Informatica 20 (1996) 331-358 331 
Informational Transition of th e Form a \= (5 and Its Decomposition 

Anton P. Železnikar 
An Active Member of the New York Academy of Sciences 
Volaričeva ulica 8 
1111 Ljubljana, Slovenia (anton.p.zeleznikar@ijs.si) 


Keywords: causality, cause-effect philosophy; circular and metaphysicalistic transition a \= a; de­
composition: canonic, noncanonic, serial, parallel, circular-serial, circular-parallel, metaphysicalistic­serial, metaphysicalistic-parallel; demarcated: frame, gestalt; informational: circle, graph, gestalt, 
transition «(=/? ; metaphysicalistic: circle, graph, gestalt; number of the transitional decompositions: 
possible, canonic, noncanonic; parenthesized: frame, gestalt; transitional decomposition 

Edited by: Vladimir A. Fomichov 
Received: December 27, 1995 Revised: February 22, 1996 Accepted: March 5, 1996 

In this paper the complexity and heterogeneity of informational transition occurring be­tvveen informational entities is studied to some formalistic details, using the technique of informational decomposition [6, 7, 9, 10, 11]. E. Birnbaum [1] has reopened an important problem of the informational theory by a formulation ofthe informational-causal chain. General informational theory can substantially concern this particular problem, that is, studying the decomposition possibilities of formula ct\= /3 and its circular, particularly, metaphysical čase a \= a. In this paper, the decomposition problems of both <x\= /3 and a \= a will be generalized and concretized in the form of several informational systems, which appear to be serial, parallel, circular-serial, circular-parallel, metaphysicalistic­serial, and metaphysicalistic-parallel, but also canonic and noncanonic. Among others, these formula systems are studied by the methodology of informational frames and ge­stalts [11] showing the possibilities of decomposition. At the end, a čase of the social informational transition and its decomposition is discussed to some principled details. 
1 Introduction
Informational transition1 belongs to the basic andmost important concepts of the general informa­tional theory [1]. Thus, formula a\= (3, and itscircular and metaphysicalistic occurrence a (= a,presents the primordial informational problemfrom which one can start the research of the fun­damental concepts of the emerging general infor­mational theory. In this context, particular casesof open and closed transition formulas can be tre­ated as, for example, the externalism a (=, theinternalism |= /?, the metaphysicalism a (= a (or/3 |= /3), and the phenomenalism a f=; |= /?.
In a particular way, by Birnbaum [1] reopened
'This paper is a private author's work and no part ofit mav be used, reproduced or translated in anv mannerwhatsoever without written permission except in the čase
of brief quotations embodied in critkal articles.
 problem of information transfer (transmission, di­stribution, broadcasting, receiving), in the form 0f the disturbance-influenced triad, consisting of  the signal (or information) transmitter (simulta­ neously, the informational source), channel, and receiver, can be formalh/ (symbolically, theoreti­Cally) generalized by the concept of the informa­ tional transition (the informer operand, opera­tor between the informer and observer, and the observer operand). Informational transition con­ cerns not only the problem of information tran­ smitting, channeling, and receiving by machines,  media, and living beings, but also the problem 0f informational arising (emerging of interior and  exterior disturbances, impacts) within ali transi­tional components in their spontaneity and circu­
^ i n th e framewor k 0 f th e informationa l s e  .. . , ... . „.. „ , i ' <• 
 rlallSm an d
 Parallehsm . Slgmfican t example s of  informational transition are the following: 
1.	
 Transmission and reception of information-carrying signals through a channel between the transmitter and receiver is a technical sy­stem with the goal to mediate the transmit­ted signal, as undisturbed (undistorted) as possible, to the receiver. In this way, along the channel, noise and other signal distur­bances can appear modifying the originally transmitted signal. Another source of noise and disturbances can appear also in the re­ceiver before the signal is converted (acousti­cally, visualb/, digitally or data-likely) for the purposes of various users (the problem of the receiver internalism, e.g., of the filtering of the arrived signal). 

2.	
 Another problem is, for instance, the writing down and shaping a message for the public distribution where the author gives his/her initial text to the inspection to his/her col­leagues, correctors and editors, who per­form in an informationally disturbing (cor­recting, lecturing) manner. Then, the correc­ted text is printed (with the removed "failu­res from the text form and contents"), and as such is distributed to other readers (in general, to the intelligent observers). Here, a strict distinction within the informational triad informer-mediator-observer is heavily possible in the sense of a strict separation of the informer, the correcting, editing and mediating channel, and the observer (indivi­dual reader, seer, listener, interpreter). The problem is also timely conditioned where the author could have already forgotten what he has written or even did not see his final result in the distribution medium. 

3.	
 Another example of informational transition happens in a live discourse, among several di­scursively interacting speakers, where more than one informer and observer interact in a speaking, listening (observing) and media­ting informational environment. In this sense we can understand the informational decom­position of an initial theme which is thrown into a group of informational actors (spea­kers) and thus, at the end of the discussion, leaves different informational results (impres­sions) to the participating informational ac­tors. 


A.P. Železnikar 
2 Technical and Theoretical 
Models of Information 
Transmission (Mediation) 
Technical model of information transmission or mediation proceeds from the well known triad transmitter-channel-receiver2 . The idealistic čase considers an informer, noise-free channel (medi­ator) and observer. The channel is commonly understood to be a transmission or propagation medium (an informationally active device) be­tween transmitter (informer) and receiver (infor­mer^ observer). If information is carried in the form of modulated or coded electromagnetic si­gnals and/or waves, the Maxwellian theory can be applied for the electronic circuits and electroma­gnetic waves to study the transmission and pro­pagation possibilities in space and/or physical de­vices. 
Such a technical system concerns usually the reliable, true, or exact transmission (mediation) of signals. It does not concern the informational systems of living beings which do not exclude the arising of information on the side of informer, the propagation of information through the informin­gly active medium and the reception (understan­ding) of information on the side of informational observer. If the technical problem is first of ali a genuine transmission (transfer) of signals irre­spective of the loaded information, informational transition in general concerns informational emer­ging not only in the space and tirne of the infor­mer but also in the space and time of the channel and the receptor, that is, the channel observer via which information is arriving. 
Therefore, the technical problem of information transmission is only a particular, purely technolo­gical problem within informational transmission. Technical problems of information transfer are more or less solved within determined technologi­cal systems where it is known under which circum­stances these systems can function satisfactorily. 
2The technical (telecommunicational) problem was ma­thematically formulated by Claude Shannon [4] where, as he said, meaning does not travel from a sender to a recei­ver. The only thing that travels are changes in some form of physical energy, which he called "signals". More impor­tant stili, these changes in energy are signals only to those who have associated them with a code and are therefore able, as senders, to encode their meanings in them and, as receivers, to decode them [2]. 
INFORMATIONAL TRANSITION... Informatica 20 (1996) 331-358 333 
On the other side, the informational problems of transition, concerning spontaneous and circular information arising within of informationally li­ving actors environments represent substantially different philosophy, methodology and formalism. Informational theory covers essentially this philo­sophy by a new sort of formalism, implicitly in­cluding the informational arising in a spontaneous and circular way. There does not exist a proper theory of this naturally conditioned problem of in­forming of informational entities. Contemporary philosophies seek their approaches and interpre­tations within the more or less classical philoso­phical orientations (doctrines of the so-called rati­onalism, especialb/ cognitive sciences) performing within natural language discussions and debates and outside promising ways of new formalizations. 
3 Information Transmission at th e Presence of Noise 
Noise as an unforeseeable, spontaneous, chaotic and disturbing phenomenon remains in the realm of informational heterogeneity. A disturbing in­formation does not only mean a distorted, use­less or undesired phenomenon, but also the ne­cessary and possible informational realm of chan­ges, formations and origins, for example, in the form of the so-called counterinformation being a synonym for a spontaneously and circularh/ ari­sing information, its informational generation as a consequence of occurring informational circum­stances in space, tirne and also in brain. In this view, the informational noise carries the possibi­lities and necessities of informational emerging as a regular, desired or undesired, unforeseeable or expected informing of informational entities. 
Instead of information transmission at the pre­sence of noise we can use a more general and also more adequate term called the transition of information in an informationally disturbing en­vironment, where the spontaneously arising na­ture of informing of entities comes to the surface. Informational disturbance can be comprehended as a cause generating informational phenomenon from which informational consequences of vari­ous kinds are coming into existence. The ari­sing mechanism of the informational roots also in the disturbing, causing and effecting (causing-to­come-into-informing) principles where disturbing is the phenomenon which rises the cause of the consequence. 
4 Possible Informational Models of Transition 
On the introductory level, we can list and describe shortly the main informational models of transi­tion, marked by a f= /3. Some of this models are very basic and some of them can become more and more complex in a circular, recursive, also frac­tal3 manner and, certainly, in this respect, also spontaneous. The discussed models of transition a (= P will be nothing else than informational de­compositions (derivations, deductions, interpreta­tions) concerning particular elements of the tran­sition and the transition as a whole. So, let us list the most characteristic models of informatio­nal transition. 
1. A decomposition of a f= j3 can be begun by operator |= which becomes an initial operator frame [10, 11], that is, 
a \= P 
Usually, at the beginning, we introduce the so-called parenthesized operator frame and, the con­sequence of this choice is that the operator frame becomes split, in general, into three parts, of the form 

(...( a h-N & )•••) 

where the left and the right parenthesis frames (... ( and ) • • •) , alternatively, can be empty. 
2. A more expressively compact form of the operator-decomposed transition is obtained by means of the so-called demarcated operator4 
3Fractal is a mathematically conceived curve such that any small part of it, enlarged, has the same statistical character as the original (B.B. Mandelbrot, 1975, in Les Objects Fractal). Sets and curves with the discordant di­mensional behavior of fractals were introduced at the end of the 19th century by Georg Cantor and Kari Weierstrass. Parts of the snowflake curve, when magnified, are indistin­guishable from the whole [12]. 
4The so-called demarcation point, '.', was introduced in metamathematics by Whitehead and Russel [5]. The pri­vilege of such denotation is that the sequence of operands and operators in a formula remains unchanged, which does not hold for the Polish prefix or suffix transformation of formulas. 
334 Informatica 20 (1996) 331-358 A.P. Zeleznikar 
frame, where instead of each parenthesis pair with  ")> on e
operator, that is, (•••)!= an d N ('' demar­cation point is used, that is, • • •. (= and \= . • • •, respectively. The consequence of such notation is the disappearance of the parenthesis frames and, in this way, the appearance of only one unsplit operator frame in the decomposed transition (and also other) formulas. In general, the possible de­marcated forms of the decomposed transition be­comes 
pCJl. p H /?; 
a 
^7 1 
(= ui. p • • •. p . Ui \= . • • • p . un p P;
a 
a p . CJI • • • p . con p P 

