is stopped when it covers only positive examples (is consistent) or when no more bits are available for adding literals to its body. The search for clauses stops when no new clause can be constructed under the encoding length restriction, or alternatively, when aU positive examples are covered. One should be aware, however, that there are several problems with the encoding length restriction that actually degrade foil's performance on both noisy and non-noisy data as shown in [Džeroski and Lavrac 1991]. The most important differences between mFOIL and FOIL are related to the noise-handling mechanism used. mFOIL uses Bayesian probability estimates, namely the Laplace and the m-estimate [Gestnik 1990], of expected clause accuracy as search heuristics. These estimates have been successfully used in a similar way in proposi-tional learning systems [Clark and Boswell 1991, Džeroski et al. 1992]. mFOIL also uses significance tests, similar to the ones in [Clark and Boswell 1991]. It achieved better results than FOIL on a test domain with artificially added noise and on a real-life domain of learning rules for finite element mesh design [Džeroski 1991, Džeroski and Bratko 1992]. Another key difference is the capability of mFOIL to use background knowledge which may contain rules and not ground facts only. This feature is especially important for learning qualitative models, since the QSIMtheory consists of rules and not ground facts only. Other differences between FOIL and mFOIL are related to the search strategy and the space of possible hypotheses. As opposed to the hill-climbing search in FOIL, where only the best partially built clause is kept, mFOIL uses beam search and keeps several most promising clauses (the beam), which are refined gradually. mFOIL can also use information about the background knowledge, such as symmetry of predicates and types of predicate arguments, to reduce the space of possible hypotheses. 3 Qualitative modelling In this section, we first introduce the QSIM [Kuipers 1986] formahsm and then illustrate it on the U-tube system. We also describe how the QSIM theory can be formulated in logic [Bratko et al. 1992], so that it can be used as background knowledge in the process of learning qualitative models from examples. The QSIM formalism In the theory of dynamic systems, a physical system is represented by a set of continuous variables, which may change over time. Sets of differential equations, relating the system variables, are typically used to model dynamic systems numerically. Given a model (a set of differential equations) of the system and its initial state, the behaviour of the system can be predicted by applying a numerical solver to the set of differential equations. A similar approach is taken in qualitative simulation [Kuipers 1986]. In QSIM, a physical system is described by a set of variables representing the physical parameters of the system (continuously differentiable real-valued functions) and a set of constraint equations describing how those parameters are related to each other. In this case, a (qualitative) model is a set of constraint equations. Given a quahtative model and a qualitative initial state of the system, the QSIM simula- tion algorithm [Kuipers 1986] produces a directed graph consisting of possible future states and the immediate successor relation between the states. Paths in this graph starting from the initial state correspond to behaviours of the system. The value of a physical parameter is specified qualitatively in terms of its relationship with a totally ordered set of landmark values. The qualitative state of a parameter consists of its value and direction of change. The direction of change can be ine (increasing), std (steady) and dec (decreasing). Time is represented as a totally ordered set of symbolic distinguished time points. The current time is either at or between distinguished time-points. At a distinguished time-point, if several physical parameters linked by a single constraint are equal to landmark values, they are said to have corresponding values. The constraints used in QSIM are designed to permit a large class of differential equations to be mapped straightforwardly into qualitative constraint equations. They include mathematical relationships, such as deriv{Velocity, Acceleration) and mult{Mass, Acceleration, Force). In addition, constraints like M"^ (Price, Power) and M~ {Current, Resistance) state that there is a monotonically increasing/decreasing functional relationship between two physical parameters, but do not specify the relationship completely. The U-tube system La Lb Fab Fba Figure 1: The U-tube system. Let us illustrate the above notions on the connected-containers (U-tube) e)tample, adapted from [Bratko et al. 1992]. The U-tube system (illustrated in Figure 1) consists of two containers, A and B, connected with a pipe and filled with water to the corresponding levels La and Lb. Let the flow from to i? be denoted by Fab, the flow from J? to >1 by Fba. The variables La,Lb,Fab and Fba are the parameters of the system. The flows Fab and Fba are the time derivatives of the water levels Lb and La, respectively, and run in opposite directions. Let the difference in the levels of the containers A and B be Diff = La — Lb. The pressure Press along the pipe influences the flow Fab: the higher the pressure, the greater the flow. A similar dependence exists between the level difference and the pressure. The above constraints can be formulated in QSIM as follows: —La = Fba at —Lb = Fab dt Fab = -Fba Diff = La-Lb Press = M+{Diff) Fab = M+(Press) If we are not explicitly interested in the pressure, the last two qualitative constraint equations can be simplified into one: Fab = M+{Diff) For comparison, in a numerical model, the last two equations might have the form Press = cj • Diff Fab = C2 ■ Press or, when simplified Fab = c- Diff where c, ci and C2 are positive constants. In this case, the relationship between the variables Fa6, Press and Diff is completely, and not only qualitatively, specified given the values of c,ci and C2. The landmark values for the variables of this model for the U-tube, ordered left to right, are as follows: La : minf,0,la0,inf Lb : minf,0,lb0,inf Fab : minf, 0, fabO, inf Fba : minf, fba0,0,inf Time La Lb Fab Fba to ito,ti). tl itl,inf) laQ/dec 0..la0/dec 0..la0/std 0..la0/std IbO/inc lb0..inf/inc lbQ..inf/std lb0..inf/std fabO/dec 0..fab0/dec 0/std 0/std fbaO/inc fbaO..O/inc 0/std 0/std Table 1: Qualitative behaviour of the U-tube system. These values are symbolic names corresponding to minus infinity, zero, infinity and the initial values of the four variables. The left-to-right ordering corresponds to the less than relation between the corresponding numerical values. The QSIM simulation of the U-tube system produces the trace given in Table 1. From the trace we can see, for example, that in the initial state the value of the level La is equal to /aO and is decreasing {dec). This is represented as La = laO/dec. In the time interval that follows. La is between 0 and laQ and decreasing, which is written as La = 0..la0/dec. Formulating QSIM in logic Bxatko et al. [1992] translate the QSIM approach to qualitative simulation into a logic programming formalism (pure Prolog). A sketch in Prolog of the QSIM qualitative, simulation algorithm is given below. simulate{State) transition{State, NextState), simulate(NextState). transition{stdte{Vl,...), staie(NeiuVl, ...))«—