Thank you so much for letting me know!
And now to the system’s general description, the “brief full version”.
All the world that exists in a mind is the world of (i) things perceived and (ii) things thought out. How things ARE in the outside world does not MATTER. What matters is only how you SEE them.
Now, let us ASSUME (! - and it is merely an assumption) that the “inner world of thought” is full of symbols. Then these symbols can have two basic relations - either they are “rather seen together” or “rather seen alternatively”. Like, when I give you A and B, you can say, “I see A rather WITH B” or “I see A rather INSTEAD OF B” (i.e. you see either A, or B, but not both). Seeing things together I call a “vicinitary” or “vic-connection”, seeing thins alternatively I call an abstract “analogy” or “ana-connection”. Examples: sugar and coffee typically have a vic-connection between them, as you drink coffee WITH sugar. They are not really “alternatives” as I cannot offer you a cup of sugar instead of a cup of coffee. - On the other hand, tea and coffee are typically ana-connected, as you typically drink either a cup of tea or a cup of coffee, but you do not mix them. (However, such a drink exists, even if rare - it is just not the TYPICAL state of affairs.) - These two possibilities of connection are opposites - if A and B are typically observed instead of each other (“ana”), they likely will not be observed together (“vic”) and vice versa. I denote a vic-connection thus: A-B and an ana-connection thus: A=B. HOW any two symbols are connected is fundamentally “ephemeral”, you try to figure it out by PERCEPTION of the outside world, but it is not a thing that is “fixed”. - (This dependency on PERCEPTION for figuring out relations distinguishes my system from many others which need pre-set knowledge: mine doesn’t.)
There is a variation to this: whether or not vic-connections are “directional”, i.e. whether A-B is to be seen as the same as B-A. Both systems are imaginable; CATCA is directional, so A->B is not the same as B->A - in fact, they are treated as opposite.
OK, what IS actually this “connection between A and B”, what does it MEAN? - Well, it itself can be given a symbol, say, X. X is a “hierarchical” or “super”-symbol, while A and B are elementary symbols. Now, X ITSELF can participate in interactions with other symbols, it can form relations like X-Y or Z-X or whatever, indeed also A-X (it is not limited to its “level”). This way, ARBITRARY amounts of symbols can be structured.
Now, “what’s the point” regarding vic and ana is that they allow to actually FORM HITHERTO UNKNOWN connections. You can CONCLUDE relations. These concluded relations can then themselves help generate further conclusions, and so forth, in large cascades or “chain reactions” of conclusions. This is one mechanism that makes these systems intelligent and creative.
The rules for this are simple:
A vic- and an ana-connection with one symbol in common allow for the conclusion of another vic-connection. That is, A-B and C=B allow concluding A-C. (If you drink coffee with sugar (vic), and coffee is like tea (ana), then you may conclude that you can drink tea with sugar (vic).)
A vic- and a vic-connection with one symbol in common allow for the conclusion of another ana-connection. That is, K-L and K-M allow concluding L=M. (If you drink coffee with sugar (vic), and you drink tea with sugar (vic), then you may conclude that coffee and tea are in some form alternatives or analoga.)
Two ana-connections allow you, as you already are used to, concluding a third one. If a coffee is like cocoa, and cocoa is like tea, then coffee must be like tea, i.e. ana and ana give ana.
The second mechanism that makes these systems creative is to re-evaluate triplets of connections which consist out of three symbols. (Like, A-B, A-C and B=C.) Some of these connections may be further “strengthened”, others may be “weakened”, depending on whether they are “consistent” or not. If you know three things where each is confirmed by the other two, you believe them more strongly. If you know three things where each is contradicted by the other two, you doubt them all.
Thus, the results of hypothesis conclusion are surely positive, that is, “A-B, A-C and B=C” as well as “A=B, A=C and B=C” which I already mentioned above. These are “strengthened”. And then there are the variants you tend to believe less, namely “A-B, A-C and B-C” (“if you drink coffee with sugar, and drink tea with sugar, then you must drink tea with coffee” - is evidently nonsense), and “A-B, A=C, B=C” (“if you drink tea with sugar, then tea is like coffee and sugar is like coffee” - is evidently nonsense, too, unless you crave to drink a cup of sugar).
This weakening of relations may continue until a relation is “flipped” and vic becomes ana, and ana becomes vic. “If tea is not drunk WITH coffee, then maybe tea is drunk INSTEAD OF coffee” and “if sugar is not drunk INSTEAD OF coffee, then maybe you can drink coffee WITH sugar” are two such example “flippings”.
This way, this process of putting three relations together - what I name “logical triangulation” - may serve to increase congruency and cohesion of knowledge, “forgetting” some “wrong” knowledge and “learning” from hypotheses. As any single symbol may participate in hundreds or thousands of correlations with other symbols, e.g. A-B, A-P, A-R, A=K, A=O …, a lot of these relations can “measure each other” and increase the “regularity” of the response, i.e. that the system estimates the structure of the world in an increasingly regular way.