The first and the last operator frame do not in­clude the demarcated form. p . because the plače of the main operator is at the end or at the be­ginning of the formula and operands /3 (the first formula) and a (the last formula) are not paren­thesized. Thus, the main informational operator P is in the first formula at its end and in the last formula at its beginning. 
3 . The next two examples concern informational transition a \= P in its form of operator composi­tion, tha t is, 
a K H/3 0 

In this way, simultaneously, to some extent, the meaning of the operator composition denoted by p o |=, comes to the surface. In this context, it can be decided, where the separation of operators p a and \=p actually occurs. The one separation point is certainly the composition operator 'o' and the other two are operands a and p. One must not forget, that operator |= a is an informationally active attribute of operand a and similarly holds for operator \=@ in respect to operand p. 
Let us decompose the parenthesized, operator-composed transitional form a \=a ° p/j P- The ge­neral form will be 
(...( a |=...|= o [=...|= p )..-) 

where |= a and \=p are split to the left parenthesis frame and the right parenthesis frame, respecti­vely. Parenthesis frames can also be empty. This situation becomes clear when one imagines that the o-operator stands at the plače of the main operator |= of a formula and that just this opera­tor is split in the sense of (= o [=, where the left P belongs to pa-decomposition and the right |= belongs to p^-decomposition. 
4. The next possibility of the informational tran­sition decomposition is the one of the previous čase when the parenthesized form is replaced by the demarcated one. In this situation, operator frames p a and p ^ are not anymore split and the expression becomes compact and more transpa­rent. Characteristic cases of such possibility are 
p Wi . p • • • . p Wn . p O \= P 
a 
pu/i . h-P • w,+i p 
a 
• \= N -wn p P; 
p O |= . LJl f= . • • • f= . W„ |= P
a 

No operator frame does include the form . p . (the plače of the main operator of a formula) because this operator is hidden in the operator composi­tion p o |=. 
5. The next question concerns the so-called circu­lar transition. An informational entity, in itself, can function as a serial circular informational con­nection of its interior components which inform as any other regular informational entity. There is certainly possible to imagine an exterior circular informing in which a distinguished entity takes over the role to function as the main informati­onal entity in a circle of informing entities. In principle, these circular situations do not differ substantially from the previous cases. The origi­nal informational transition a (= P is replaced by the initial circular notation a j= a. 
There are various possibilities of studying de­composed circular transitions. For instance, in Fig. 2, there is a unique simple čase of a transi­tional loop. Fig. 3 offers another interpretation, where to the serialh/ decomposed loop there exi­sts a parallel, yet non-decomposed circle. And la­stly, in Fig. 5, the non-decomposed circular path can be replaced by the reversely decomposed first loop, bringing a senseful interpretation and in­formational examination of the first loop by the INFORMATIONAL TRANSITION... 
second one. 

6. The next čase provides an additional pertur­bation of the already decomposed components ui, <*>2j • • •) wn by means of some disturbing compo­nents 6\, 82, •••, 6n, respectively, as shown in Fig. 10. These components impact the w-chain from the interior or the exterior. An interpreta­tion of this disturbance is possible by means of parallel formulas, that is, 
SJ \=Uj\ 3 = l,2,---, n 

This situation is studied in detail in Section 5.14 and represents an informational extension and theoretical interpretation of the čase opened by Birnbaum in [1]. 
7. Finally, there is possible to expand the ba­sic decomposed informational decomposition with the initial components ui, (J2, • • •, wn in a fractal form as shown in Fig. 11. Thus, to the internal components ui, U2, •••, wn of the first transition similar other transitions take plače in an unlimi­ted manner regarding the number of transitions. In this way, a complex transitional fractal is ob­tained consisting of variously connected informa­tional transitions. In this way, the basic system of decomposed transition is extended by the ad­ditional system of informational formulas, that is, 
(• • • (("t h w i,i ) F ^,2 ) F • • • wi,„; -i ) |= u)iini; "i,j F uhj'i 
i = 1,2 , ••• ,n; j = l,2,---,m 

This formula system represents only a part of the graph interpretation in Fig. 11, not being presen­ted in an informational gestalt form yet. 
5 Serial, Parallel, and Circular 
Structur e of Informational 
Transition Decomposition 
5.1	 Decomposition Possibilities 

Informational transition of the form a \= (3 can be decomposed in several informational ways— from the simplest to the most complex ones, but also in a serial, parallel, circular, and metaphysi­calistic way. Ali components of transition a\= (3, that is, operands a and /3 and operator |=, can be 
Informatica 20 (1996) 331-358 335 
decomposed (analyzed, synthesized, interpreted) to an arbitrarily necessary or possible detail. By advancing of decomposition, informational boun­daries between the occurring entities a, |=, and (3 can become unclear and perplexed within the complexity of the structure which arises through various decomposition approaches. 
One of the basic problems is the systematiza­tion of decomposition possibilities (processes, en­tities) and their symbolic presentation. Decompo­sition of the general transition a f= (3 or its me­taphysicalistic čase a (= a can concern the serial, parallel, circular, metaphysicalistic, and any mi­xed čase of the informational deconstruction of a |= /3 and a \= a. Let us introduce the following general decomposition markers: 
|A_ (a |= (3) serial i-decomposition A of 
a \= (3 of serial length L (5.2); 
^A..(a! \= P) parallel decomposition A of 
a \= (3 of parallel length t (5.8); 
\A^ (a \= a) circular serial i-decomposition 
A of a \= a of circular-serial 
length	 t (5.9); 
eA^(a |= a) circular parallel decomposition 
A of a \= a of circular-parallel 
length	 L (5.11) 
where for subscript i (look at Subsubsection 5.12.6) there is 
Metaphysicalistic decomposition is specificalh/ structured, that is, metaphysicalistically standar­dized. We introduce 
fdJl^(a \= a) metaphysicalistic serial 
i-decomposition TI of a (= a 
of circular-serial length t (5.12); 
i9Jl<?(a \= a) metaphysicalistic parallel 
decomposition 97t of a |= a of 
circular-parallel length L (5.13) 
5.2	 A Serial Decomposition of a f= (3-, that is, n+\A^(a \=/3) 
Let us start the decomposition process of tran­sition a \= (3 with the simplest and most usual serial čase. Let us sketch this simple situation by the graph in Fig. 1. This figure is a simplifica­

d wn_i 

Figure 1: A simple graphical interpretation of in­formational transition a (= (3 divided into the in­former part (a), serially decomposed channel or internal part with informational structure of u\, b>2> " • • ; u n, o.nd the observer part (P). This graphical scheme represents the serial gestalt of a f= P serial decomposition, that is, ali possible serially parenthesized or demarcated forms of the length t = n + 1. The zig-zag path illustrates the discursive (spontaneous, alternative, also intenti­onally oriented) way of informing. 
tion of the model given by Fig. 1 in [1]. On the other side, we have studied several forms of serial informational decomposition of informational en­tities and their transitions (e.g. in [6, 7, 9, 10]). The graph in Fig. 1 represents an informational gestalt [11] because various interpretations of it are possible. 
Let us interpret this graph in 'the most logical' manner. This interpretation roots in the under­standing of technical systems where we conclude in the following way: 
-	 Transition a |= P is understood as a process running from the left to the right side of the formula. We rarely take a (= (3, according to a parallel decomposition possibility, as a pa­rallel process of components a, /3, and a [= /?. 
—	 Processing from the left to the right, we come to the conclusion that the adequate informational formulas describing the inter­nally structured decompositions of transition a (= P are, according to Subsection 5.1, 
A.P.. Zeleznikar 



((((•••(•••(((«h^)h^)H^)|=---
Wi) N • • • Un-2) \= wn_i) |= uin) |= /?); 
(((•••(•••(((ah"i)h" 2 )|=W3)|=-" 
Wi) |= • • • ujn -2) |= w n _i ) | = (un (= /3)); 

w2B n +t}A^(aM)^ 
n+2 V n+1 J 
(a \= (ui \= {u2	 \= (w3 |= • • • (ui \= • • • 
k-2 hk-i N K h iS))) •••)•••)))) 

where ^ is read as means or, also, informs meaningly. 
This conclusion delivers (=-operator decom­positions of a (= (3 which, in the frame-parenthesized form [10, 11], are 
\=Ul) \=U2) \=• w3) 

(((•••(•••(( ( a 	h-• • Ui) \= • • •Wn-2) /3; 
|= un-x) |= un )N 

. |= Wl) |= fa/2) N ^3 ) 
((...(...(( ( h-• • Wi ) | = • • 'WB-2) 

a 
>B 
(= Wn-l) (= (^n H 
|=	 (wi |= (u2 |= (w3 

a: 	h -• (wt N • •• K-2 /3 )))•••)•••))) hO* n-l |= ( ^ . H 
More clarity could be brought to the surface by the use of the so-called frame-demarcated decomposition [11] which for the the first de­composition formula gives 
\=ux \= UJ2 . N^3 ­
a 
!=• • Ui h OJn-2-P \=un • h •\=
-! •*>n 

As we see, the operator decomposition in a \= P is externally independent; there are only internal components by which the inter­nal structure of operator is interpreted, that is, decomposed into details. 
INFORMATIONAL TRANSITION... 
The first formula is actually the strict informer a's view of the transition phenomenon a \= (3. The strict observer /3's view of the transition pheno­menon a \= P is the last formula 
(a f= P) ^ dc n 
(a \= (UJI |= (a>2 |= (a;3 |= • • • (ui \= • (uJn-2 (= (w„_ i | = (u>n \= P))) •••)• •)))) 
The viewpoint of the observer P proceeds syste­maticallv from the right to the left of the tran­sition formula and so delivers a decomposed for­mula which, in respect to the positions of the pa­renthesis pairs, is structured in a mirrored form to the formula of the viewpoint of the informer5 . 
The graph in Fig. 1 represents a gestalt belon­ging to any of its informational formula. Gestalt is a set of formulas which can be constructed for an informational graph. The strict informer and the observer viewpoint are only two possibilities: ali the other are between the both. We will show how ali formulas of a transition gestalt can be, to some extent, differently interpreted by the so-called operator composition \=a o \=p. 
5.3	 A Transparent Scheme of the Canonic Serial Decomposition of 
Let us introduce the general transparent scheme & of the canonic serial decomposition, marked by 
* can 
n+ l
i+ l A^'( a |= P), in the form 


e(XlAZ"(a\=p))^ 
aUlU2^3 • • • U{-\Ui | Wi+iO;,+2 • • • Un-2^n-l^nP 
where the schemes for the first (pure informer or informingly structured informer) and the last (pure observer or observingly structured obser­ver), that is, (n + l)-th canonic decomposition are 
In this respect, there is interesting to mention, that some traditional implication axioms can be structured in a circular-observational manner. E.g., the propositional axiom of consequent determination, A —• (B —^ A), as the first axiom in different proposition and predicate calculi is identically true while (A —> B) —> A is not. 
Informatica 20 (1996) 331-358 337 


e(n+lAZ"(a\=p)) ^ 
aUlUJ2UJ3 • • • Ui-iU!iUi+lU!i+2 • • • Un-2^n-l^n \ P\ 
6 (H\A-(a ^pj)^ 
a | U1UJ2LU3 • • • U)i-iU>iUJi+iLUi+2 • • • Un-2Wn-\UnP 
where 
0 < i < n 
Each underline marks one parenthesis pair at its ends, symbol '|' marks the main operator (|=* or 
|= ) of decomposition, and between two ope­rands (e.g., concatenation a^j+i ) an operator |= appears, according to the underlined formula se­gments. 
A serial decomposition is canonic if and only if its informer part is purely informer-canonic and its observer part is purely observer-canonic. For a serial decomposition of a |= p of length L — n + l there are exactly n + l canonic formulas. 
5.4	 Introducing Canonic Gestalt of Serial Decomposition of a \= /? 
Canonic gestalt rca" is a particular, reduced form of gestalt T, concerning an arbitrary serial decom­position of transition a f= /?, that is (also a non-canonic), n+jA^(a (= P), where 
1 lln + V 
i<i < 
n+2\n+l 
The canonic gestalt is nothing else than an infor­mational system of exactly n + l canonic decom­positions 
n+l 
i 1 A7(aM);...;LiA:r(a|=/3 ) 
Thus, we introduce the following definition of the canonic gestalt of a transition decomposition: 

rcon("+JA_(ap/3))^Def 
/(((• • •(•••(((at=w 1 )|= W 2)Nw3)|=---\ 
Wj) p • • • Wn _2 ) p UJn-l) \= Wn) N Z?! 
((•••(•••l«Ni)N2)N^)N­
^i) p • • • wn_2) p un _i ) p (wn p /3); 
(•••(•• • (((a |= Wl ) |= w 2 )|=W3) N 
Wi) p • • • wn_2) |= (w„_i p (un p /?)); 
((a p wi) p w2) |= (^3 1= • • • (ui p 
(Wn-2 p (w n -l |= (^ n H /?))) •••)•••) ; 
(a (= wi) p (w2 (= (^3 (= • • • (WJ p 
(Wn_2 H (wn-l |= (Wn N /?))) •••)• • ')); 
a p (Ul (= (u;2 |= (W3 p • • • (Wj p 

The main operator (= in each of n + 1 formulas of the array is framed, that is, p , to be easily surveyed. 
Let us use, instead of the lengthy denotation for a canonic gestalt r°a n (n+JA^(a \= /3)), the sym­
bol r"un - Canonic gestalt6 TcTji is a parallel sy­stem of formulas where each formula can be mar­ked by an indexed component fai-g representing the adequate canonic decomposition of transition a p 0. The number of possible decompositions in the gestalt depends on the number of the in­terior components Ui, that is, n. By induction, the number of different canonic decompositions of the length L = n + 1 (the number of the occur­ring binary operators p in a formula) of transition a p /3 is n + 1. Thus, 
•p can can n, l cann,2 can «n n ,n+l \ 
n (

where 
6There exist exactly ^W ( n+i) — (n + 1) noncanonic decompositions of length i = n + 1 of transition a |= /3. They can be gathered in the form of a noncanonic gestalt r° c ^ n of length L 
A.P. Zeleznikar 
can?i,» 
(n+2-i)-th 
• ­
(•••(*!= "i)l=-^n+l-i) H n+l—i (un+2-i p • ••Nkh/s)-) i-1 
i = 1,2,- • • , n + 1 

The parenthesized operand gestalt r^g , as a consequence of serial decomposition of transition a p /3 by informational components u>i, o>2, • • •, uin, can be expressed by means of parenthesis gestalts ri/an n and nr"n , discussed in Subsec­tion 5.6, and the particular operator gestalt r\i/ n , that is, 
P X1)
• a\=P ^~U ( a l )|=(

where 
and 

<t>)H ­
(n+2-t)-th 
p Ui) p •••OVi+l-t) N (<^n+2-i |= 
• • • N (Wn |= 

« = l,2,---, n + l 
and, finally, 
cann,ž __,. cann,i j.cann,i 0 cann,i 
i = l,2J..-,n + l 

Evidently, for the parenthesis frames there is 
•K, ^ ((• • • ( an d 7i\ 
ti 
n+1—t t-i 

We can also reverse the process of the right-left enumeration, replacing subscript i by j , reversing INFORMATIONAL TRANSITION... 
the order of formulas (the last one becomes the first one) in r^T ^ and setting 
j-t h 
(•••(a|=wi ) \=---uj-1) (= (Wj | = 
'••H^N/5)-) 
n+l-j 
j = l,2,---, n + l 
For the parenthesis frames one obtains 
7T/	 ^ (.(••• ( an d 7I\ ^ 
ti 
i-i 	71 + 1-J 
Partial (inner) frames of particular formulas are 
0)K ­
j-th 
Ml)h-•Wi_l) N to N • • N K N 
j = l,2,---, n + l 
and, finally, 
j = l,2,---, n + l 
5.5	 Demarcate d Čase of Canoni c Gestal t of Serial Decompositio n of 
A compact presentation of the operational effec­tiveness of a gestalt belonging to informational transition a \= /3 is obtained by the introduction of framed demarcated canonic gestalt. This me­ans that a framed gestalt of framed demarcated particular formulas of length t = n + 1 is used. The effect of such use it to get a vectored gestalt formula of the shape Informatica 20 (1996) 331-358 339 
\= U\ . | = U2 . \= W3 . |= • • • Ui . | = 
• • • ^n-2 • \= w n-l • f= Wn . [ |= 
| = W l . | = U2 . | = W 3 . | = • • •Ui. \= 
' • • ^n-2 • | = <*>„_1 • (= 
U3.\=---Ui..\= 
•••W„_2 . • Un-l \= . Un \= 
a 	/? 
\= Ui . (= U2 . . u3 f = • • • .Ui 
\= ••••	 W„_ 2 
\=Ui. . u2 \= . uz f= • • •.Ui 
.u n-2 | = -^n-1 (= 
(= . U\ |= . U2 \= (u/3 ( = • • • .Ui 
|= • • ••W„-2 |= .W„_i |= 
The frame between operands a and (3 is an ope­rator frame replacing now, after a gestalt-like de­composition, the general informational operator |= in transition a\= /3. The main operator frame of the transition is a parallel frame of n + 1 serial operator frames constituting the parallel-serial ca­nonic operator decomposition of the original ope­rator |= in a \= /3. As we see, the demarcated style of formula writing brings the advantage of a compact complex informational operator expres­sion. 
Instead of the parenthesized, canonic transi­tion-operand gestalt r^Tjg, in which operands a and (3 are included, the canonic transition-operator gestalt (in demarcated form), T^ " is a parallel array of demarcated decomposed ope­
caii — • 
rator frames, </>, ' , i = 1,2, • • •, n + 1. Thus, a decompositionally complex structure of the sim­plest transition has the form 
/ 	j. cann,l \ 
Acann,2 
(a\=P) a 	P 
^»n.n+ 1 
J 
where 

340 Informatica 20 (1996) 331-358 	A.P. Železnikar 
can 
1
n 2 n 
a 	a (j),•h-' P; 
, cann,n+l r, 
\ 

That what is possible in čase of using demarcation points, that is, 
a rL" /3 

instead of parenthesis pairs would never be pos­sible in such a compact and clear form. For in­stance, we can have r^p l where operands a and P appear implicitly. But certainly, a rv n / 3 ?=* 
pcann 
5.6	 TheMeaning of Operator Composition \= o |= and Decomposition in Čase of the Canonic Serial Decomposition of Informational Transition a \= (3 
How could the operator composition of the form 
a \=a o \=p P 

concern the canonic serial operator decomposition of types r"ijg and T T'"? Could it, in comparison of both cases, come to an informationally meaning equivalence? 
Let us introduce the rule by which operator (= can be replaced by the composition j= o |= or, for­mally, 
This rule will be used at the places of the framed (main) operator |=, that is, An operator-
H 

framed plače will represent the plače of the com­position operator o, so, the formula part on the left of it will be something marked as |=Q and the formula part on the right of it will be something marked as \=p, when proceeding from the transi­tional čase a\= (3. There is 
(a (=<* ° \=p P) 
( 
W3) (=	 • • ' "i) \=

(((•••(•••((( "n,l 
• • • W„_2) |= 

Wn-l )	 \= Wn) (= 
, cann,l *)|=o 
can« i J 
1 ]<Pnt=f I—IT, ' 
r0\=( 
f=Wl) |=W2) 1= 
W3) |=	 • • • W*) N 

((•••(•••(( ( 
•••W n _ 2 ) 
|= Wn_i) |= 
Acann,2 
*>l=o 
|= (Wn	 N ,ca„n,2 /? ) 
'n,2! 
'*oH L 

0»»°».» a|N:^i) 1= 
' N 
(= (^2	 (= (w3 
• • • (W i ( = • • • / 3 )))•••)•••) ) 
(wn_i	 |= (LJ„ 
'• H 

I j canji,n+l F , can n,n+l 
P)\=o 
\= (wi	 |= (w2 |= 
(w 3 | = • • • (Wj 
h 
/3 )))•••)•••))) cann,n+l
• • • K-2 N 
K-l	 N (w„
N , can ra,n+ l 

To obtain the transparency of the last parenthe­sized formula, we can use the frame subscripts in the last formula, <*™> * and ffig*. where, 
can„ ; 

for example, -K, ' marks n + 1 — i consecutive 
symbols '(', n\ " J marks j — 1 consecutive sym­
can„ t, 

bols ')', </\i_0 ' marks the fc-corresponding opera­tor frame on the left of composition operator 'o' 
can„ iu 

and 0OL_/' marks the fc-corresponding operator frame on the right of operator 'o'. Thus, for a compact presentation of the last formula we have 
INFORMATIONAL TRANSITION... Informatica 20 (1996) 331-358 341 
(a K »N^ 
nn,l "71,1 n,l 1171,1. 
/V 
; 71,1 i /t, l n 
( K 
can n, 2 /—"n,2 n. i i—n,Ln,2 n _ "n,2. 

717 a
 ^)|=o 0<?oKK  P n­
"n,7i 
"Kt « 0)|=o °?o|=( P *) 
"n.n+ l 3Tl,Tl+ l , CanTl,7J + l n,n+ l 
a </>• ) M 0(t>oH P *) J
\ \ 
One can introduce the parenthesis-canonic gestalt of the left parenthesis frames, for example, 
np« 
where the replacement for the right-left or the left-right enumeration is 
or 
respectively. Similarly, for the right parenthesis frames there is 
"n, l 
K\ 
»n,2 
7t\ 
np 
7T\ "n.n+ l 
7T­
with the replacement concerning the right-left or the left-right enumeration 
n 
"71, 1 
nn,2 n 1
7T\ or iP) 
' ) can n,n+ l )
7T ) 
D 
respectively. In this way, the gestalt of the par­tial, main-operator composed, parenthesized left operator frame is 
can« i
l 71,1 
cann -^ 
C"'2 
)N ^ 
^o' B+ 1 
The gestalt of the partial, main-operator compo­sed, parenthesized right operator frame is 
1 
2 
T"* "7 1 _ A 
, can 7 i 71+1 
The framed components can be recognized from the general parenthesized formula a \=a o \=p /?. This formula is a concatenation of the discussed parenthesis frames, main-operator composed left and right operator frames and the addressed in­formational operands a and (5 in the form 
( a K °\=pP)^ 
(n p a r p o r;j^ p np ) 
Because of the parenthesis form of basic formu­las, the last gestalt formula is split in several segments, which are the left parenthesis gestalt, operand a, the left operator gestalt, operator 'o', the right operator gestalt, operand /3, and the ri­ght parenthesis gestalt. 
To obtain a more compact expression of the for­mula where the left and the right operational fra­mes are not split and can be, finally, also regularly vectored (in an operator-gestalt manner), we can use the demarcated style of formula notation, that is, 

a K* ° f=/3P- ^ • 
(= Wl • h to>2 f= w3. 

a (=•• • U!{. N • • W„_2 . 
*o|=. 
\=0Jn -1 • \=UJn.\= 
, cann,l 
\=Ul. 	hU2 N 
^3 - |= •Wi •H 
P.w n	 (= cin„ 2 p ; 

a. •••un. -2 • •^n-l 
'*o|=. 
h 
• \= 
• No 
N ^2	 |= ^3 |= 

a (=wi.|= 
,cann•Ui P •••N /?; .wr-i h wn f= 
n 
'»K 
N o>i 	H H• W3 
.U>2 

a p 	, can n,n+: T h u>i N-W n -2 
P.|=o 
N ^ n -1 N-w„N , can n,n+ l 

The outmost frame is nothing else than the ope­rand staying on the right of the operator of me­aning, ==\ Formula is written in the consequent demarcated form where semicolons perform as se­paration markers between parallel formulas. 
To get an extremely compact expression of this formula, one can contract the occurring operator frames into two operator gestalts on the left and the right side of the composition symbol 'o', mar­ked by r*u " and rX" , respectively. Evidently, 
can can
can7i
rn _^ r „ rn 

where 
, can n, l 
iT?'1 
>2cf>Zn
can 	can

p n	 _>. rn _^ 
j. cann." 
<t>Zn'n+l 

and for the informational transition of the form Oi \=a ° p/3 P, finally, one obtains 
A.P. Zeleznikar 
, can n, 2 
«T>2 
O
a 	P 
, can n, n 
j. cann," 
^n,n+l , ca"n,n+l 

In the last formula, there must be a strict corre­spondence between the elements of the enframed left and right operator gestalt in respect of the superscript z, where 
|= Ul . j = U)2 (= . • • • Uln-i • | = ^n+l-i (= 
j 

/ca "n, t	 _^ 
F • ^n+2-t P • ^>n+3-i ' ' P • ^Vi-1 (= • w n |= ) 
i = 1,2,- • • , n + 1 
and uij for j < O and j > n does not exist. 
The symbolism concerning canonically decom­posed gestalts and their formulas for transitional cases a\= P and a \=a o \=@ /? is shown in Table 1. 
5.7	 Noncanonic Serial Decomposition of a |= p, that is, n+jA"n(a |= P) 
Both canonic and noncanonic serial decomposi­tions constitute the realm of ali possible serial decompositions of transition a \= /3. As one has learned, there are exactly ;^>(2 7 ^" 1 2) possible de­compositions of one and the same decomposition components a>i, • • •, un, that is, of length n + 1. 
Noncanonic decompositions are exactly those which are not canonic, that is, 
'2n + 2^ 
(n + 1) n + 2 U + l 

of them. 
Let us introduce the general transparent scheme © of the noncanonic serial decomposition, marked by n+qA™"(a \= /3), in the form 
6 (^A: > M)) ^ 
a U1UI2U/3 • • • OJj-iUj | Ui+iU/j+2 • • • U)n-2Wn-lUnP 
INFORMATIONAL TRANSITION... Informatica 20 (1996) 331-358 343 
Canonic Gestalts for (a \= /3)­Decomposition  Gestalt Formulas: * = l,2,---, n + l  Canonic Gestalts for (a \=a o \=p p)­Decomposition  Gestalt Formulas: i = l,2,---, n + l  
can n, i  p can n 1 a|=ot=/3  
p can n La.jF.P  can n, i  cann la.\=o\=./3  can n, i ^a.|=o|=./ 3  
TT(  a^)|= (  nparpo  ?r(  a«^»)No  o  
p n;an "  rt/ D  can „ „•  *»•) *  r can n  /D TTcann  , ca"n,i  a  cann,i  
a T^  p  can ^ ^  «r; p o r;a^ p  can „  „•  can-. ,- n  

Table 1: A systematic overvieui of possibilities (and possible markers) of the serially decomposed parenthesized and demarcated gestalts and framed formulas belonging to the informational transition a \= P, uihere there are n decomposing operands, that is, transition-interior informational components (jj\, L02, • • •, uin. A gestalt Y™n is a parallel system of n formulas consisting of different frames <j>... n'1 and operands a and p. 
where the characteristic schemes of the pure ob­serving^ structured informer part and the pure informingly structured observer part noncanonic decompositions are 
e(n+tAZ\a^pj)^ 
aUiU)2U)3 • • • Ui-iUiUi+iUi+2 • • • UJn-2^n-l^n \ P', 
e(nf2An:n(<x^p))^ 
a | UJlLU2U>3 • • • LOi-iUiUi+lLJi+2 • • • UJn-2^n-l^nP 
where 
2n + 2' 
n + 2 <q,q1,q2 < 
n + 2\n + \ 
Each underline marks one parenthesis pair at its ends, symbol '|' marks the main operator ((=* or 
|= ) of decomposition, and between two ope­rands (e.g., concatenation ujiUi+i) an operator (= appears, according to the underlined formula se­gments. 
What could the last example (subscript q) of noncanonic decomposition represent? If one considers that the decomposition components wl, • • • ,o;i belong to the informer entity a, the last component, a>j, is the final observer of the in­forming on the way from a (the topic informer) to u>i itself, so, it can decide upon that which will be mediated to the topic observer./?. In this respect, u>i functions as a decisive output filter or a cen­sor of that what a informs. On the other hand, the decomposition components Ui+i,- •• ,un can be understood as belonging to the observing en­tity P where w;+i functions as a decisive input fil­ter or a censor of that what will be informed thro­ugh the informing chain from un+i to /3. While in the informer part (a, o>i, • • •, u>n) the censor­ship functions observinglv, in the observing part of the decomposition (un+i, •'• • ,un, P) the censor­ship functions informingly. 
A serial decomposition is noncanonic if and only if its informer part is not purely informer-canonic and its observer part is not purely observer-canonic. 
Some of the noncanonic decompositions deserve a particular attention because they can be gra­sped as characteristic cases which can be inter­preted by some conventional notions of informing like conscious, informer and observer controlled, intelligent and, first of ali, senseful and causalh/ structured informing of entities. 
The next example of a noncanonic decomposi­tion illustrates an arbitrarily structured formula where the informer as well as the observer part of decomposition explicate embedded informer and observer structures. In this way 

a | U)iUJ2_U3 • • • Uj-lUj Uj+iUJi+2 • • • U)n-2UJn-l Un(3 
is one of the possible diverse decompositions where informer and observer views are hiddenly present in the informer and observer part of the decomposition. 
5.8	 A Parallel Decomposition of a\=p, that is, n+1 A„(a|=/3 ) 
How can a transition a |= /3 be decomposed in a parallel way and what does such a decomposition represent? In which way does it differ substanti­ally from a serial decomposition? 
As one can grasp, informational parallelism conceals some very complex serialism which is again nothing else than a parallelism of serialism. That which is significant for one's comprehension roots in the simplest possible parallelism, that is not in a parallelism of long serial decompositions but in the shortest ones. So, which is the shortest (simplest) part of a decomposition? The answer is: the basic possible transition from one operand to the other. The study of a parallel decomposi­tion system of such basic transitions is the topic of this subsection. 
Thus, let us introduce the basic parallel decom­position of informational transition in the form 
(a\=ux\ \ 
n+X(«M) 
Wn-1	 |= un', 
\"n \= P J 

What does this decomposition represent? 
Informational system n+1 A|| (o ; (= /3) can be in­terpreted in the following ways: 
1.
 n+1A..(a (= /3) is a parallel system of con­sequently followed, the most basic transiti­ons, between the initial informer operand a and the final observer operand /3; 

2.
 n+1A..(a \= /3) represents the serial cau­sal chain (decomposition) of consequently followed operands a,u\, • • • ,un,0, and ali 


A.P. Zeleznikar 
from this decomposition derived decomposi­tions belong to the gestalt r^A^ a |= (3)), where the number of serial decompositions of length n + liss i5 (2 n n +2 );an d 

3. n+1 A|| ( a |=/3) is the formal counterpart (equivalent) of the informational graph <3 (Fig. 1), by which ali decompositi­ons belonging to the informational gestalt r(n+1 A„( a |= /3)) are determined. 
5.9	 A Circular Serial Decomposition ofa^a , that is , n+lA°(a |= /?) 
What does happen if the graph in Fig. 1 is circu­larly closed according to Fig. 2? Which are the possible interpretations of the graph? 
Figure 2: A simple graphical interpretation of the circular transition a \= a divided into the infor­mer part (a), seriallv decomposed internal part with informational structure of u\, u>2, • • •, u>n, and the observer part ivhich is a itself. This graphical scheme represents the simplest gestalt of a \= a, that is, ali possible serial parenthesized or demarcated forms of the length i = n + 1. 
Formalh/, there is not a substantial difference be­tween transitions a |= /3 and a \= a and, for the circular čase, where P was replaced by a, operand a becomes the informer and, simultaneously, the observer of itself. The o;-structure can be under­stood both to be its interior or interior informa­tional structure or even a mixed interior-exterior structure. 
INFORMATIONAL TRANSITION... 
For us, the circular interior structure is si­gnificant in the so-called metaphvsicalistic čase. Further, if an u is an interior structure, the prin­ciples of informational Being-in [9] hold, so, 
CJl,W2 , , U>n C a 
Further, we must not forget the separation pos­sibilities between the informing and the informed part of a. In the circular čase, there is, 
where the operator composition operator 'o' is a unique separator between the informing and the observing part of a. This informer-observer dis­tinction becomes extremely significant in the me­taphvsicalistic čase when, for instance, informa­tion produced by counterinforming of an intelli­gent entitv a has to be informationallv embedded, that is, observed and connected to the existing informational body of entity a. Thus, a circular informational structure is not only a trivial, non­sense, or an abstract entity: it has its own func­tion of informational production and evaluation in the sense of spontaneous and circular informa­tional arising, that is, changing, generating and amplifying the informational change. 
In circular informational structures, the pro­blem of the informing and the observing part wi­thin a cyclically informing entity come to the su­rface. This problem is significant at the concep­tualization (structure, design) of a circular infor­mational entitv. In principle, each entity informs also cyclically, for instance, preserving its form and content and changing it in an arisingb/ spon­taneous an circular way. This principle belongs to the basic axioms of informing of entities (see, for example, [6, 8]). 
Let us proceed from the operand frame of the gestalt r"^ , that is, of a circularly decomposed informational transition 
(n+2-i)-th 
(•••(ah"i ) K" ) h (.Un+2-i \= ••• 
n+1 —i 
|=(w„ (=«)•••) 
t-1 
» = l,2,--., n + l 
Informatica 20 (1996) 331-358 345 
6 Un-l 
Figure 3: Another graphical interpretation of the circular transition a \= a, which is divided into the informer part (a), serially decomposed inter­nat part with informational structure of oj\, ui, • • -, iun, and the observer part uihich is a it­self in the decomposed path and, ivith the non-decomposed backward path. 
The framed operator, |= , is at the {n + 2 — i) th position of the framed formula and represents the so-called main formula operator, at the plače where formula is split into the left informing part (informer a) and the right observing part (obser­ver a). But, the framed operator, can be 
h 
further split and, according to Table 1 (and the previous discussion), there is, 
can n, i , can n, i , ca "n, i a can n, i 7T( M )N o °(poH ' /?7T) 
i = 1,2,- • • , n + 1 
ca ic!lnni
•»ni ;canni
0\=(' an< l
where partia l irames ir, ' , <p\v-0' , 4> 
can „ ,* 
7Ts ' can be easily identified from the previous discussion. Thus, the separated informing and ob­serving parts of circularly decomposed transition a (= a are 
n+l-i (n+2-i)-th 
((•••(a|=wi ) |= •••) t=un+i-i) h ; 
|= (uJn+2-i \= • • • \= K-i \= (wn \= a)-- •)); 
i = l,2,---, n + l 
Another, slightly modified graphical presentation in Fig. 3, following from Fig. 1 and Fig. 2, offers 

346 Informatica 20 (1996) 331-358 	A.P. Zeleznikar 
U). •(w n-i\ 

a —{^3 	J u 
Figure 4: The circular informational graph corresponding the graphical interpretation in Fig. 3. In an informational graph, the one and the same operand must appear only once (concerns a). 
an essential interpretation, namely, the paralle­lism of the w-decomposed path and the backvvard non-decomposed path a (= a. It does not repre­sent the so-called informational graph in which each operand must appear only once. The cor­rect informational graph is shown in Fig. 4. The formal parallel presentation of this graph is the formula system 
a (= a; 
un \=Un--i; w„_i |= w„; un (= a 

using, entirely, the basic transitions only (from one operand to the other, or the same). 
5.10	 A Circular Forward and Back­vvard Serial Decomposition of Informational Transition 
The problem of the circular forward and back­ward serial decomposition emerges in cases of the so-called metaphysicalistic informing when enti­ties inform in an intelligent way and the question of the informing and the observing parts of enti­ties becomes significant. In this situation, we have a general scheme of informing as shown in Fig. 5. Before we begin to discuss the circular and the re­versely circular form of informational transition, let us construct Table 1 in which, in a surveying way, the operand and operator gestalts of diffe­rent sorts, as the result of serial decomposition, are listed. In this table, the parenthesis gestalt 
n+l li-l

pairs of the form <f>, an d </)•.are replaced 
Ci 
and 7r. 

by systematically marked pairs ir, 
where -K. for 

((•••( and 7r ') n+l­/ = 1.2 . n + l. 
un-\ <>• 
* OJn-l
CJ2 9 * 

Figure 5: A graphical interpretation of the for­ward and backward circular transition a \= a, representing a parallel sijstem of a forivard and backivard loop, being appropriate for an intelli­gent entity (e.g. fortvard and backuiard anahjsis and informational synthesis). 
5.11	 A Circular Parallel Decompo­sition of a |= a, that is, 
n+1Aj>(a h a) 

There is not an essential difference between paral­lel and circular parallel decomposition in respect to the formal informational scheme 
"+1A«(« t=a)^ 

But, the essential difference occurs in the follo­wing: 
1. n+1A^(a \= P) is a circular parallel system of 
INFORMATIONAL TRANSITION...	 Informatica 20 (1996) 331-358 347 
;Q*—jQr—^2)^=^3)1^::: r^)r^::: r^n^—^^f —;Q : 
Figure 6: The bicircular informational graph corresponding to the graphical interpretation in Fig. 5. 
In an informational graph, the one and the same operand must appear only once (concerns a, u\, • • • 

, <JJn). 
consequently followed, the most basic transi­tions, between the initial informer operand a and the final observer operand, which is the same a; 
2.
 n+lA^(a \= /3) represents the circular (se­dal) causal chain (decomposition) of con­sequently, in a circle followed operands a,u\,- • • ,un, and ali from this decomposi­tion derived decompositions belong to the circular gestalt T( n+1 A^( a f= /3)), where the 

number of decompositions is ^ 5 („+i)> an(^ 

3.	
 n+1A^(a (= /?) is the formal counterpart (equivalent) of the circular informational graph (S (Fig. 2), by which ali decomposi­tions belonging to the informational gestalt F(n+1A<~>(a \= j3)) are determined. 


5.12	 Standardized Metaphysicalistic Serial Decompositio n of a |= a, that is, l<m°(a \= a) 
5.12.1	 Introduction 
Metaphysicalism means circular informing origi­nating in the initial transition a \= a and its metaphysicalistic decomposition which, to some extent, was standardized [6] in a reductionistic manner. In this Subsection, our attention will concentrate on parenthesized, demarcated, nor­mal and reverse cyclic, operator-compositional ca­nonic and noncanonic metaphysicalistic informa­tional decompositions and the corresponding ge­stalts. As we see, there is a couple of metaphysica­listic gestalts of a decomposed entity a which can be investigated from the standard metaphysicali­stically generalized and reasonably reductionistic point of view considering the variety of possible decompositions and gestalts. 
5.12.2	 Generalized Metaphysicalistic Decomposition of an Informational Entity 
Let a represent an informational entity concer­ning something /?. Let this entity be metaphysi­cally decomposed in its serially connected but also in its parallel informing components: 
—	 informing components (superscript i) 
«i,«2> ---,<*j 
—	 counterinforming components (superscript c) 
«D«2»---,Oi.
p 
and 
informationally embedding components (su­perscript e) 
<*i,a2, ,a„ 
Besides, some circular forms of informing of invol­ved metaphysicalistic components, including en­tity a, occur, thus obligatory, different loops exist regarding the metaphysicalistic components. Let this situation be concretized by the informational graph in Fig. 7. As a standardized (artificialb/ constructed) situation, three substantial groups of an entity's metaphysicalism exist: intentional in­forming ensures the preservation (physical, men­tal, informational character) of the entity; coun­terinforming represents the emerging and essen­tially changing possibilities and character of en­tity's informing intention, so that the character of the entity can emerge and change as a con­sequence of the exterior and interior impacts con­cerning the entity; informational embedding is a sort of final acceptance and conflrmation of the emerged and changed possibilities and state of the entity's character. 

a's intentional informing 
a. 	a2h—(«! a's counterinforming 
ai)—\a2 	a„ 

o;'s informational embedding Figure 7: A generalized metaphysicalism of en­
tity  a  with  interior  informing,  counterinforming  
and  informational  embedding, concerning  some­ 
thing /3.  

Another comment of Fig. 7 concerns the lo­ops of the informational graph. Six basic lo­ops are recognized, however, this does not mean that in a concrete čase additional loops between metaphysicalistic components can be introduced. The following principle seems reasonable: 
Principle	 of Metaphysicalism of Metaphysicalism. 
Components of a metaphysicalistic entity are, in principle, metaphysicalistic entities. Such a de­termination causes an endless fractalness of me­taphysicalism (metaphysicalistic fractalism). • . 
Let us study some basic properties of the graph in Fig. 7. 
5.12.3	 Reductionistic Basic Meta­physicalistic Model of an Informational Entity 
Let us begin with the basic (most primitive) čase, where the metaphysicalistic decompositional com­ponents of operand a within transition a j= a are 
JQ J IQ I *^Q;J CQ ) ^a i *•& 

called 
1.	 (intentional or entity's characteristic) infor­ming, 
A.P. Zeleznikar 

2.	
 intention of the entity (its instantaneously arising character, concept, definition), 

3.	
 counterinforming (opposing, synonymous, antonymous, questioning intentional infor­ming), 

4.	
 counterinformational entity (informational opposition, synonyms, antonyms, questions requiring answers as consequences of the in­tention), 

5.	
 embedding (the process of the connection of new information arisen by counterinforming, e.g., in the form of answering), and 

6.	
 embedding entity (information) by which new products are regularly connected with the existing informational body of the entity, 


respectively. These operands come at the places of the decomposition components ui\, u>2, ct>3, u^, W5, and U>Q, in this order, so, n = 6 and the num­ber of formulas in the canonic gestalt concerning solely the topic circular entity a is 7, in nonca­nonic gestalt 422, and altogether 429. The same number of formulas appear in gestalts belonging to the remaining six circular (metaphysicalistic) operands (components). 
5.12.4	 Canonic Metaphysicalistic (Reductionistic) Gestalts 
Let us construct the canonic (informer-observer regular) gestalts according to Table 1 on one side and, then, in the next Subsubsection, sketch the structure of and determine the number of the re­maining noncanonic gestalts. 
There are the following cases of the redu­ced (standardized) canonic metaphysicalistic (the front superscript 'met') gestalts: 
—
 metaphysicalistic, parenthesized reductioni­stic canonic gestalt (PRCG for short) me TT^; 

— 
metaphysicalistic, demarcated	 reductionistic canonic gestalt (DRCG) metp^an6 ^. 

—
 metaphysicalistic, parenthesized, operator-


composed reductionistic canonic gestalt (POCRCG) CPoN,; «"«! 

-	 metaphysicalistic, demarcated, operator-composed reductionistic canonic gestalt 
^cang 
(DOCRCG ) T, b 
a.f=o)=.Q 
INFORMATIONAL TRANSITION... 
The PNCG consists of canonic formulas only and the number of formulas in a PNCG depends on the length L being equal to the number of binary operators in a canonic formula of PRCG. In a standard metaphysical čase this number is always t = n + 1 = 7. Thus, 
met._canf j 
/((((((« \=la)\=ia)\= ON \ 
Ca) \= CQ) \= ta) \= a; 
(((((a h J«) N i«) N CQ) N 
Ca) |= Ča) 1= (ea |= «) ; 
((((« h 3a) h ta) N Ca) N 
Ca) |= (Ca N (ea (= ")); 
(((« H 3a) h U) t= Ca) |= 
(ca |= (^ N (eQ N «))); 
((« |= 3a) N ia) 1= (Ca \= 
(Ca N (C a N (e a N «)))) ; 
(a |= 3a) (= (ia (= (Ca N 
(Ca H (C a H (e a H «))))) ; 
a H P a H ( ^ N (Ca \= 
V (CQ h (Ca \= (eQ |= <*))))))/ 
The structure philosophy of this gestalt can be 
1 5 
OL «Jq l a ^"a Ca *~q ^ot \ OL O- ~*a ' a | *~a Ca ^ a Cg C* 
2 T • rt* /Č l 6 T I • rt1 /C Q? J g ^a ^ g Cg V^g | Cg Of OL Jg | I g C g Cg V^g Kg Qf 
3 7 i Of J a I g ^ g Cg V^g Cg O O; J a I g L-g Cg C g Cg OL 
OL *JQL I g ^ a Cg ^ g Cg Q? 
Figure 8: A schematic presentation of the seven metaphvsicalistic reductionistic canonic gestalts of different forms, that is, """T^ , ^'T^^ , 
me XT6 oNQ , and meXT|L|=.g- Symbol '\' marks the plače of the main operator and a line marks a subformula ivhich is inside of a parenthesis pair. 
understood by means of Fig. 8 which represents the specific (canonic) arrangement of parenthesis pairs within a metaphysicalistic 'Vmula of length 
Informatica 20 (1996) 331-358 349 

l — l. The reader can see that the so-called cano­nic formulas are nothing else than a strict conside­ration of a systematic informer-observer principle which is consequently sequential from the view of the informer and the view of the observer infor­ming on the left and on the right side of the main operator |=*. Sketches 1, • • •, 7 in Fig. 8 show this regular (canonic) principle in a transparent and instructive manner. 
Another comment to the sketches in Fig. 8 con­cerns the recognition process when the informer appears in the scope of the observer, that is, when it is gradualh/ recognized into more and more de­tails by the observer. This process can be under­stood as the shifting from the initial, informer-governed situation when the observing entity j ust senses the informer and becomes aware of its pre­sence (sketch 1 in Fig. 8). But, that what is initi­ally hidden in the informing of the informer, pro­gressively transits to the observer site building up the recognition of the informer by the observer and, in this way, shifting to the transitions sket­ched and marked by 2 to 7. 
The sketch 7 in Fig. 8 demonstrates the situa­tion in which the observer a observes metaphysi­cally ali its inner components, that is, 3 a , i a , Ca, Cg, ČQ, and eQ. The reader can comprehend how the čase 1 is important for the informer's point of view where information about the components is mediated to the observer site. In the čase 7, the observers point of view comes to the surface when the inner components have already become a part of the observing entity a. Of course, both situati­ons can have a permanent importance during the metaphysical cyclic informing, so they can coexist equally, together with other possibilities. 
The next gestalt form corresponding to the pa­renthesized metaphysicalistic gestalt is the' de­marcated one (DRCG) and we show it exclusively for the sake of the completeness of the metaphysi­calistic čase of informational transition. Thus, 
a.|=. a " /aF=ja.|=i«-l=e«-l= \ 
ca. f= cQ • \= ta Q
•l= . 
&	 F" *-*a • F" ^a • F1 ^~a • H CQ • f= L a • H -Ca | = " i 
Cn \= 3 Q• F : t a • F1 *"<* • h Ca •H-*~a F1 " ^a F ^i 
L* p1 J Q • r3 * a • F 1 *-a • K Ca f= • l~Q (= '^ a (=a ; 
a |= 3a |= ia • K <-a F1 " Ca — • ^-a F1 • Ca |=a ; 
« (= 3a •f= . ta > F1 " ^a F1 " Ca = • ^a |= . ea |= a ; 
a 
• h-•Ja F1 • t a F1 • ^~a F1 • 
\ ca |= . LQ f= . ea |= « / 

The parenthesized, operator-composed reductio­nistic canonic gestalt (POCRCG) for the reductio­nistic metaphysicalistic čase is 
af=o|=:a ' 
/((((((« h 2>a) | = ta ) H <^a) 1= Ca) 

N<sQ)Nca) N° h a; 
(((((a	 | = Of«) h= ia ) h Ca ) H Ca) 
h ^ ) h° h (ca(=a); ((((« |= 3 a ) (= iQ) f= C«,) |= Ca) |=o|= (eQ ^(ea h«)) ; (((«(=aa)Nia)NCa) H h 
(Ca | = (C a | = (Ca (= <*))); 
((aH^a)Nia) N°N 
(CQ \= (Ca (= (C a | = (ea 1= «)))); (a|=0fa ) f=o(= (iQ |= (C a | = (Ca H (C a h (Ca | = a))))); 
a H°H P«l=(ia|= 
V (C a \= (Ca |= (C a N (Ca H a))))))/ 
A.P. Zeleznikar 

Finally, we can write down the demarcated, operator-composed canonic gestalt (DOCCG) in the form 
met_canf j 
a.j=o|=. a "' 

/ a (=3Q . |=i a . |= Ca . (= ca \ 
. |= <Sa. |=e Q . F=° N 
a: 
C^ F 1 *^a • F1 ^a • F1 ^"a • F1 CQ 
|= CQ . |=o(= . ea F=a! 
^ F1 a » r^ *a • F 1 *~a • p1 Ca . [=o|= . ea \= .eQ (= a; 
a |= a«.. f= i a . |= Ca . |= o f= 
Ca |= • Ca f= • Ca |= «; 
a \= 3a.	 (= i0 
Hh 
La F1 • CQ F1 • *~a F " ^ F ^i 
a (= . aa	 . |= o (= . ia (= 
(-a F1 ' Ca F1 • »-a F ' ^a P '"i 
a t=°l= • ^a (= -i« H • \ *-a F1 • Ca F1 • ^ a F1 • Ca F 1 ^ / 

Evidently, there exist many other metaphysicali­stic formulas of length L = 7 which can become senseful in a particular situation. The canoni­cal concept follows a strict (systematic) sequen­tial 'propagation' of parenthesis pairs from the left side for the informer point of view and from the right side for the observer point of view, simul­taneously. Between these points of view lies the main (informer-observer-separating) operator. 
5.12.5	 Gestalts and Schemes Belonging to the Partial Decomposition of Canonic Metaphysicalistic Formulas 
Partial decomposition of a canonic formula of any length means that the main operator retains its position, and only the left and the right part of the formula can be decomposed arbitrarily. In this manner, the number of the obtained formulas for a canonic formula is equal to the product of numbers of formulas proceeding from the left and the right part of the original canonic formula. 
Noncanonic metaphysical gestalts can be, simi­larly as canonic ones, marked in the following way: INFORMATIONAL TRANSITION... 
—	
 parenthesized normal noncanonic (super­script 'non') gestalt (PNNCG) metT™l^; 

—	
 demarcated normal noncanonic gestalt 


/ x met_none 
(DNNCGJ r L :
v ' a. p. a' 
—	
 parenthesized, operator-composed nonca­nonic gestalt (POCNCG) ""C^ ; and 

—	
 demarcated, operator-composed noncanonic gestalt (DOCNNG) TQ ^ o(=a . 


Let us show systematically which canonic and noncanonic formulas follow by decomposition from each canonic formula according to Fig. 8 and Table 2. 
1 .	 Possible noncanonic decompositions of the first metaphysicalistic canonic formula 
Let us analyze systematically the first canonic for­mula in respect to ali possible canonic and non­canonic formulas which can be derived according to the scheme superscribed by 1 in Fig. 8. In this way, the causal analysis answers the question of ali possibilities concerning the pure metaphysica­listic informer situation, presented by formula 
u\=3a) |= i«) h O 1= c«) h Č«) |= eQ) 
\= 	a 
The position of the main operator remains pre­served and the subformula 
(((((« h 3« ) 1= ia ) N Ca ) \= Ca) (= <La) \= *« 
with exception of its own parenthesis configura­tion, which is embedded in the original formula, has to be presented by ali possible other configu­rations. This means that the original scheme 
1/ 1 
Qf Jot ^ a ^ a C a *~a Cq | ^L 
has to be varied, keeping the informer principle, where ali decomposition content is within the in­former part of the decomposition of a \= a. Thus, according to Table 2, the informational schemata of noncanonic decompositions are 
1/ 2 Q^ J g ^ a *~a Cq ^~g CQ 
a 
1/ 3 OZ Jg l a *~a C a w t Cq OL 
1 / 132 
OL J a. I a *~g Za ^ a Cq \ OL 
Informatica 20 (1996) 331-358 351 
In these schemes, various possible causal situati­ons of the so-called pure-informingly structured metaphysicalism of entity a come to the surface. Let us introduce the general gestalt marker 
%^r(»+;ijah/5)) 
 me
What does the formula T5 , \= a mean at ali? Evidently, the previous discussion of the de­composition, regarding the first metaphysicalistic canonic formula, can be interpreted by the intro­duced formula, where 
rv^ >a ) ** • 
a\=3a)\= ia) \= Ca) \= Ca) \=\ ^~a) r ^ Caj a\=3a)\= i«) |= CQ) \= ca) \= (,^-a F L Q) I |= a 
a\=(3a\= (ia |= (Ca |= (c« |= 
VV (C« H e« P 	/ / 
where me T^, represents the union of the cano­
 me
nic gestalt r]T5 and the noncanonic gestalt 
met — non r -. . . 
^ a ^= a or, formally, 
a\= a ' a| = a 
' a\= a 
The number of different formula decompositions isI(1 5 2 )xHo ) =1 32,where O = l. 
2.	 Possible noncanonic decompositions of the second metaphysicalistic canonic formula 
One of the basic question is how many formulas can follow from the second metaphysicalistic ca­nonic formula when the position of the main ope­rator remains preserved. Evidentlv, in the form of the informational schemes, according to Fig. 8 and Table 2, 
2/ 1 
OL *) a l a ^-a C a *~g Cq OL 
2/ 2 
O-*)g Ig *~a Cq \~a t a OL 
2/42 
OL J(x l a *^a Cq \~g j Cq OL 

where formula schemes 2/2, 2/3, .. . , 2/42 are noncanonic. One can observe that the number of different formula decompositions is g (1 5°) x \ (^) = 42 (the product of the formula left and right part possibilities). 
3.	 Possible noncanonic decompositions of the third metaphvsicalistic canonic formula 
Evidentlv, in the form of the informational sche­mes, according to Fig. 8 and Table 2, for the third metaphvsicalistic canonic formula decomposition, there is 
3/ 1 Oi *J a * a *~GL ^ a j *~ct ^ a O­
3/ 2 
Ct *J Q *a ^ a ~a ^* a ~a Oi 
3/28 
(X J Q l a \~a Ca \~a ta Oi 

where formula schemes 3/2, 3/3, .. . , 3/28 are noncanonic. One can observe that the number of different formula decompositions is \ (4) x | (2) = 28 (the product of the formula left and right part possibilities). 
4.	 Possible noncanonic decompositions of the fourth metaphvsicalistic canonic formula 
Further, in the form of the informational schemes, according to Fig. 8 and Table 2, for the fourth metaphvsicalistic canonic formula decomposition, there is 
4/ 1 OL A)(X *•& V^c* I CQ : ^"OL ^ a ™ 
4/ 2 
Oi Jot >ot *~a I ^ot *~a *a Oi 
4/2 5 
Oi J & Ig L Q V(X L Q Z(X Oi 

where formula schemes 4/2, 4/3 , .. . , 4/25 are noncanonic. One can observe that the number of different formula decompositions is \ (jj) x | (3) = 
25. 
5.	 Possible noncanonic decompositions of the fifth metaphvsicalistic canonic formula 
The čase of the fifth metaphvsicalistic canonic for­mula is scheme-svmmetric to the čase 3. Thus, 
A.P. Zeleznikar 
5/ 1 
Oi *) ct ^<x *~a t-ct *~a °a O­
5/ 2 OL u cc IQ: *~a C-ct ^~ a * a Oi 
5/2 8 Oi J q I g v-g Ca \^a t a Oi 

where formula schemes 5/2, 5/3, .. . , 5/28 are noncanonic. One can observe that the number of different formula decompositions is 5 (2) x 5 (4) = 
28. 

6.	 Possible noncanonic decompositions of the sixth metaphvsicalistic canonic formula 
The čase of the sixth metaphvsicalistic canonic formula is scheme-svmmetric to the čase 2. Thus, 
6/ 1 
Oi A) & I I Q L Q CQ< L Q C Q Oi 
6/ 2 OL *)g I let W * C a *~-a %•& Oi 
6/4 2 
Oi *-*a *a ^*ot ~a ^-*a *cx Oi 

where formula schemes 6/2, 6/3, .. . , 6/42 are noncanonic. One can observe that the number of different formula decompositions is 5(1) x gC5) — 
42. 

7.	 Possible noncanonic decompositions of the seventh metaphvsicalistic canonic formula 
Let us analvze systematically the last canonic for­mula in respect to ali possible noncanonic formu­las which can be derived according to the scheme superscripted by 7 in Fig. 8. In this way, the causal analysis answers the question of ali possi­bilities concerning the pure metaphysicalistic ob­server situation, presented by formula 
\=a 
P a \= (i a 1= (C a h (< a (= (C a \= (ta \= <*)))))) 
The position of the main operator remains pre­served and the subformula 
3a |= (ta \= (C« (= (ca \= (C0 \= (ta))))) 

INFORMATIONAL TRANSITION... 	Informatica 20 (1996) 331-358 353 
with exception of its own parenthesis configura­tion, which is embedded in the original formula, has to be presented by ali possible other configu­rations. This means that the original scheme 
Ct *J (x IQ; ^ G »cfc »"Ct *tt " 

has to be varied, keeping the observer principle, where ali decomposition content is within the ob­server part of the decomposition of a \= a. Thus, according to Table 2, 
Oi | Ja la \~a CQ L a CQ OL 
OL I Ja \g	 <*a CQ *~a ? a ^ 
In these schemes, various possible causal situati­ons of the so-called pure-observingly structured metaphysicalism of entity a come to the surface. The number of different formula decompositions ^ Ho) >< Me2) = 132, where 0 = 1. 
5.12.6	 The Number of Ali Possible For­mulas in Metaphysicalistic and Sub-metaphysicalistic Gestalts 
The question, how many formulas can be derived from an informational formula of length L, is cer­tainly righteous. If we know this number we are able to conclude how many noncanonical formulas are possible. And we can expect that this number will rise with the length L of a formula. 
Let Ni represent the number of ali possible for­mulas of length L. An analysis of this čase where parenthesis pairs and their possible displacements within a formula perform as binary operator per­mutations [11] gives 
= _J_ (M\ = 2t(2e-l)---(l + 2) e L+l\L) L\ 
We get the short overview in Table 2. 
Standard metaphysicalistic formulas of length L = 6 represent shells which can be further ana­lyzed {L < 6) and filled with concrete, e.g. con­crete intelligent subformulas, so the length of a formula becomes L > 6. Under such circumstan­ces the number of other senseful possibilities can, according to the ^/iVrtable, rise extensively. 
L 1  Ne 1  • e 6  Ne 132  L 11  Nt 58 786  
2  2  7  429  12  208 012  
3  5  8  1 430  13  742 900  
4  14  9  4 862  14  2 674 440  
5  42  10  16 796  15  9 694 845  

Table 2: The dependence of the number of formu­las Ne on the length L (number of binaru opera­tors) of a formula. 
Because the number of canonic formulas of length L is N™" = L = n + 1, where n is the number of decomposed components in the transi­tion a \= a (or a \= P, in general), the number of noncanonic formulas of length L is 
iV;°n =NL-L 
Let in a formula, divided by the main operator into the left and the right part, mark by L\eft the length of the left part and by 4ight the right part of the formula, where L\e{t + 4ight = L — 1. Then, the number of possible decompositions when the position of the main operator remains preserved, is, evidently, 
1 MrfA x 1 f2Llisu\ ^left + 1 \ ^'eft / ^"ght + 1 V ^r'ght / 
After that, from the noncanonic decomposition of canonic formulas, for a formula of length L, with (°) = 1, immediately follows 
— (") -L+l\L)  
'  1  (2(L -k)\  1 (2(k  ­ 1)\  
Lr[L-k-hi\  i-k  J  k\  k-i  J  

Thus, for the debated metaphysicalistic čase, where l = 7, there is 429 = 132 + 42 + 28 + 25 + 28 + 42 + 132. 
5.12.7	 Canonic and Noncanonic Metaphysicalistic Gestalts 
The canonic metaphysicalistic gestalt presents ali possible pure informer-observer decompositions of the standardized metaphysicalistic structure a, 3a, iQ, Ca, c„, <La, and eQ. The number of ca­nonic formulas, within this structure, is 7 (equal to the number of metaphysicalistic components). 

The noncanonic metaphysicalistic gestalt uni­tes ali possible causal cases of the parenthetically structured standardized metaphysicalism of en­tity a. The number of noncanonic formulas, wi­thin this structure, is i(x 7 4) - 7 = 422. 
The presented discussion of standardized me­taphysicalism of an entity a did not consider other possible loops (with exception of the main loop) which can be introduced between the standard metaphysicalistic components. This, standardi­zed situation too, is presented by the informatio­nal graph in Fig. 9. 
5.13	 Th e Metaphysicalistic Parallel Decomposition of a (= a, that is, 
'"M^ia	 \= a) 

5.13.1	 The Generalized Čas e 
Any serial metaphysicalistic formula kf^.(a N a) belonging to the metaphysicalistic gestalt can be parallelized, that is U(m°-(p^(a j= a)). The re­sult is, according to Fig. 7, for the parallelization of the main (the longest) decomposition, 
n^+p+o+i^jV 1= «)) ­
(a \= ax\	 \ 
"i 1= OL2\ a2 \= a3; • • • ; aj_x (= a-; 
OLX [= a2; a2 \= a3; • • • ; ap_x |= ap; 
ap \= ax; 
« i N <*2; a2 (= a3; • • • ; aq_x \= aq; 
\aq\=a	 ) 

5.13.2	 The Reductionistic (Standardized) Metaphysicalistic Čase 
Virtually, the so-called standardized metaphysi­calistic čase is the minimal one, which appe­ars to be senseful in the context of informing, counterinforming, and informational embedding. These three components, each of them including the component of informing and informing en­tity, should guarantee the informational arising in a spontaneous and circular way, together with the topic(s) entity a. Thus, the parallelization of any metaphysicalistically decomposed formula of length 7 delivers the result in the form 
A.P. Zeleznikar 
fa\=3a; \ 
•Ja p 1 ^ai^ a i '-'a! 
>-a \= tai^a p^ »-a \La \= eQ;ea \= a J 

The graph corresponding to the right part of the last formula is presented in Fig. 9. 
a's intentional informing 
ca h-	,^-a 
a's counterinforming 
-H e, 
a's informational embedding 

Figure 9: A standardized (reductionistic) me­taphysicalism of entity a with basic interior in­forming, counterinforming and informational em­bedding, concerning something (3. 
The whole content of the graph in Fig. 9 must consider the externally impacting operand /3, that is, cft(/3), and the additional internal feedbacks. The most general symbolic solution for the graph in Fig. 9 upon a, in which ali of the possible me­taphysicalistic decompositions are included, is 
f/3\=a; \ a \= 3Q.; *Ja p 1 l« ! t « p^ *~a'i 
a?(0) 
^a p 1 Za\	 %a p ^ Oi] 
^a r1 -J«! Ca p 3 »~a> *a p^ »~ai \ Ca F3 J a i %a p 1 *~a / 

Solution a^(/3) describes the entirety of the graph in Fig. 9, and this informational system can be INFORMATIONAL TRANSITION... 
solved upon any other component of the system, with exception of the exterior component /3, in a particular or serial way, or in a universal or pa­rallel way. 
5.14	 A Straightforward Heteroge­neous Serial Decomposition of Informational Transition 
Let us introduce the complexity of informational decomposition of transition a j= /3 by the graph in Fig. 10. This figure is a modification of the model 
Figure 10: A graphical interpretation of the infor­mational transition a |= P divided into the infor­mer part (a with operator \=a), the channel part with its internal informational structure ofu)\, u>2, • • • , UJ\ for the acceptance of the exterior informa­tional disturbers 6\, 62, • • • , 6n, and the observer part (P with preceding operator \=p). In fact, this graphical scheme represents the so-called gestalt of a \= P, that is, ali possible serial parenthesized forms of the length L = n + 1. 
given by Fig. 1 in [1]. As one can see, at each 

internal component u%, u>2, • •• , wn, inner and/or around which other phenomena occur cycli­outer disturbing entities 61, 62, • • • , Sn come into cally as it is evident in the next subsection, game and can be differently metaphysically or in where the informational graph for a decision-some other way (linearlv, circularly) decomposed. 
making system is presented. 

In this sense, a more complex, fractal-like decomposition of the general transitional form 2. The second most visible phenomenon in po­a (= P is presented in Fig. 11, certainly, in its stcommunist svstems is corruption, marked most straightforward form. In this figure, each by the symbol c. Corruption is in the cen­component CCJ (i = 1, 2, • • • , n) is linearly decom­ter of some very specific processes, e.g., fi­posed, however, this does not mean that arbitrary nancial by-passing by firms and banks, bud-circular connections cannot exist. By this graph, get legalization of criminal-founded business, Informatica 20 (1996) 331-358 355 
the possibilities of the informational (causal, in­ner and outer impacting) complexity, which could come into existence, become conceptually and for­malistically evident. 
6 A Concept of th e Decision-
Making System Concerning 
th e Transition of a Social 
System 

Today, various forms of social transitions (also in capitalist systems [3]) are taking plače. One of the most characteristic one is that of proceeding from the communist to capitalist system, e.g. in the countries of Middle Europe and Eastern Europe. The question is which are the most remarkable phenomena and how could they be captured by informational means, that is, in forms of informa­tional formula systems. So, let us study, only in an initial way, the most remarkable terminology and basic informational processes, by the systems of informational transitions. 
6.1 Terminological Background 

At the beginning of the study, sufficiently pre­dse (remarkable) terminology is important, beca­use it constitutes the conceptual background for the development and decomposition of the cha­racteristically circular transitions and their com­plex (parallel, serial) linking within a system of social-transition phenomena. 
Let us introduce some basic informational enti­ties and their symbols (operands) and operational properties (operand-operator loops): 
1.	 First of the most remarkable phenomenon of new democracies is nationalism, marked by the symbol n. It represents the central point 

356 Informatica 20 (1996) 331-358 	A.P. Zeleznikar 
'ra-1 
ui,iii	 • 
0Ji,m-2 Vi,ni-1 ?- 9" ^i.rei—2 
Wj,3 
Oi.ni — 1 

Figure 11: A graphical interpretation of the composed informational transition a (= /3 divided into the informer part (a with operator \=a), the channel part with its internal informational structure of ui, U2, • • • , u\ for the acceptance of the exterior informational disturbers 8i, 62, • • • , 6n, and the observer part (P with preceding operator \=p)- In fact, this graphical scheme represent the so-called gestalt of a (= P, that is, ali possible serial parenthesized forms of the length l = n + 1. 
losses and bankruptcy, privatization, denati­onalization, defalcation, sanitation of banks, absence of legal legislation, etc. The informa­tional connections will be presented by the mentioned informational graph. 

3.	 The return of nationalized property is accom­panied with a sort of moratorium (restric­tion), m, called the moratorium concerning-the real-estate return to foreigners. 
4. Another kind of restriction, ti , is called the restriction of the real-estate return to citi­zens. 
5. The third form of restriction, t2, is called the restriction of investments coming from (par­ticular) foreign countries. 
6.	 The process of denationalization, D, happens between the most remarkable entities c (cor­ruption) and n (nationalism) when it is gover­ned (impacted) by c and governs (impacts) n. 
7.	 The government certainly has to improve the market functioning of some firms by the 
government (budget) subsidij of inefficient firms, Q. 
8.	
 On the other hand, the privatization of social firms, p, is taking plače, with the moratorium of reprivatization of foreigners' property. 

9.	
 This process is accompanied by the defalca­tion of social propertv, Z>2, because of badly (porously) elaborated legislation. 


10.	 To the most important financial phenomena belongs the improvement (sanitation) of do­mestic banks in debts and discounts, i. 
11.	
 One of the significant phenomena is the so-called partitocratic interesi, p2> through which, mainly, the corruption as a social pro­blem is being substantially impacted. 

12.	
 The partitocratic interest is fed by the in­dividual corruption within the ruling political 


INFORMATIONAL TRANSITION... 
parties, c2, impacting the partitocratic inte­rest, p2, and the government subsidy ofineffi­cient firms, g. 
The enumerated entities of the social transition are in no way the only relevant ones. They consti­tute an initial model of an inner-politics decision-making system for postcommunist countries. 
6.2 A Functional Model of the Syste m 
The listed entities can now be put into a circularly perplexed informational graph in Fig. 12. Within 
Figure 12: A graphical interpretation of an inner-politics decision-making system for a postcommu­nist strategy. 
this graph, by inspection, 16 mutually coupled lo­ops can be identified. As the reader can see, each entity is circularly impacted by the 11 remaining entities. Each loop can be structured in a particu­lar causal form (by occurring parenthesis pairs), or it may happen that even more than one parti­cular circular formula exists for a certain loop of the graph. In an extreme čase, the gestalt for a given circular formula can exist, that is, a parti­cular system of causal formulas can inform. On the other hand, the graph can be entirely descri­bed by the basic transition parallel circular (loop) system in the form 
Informatica 20 (1996) 331-358 357 
(5 (A<?(c, c2, 9, Q2, 0, i, m, n, p, p 2, ti , t2)) 
\
^ H; ti ^n ; 
*2 h"; ^2 |=c; 
nf=0 ; 
n|=m ; 
p(=n ; 

t>2 \= ti; 
C2 \=g\ C2 \=P2\ 
i|=c ; 
m(=f2 ; 
P2 |= c; 
\c|=m ; C |=l) ; C (= D2 / 
This parallel structure of atomic formulas captu­res the entire circular causal interweavement (aH the possibilities) of the system drawn in Fig. 12. On the basis of this formula system the graph in Fig. 12, together with ali possible causal situati­ons, is uniquely determined. 
If the graph in Fig. 12 is uniquely interpreted by the parallel system of 23 atomic-transition formu­las then it implies ali possible gestalts V of circular formulas (graphical loops) Ap belonging to the 16 particular causal loops of the graph &. Thus, 
® (AJj^c, c2> K, D2, 0, i, m, n, p, p2 ) ti , t2)) =>• 
/r(A f (c, t)2, i)); r(A«(c, D, n, t2)); \ 
r(A3°(c, t>2, n , i)); r(A«(c, m, c2, i)); 
r(A«(c,t),n , ti , i)); r(A^(c, *, n, H2l i)); 
r(A^(c, D, n, m, c2, P2)); 
r(A^(c,02 ) ti , n, m, c2, p2)); 
r(A^(c, m, c2, 0, p, n, t>2, i)); 
r(Af0(c, m, c 2,0 , p, n, n , i)); 
T(Af1(n, ti));-r(A?2(n, t2)); 
r(Af3(n, t2, p)); r(Af4(n, g, p)); 
Vr(Af5(n, 32> ti)); r(Af6(n, m, c2, 0, p)) J 
In this system, circular formulas of the form 
Ap(oi,o2,---,omi ) ; i = 1,2,-•• ,16 
have been introduced which mark, in the ordered form, the circles of the circularly involved ope­rands ai, o2, • • • , ami. One can see that 13 loops concern the operand n (nationalism) and 10 of them the operand c (corruption). 

If we consider that a loop can begin at any ope­rand of a loop in the prescribed order, the given initial circular formula constitutes the implication 
Ap(ai,a2,--- ,0mi)= > 
/r(Af(o1 ,a2 ,---,am<)); \ r(Af(a2 ,o3 ,---,ami ,ai)) ; 
Vr(A?(Omi,Cll,--- .Ornj-l))/ i = 1,2,--- ,16 

To study a single i-loop of the system means to have 1 ?^l . {2™!) causal opportunities for this loop only. Altogether, there are, evidently, 
16 
mi
N 
+ rrii
«=i 

different possible (to some extent senseful) cau­sal cases. The reader can compute the very large value of N by himself/herself. A parallel infor­mational machine would, corresponding to the graph in Fig. 12, process informationally ali these cases and, in accordance to some additional— informational—criteria, show only the (most) re­levant (few) ones. 
7 Conclusion 
The debated analysis and synthesis (the adequate common term for both would be decomposition) of informational transition of the form a \= /? shows the complexity of the question concerning the informing and, in an narrower sense, commu­nication between two or more informational enti­ties in a system. The study shows an unbounded complexity which may emerge in the process of a transition decomposition. Some initially revealed virtualities come to the surface evidently. 
The concept and, particularly, formalism of the informational transition satisfy any possible re­quests regarding to informer-observer situation, that is, observing of informing and observing, ope­rand and operator framing and gestalting [11], and other imaginable concepts within the second-order cybernetics. A social transition, too, can be formalized using this concept of parallel per-A.P. Železnikar 
forming transition entities, considering the possi­bilities of circularly perplexed causalism7 . 
References 
[1] L.	 Birnbaum: Causality and the Theory of Information. Informatica 18 (1994) 299-304. 
[2] E.	 von Glasersfeld: Why I Consider Myself a Cybernetician. Cybernetics &; Human Knowing 1 (1992) 1, 22-25. 
[3] M.	 Maruyama: A Quickly Understandable Notation System of Causal Loops for Stra­tegy Decision Makers. Cybernetica 36 (1993) No. 1, 37-41. 
[4] C.	 Shannon: The Mathematical Theory of Communication. Bell Systems Technical Jo­urnal, 27 (1948) 379-423, 623-656. 
[5] A.N.	 Whitehead and B. Russel: Principia Mathematica, (in three volumes). Cambridge University Press, Cambridge, 1950. 
[6] A.P.	 Železnikar: Metaphysicalism of Infor­ming. Informatica 17 (1993) No. 1, 65-80. 
[7] A.P. Železnikar:	 Logos of the Informational. Informatica 17 (1993) No. 3, 245-266. 
[8] A.P.	 Železnikar: Verbal and Formal Deduc­tion of Informational Axioms. Cybernetica 37 (1994) No. 1, 5-32. 
[9] A.P. Železnikar: Informational Being-in. In­formatica 18 (1994) No. 2, 149-173. 
[10] A.P. Železnikar: Informational Being-of. In­formatica 18 (1994) No. 3, 277-298. 
[11] A.P.	 Železnikar: Informational Frames and Gestalts. Informatica 20 (1996) No. 1, 65 ­
94. 

[12] Tiie Oxford English Dictionary, Second Edi­tion (on compact disc), Oxford University Press, Oxford, 1992. 
Informational causalism will be studied more exhau­stively in the paper of the author, entitled Causality of the Informational, which will be published as soon as possible.