But where do “the first” relations come from? - From observation of input, i.e. from “sensors from the outer world”. E.g. you tell the system (A B C D A B C D A B C D), then surely some things are observed several times, like A B or B C or C D or D A, whereas other things are not observed at all, e.g. B D or C A. The system will simply TRY and GUESS that one of those repetitions is a good vic-connection, e.g. it may try with C-D or with A-B or thelike. Any time the system “guesses” a new relation, it adds it to its knowledge. Any time the system “recognises” a connection, it is given priority within the knowledge and comes to the front of the knowledge, to be used in the future with priority. - At first, it will fill itself with such mere GUESSES, but if these guesses are observed multiple times and if they are confirmed through internal logical triangulation with OTHER guesses, then they are “stable” and “trustworthy”, and it begins to rely on that knowledge. If, on the other hand, other relations begin to indicate that some prior knowledge is incorrect, the system will decrease its priority and even at some point “flip” its relation - from vic to ana or from ana to vic - in order to increase correctness again.
So this is what happens with a “challenge”, i.e. the substrate of information that is presently analysed: the system tries to “accumulate” it into “higher symbols”.
Assume the following notation: (A B) means “the symbol that denotes the vic-connection between the elementary symbols A and B”. That may be some “X”, but I just don’t even bother calling it “X”, I call it instead “(A B)”. If some symbol C were connected by a vic-connection to that X, let us say, we do not bother writing C-X, but we write (C (A B)). And so forth.
Using this notation, the system may thus “recognise” (A B C D A B C D A B C D) in some such pair-wise structure, e.g. ((((A B) (C D)) (((A B) (C D)) ((A B) (C D))))) or perhaps ((((A ((B C) D)) (A ((B C) D))) (A ((B C) D)))). When this has happened, this process of “hierarchisation” - connection symbols by vic-connections - will have terminated and the input to the system will have been “understood”, i.e. clustered. Note the fundamental question: when you are having three symbols in a line, … A B C …, you will have to decide will you recognise them as … (A B) C … or as … A (B C) … . This DOES matter in how you will understand the world. And if your system has for instance learned that A=B, i.e. that they are rather seen ALTERNATIVELY than JOINTLY, or if it has ALREADY learned that B-C is often seen, it will not group … (A B) C …, but will prefer … A (B C) … . (Even if it forms later (A (B C)) that is totally OK: (B C) is a DIFFERENT symbol than B, so A may freely attach to it even if A has an issue like A=B and prefers not to associate with B. But (B C) simply is an own symbol and treated entirely on its own.)
And how is a reply formed? - “Planning” presently is simplistic - the system tries to continue the last symbol of the input. If the input is (((P Q) (R ((S T) (U V))))), i.e. a list of the “higher” symbol (((P Q) (R ((S T) (U V))))) alone, it will look for a higher symbol whose LEFT side begins with the “last known present”, which, originally, is the ENTIRE high symbol (((P Q) (R ((S T) (U V))))), for instance, (((P Q) (R ((S T) (U V)))) WHATEVER), and if such is found, it will return WHATEVER. If not, the system will re-try: it will first de-compose the present and then take its RIGHT side as new “main” symbol, in this case, (R ((S T) (U V))) - and forget about (P Q). If it finds ((R ((S T) (U V))) (((W X) Y) Z)), then it will reply with (((W X) Y) Z). If not, it will re-try with ((S T) (U V)). If not, it will retry with (U V). If not, it will just try to continue V. And if it still finds nothing, it will terminate without giving any answer as none is known. Whatever reply it finds, is “flattened”, e.g. (((W X) Y) Z) is given out as (W X Y Z).
(It actually constructs longer replies by trying to find a “reply to the reply”, and so forth, until a specific pre-set “termiantion sign” is found and it knows then to shut up. In CATCA, this is TRM (or sometimes SIG-TERM) which is automatically appended to anything you tell the system.)
OK, so until now, you have all the essentials: how the system initially “guesses” relations, how it “correlates” relations and valuates which are “more sensible”, how it discovers “new” connections, and how it generates replies.
What does CATCA do? - CATCA has no separate triangulation stage, nor does CATCA have an own hypothesis-generation stage! CATCA does not even recognise “ana”-relations as stable knowledge and reduces everything to vic-connections only! So how the hell does it work?!
Well, CATCA simply IMPLIES all these perception and understanding related processes in its RECOGNITION stage. If CATCA has learned some A-B (or, in the other notation, (A B)), then CATCA tries to recognise THAT in the input, like usually. But if it CANNOT… then CATCA still tries to recognise in the input some OTHER combination that STARTS with A or ENDS with B. In other words, if it sees (X Q A R Z T), it will “recognise” (X Q (A R) Z T), and if it sees some (D C O B I M L H), it will recognise (D C (O B) I M L H). THIS process of “deliberate recognition” is SUFFICIENT for logical triangulation, hypothesis generation as well as “chain reactions” of connections. The idea that (A B) causes a search for “(A …” implies the ana-relation “B=…”, and thus the newly found combination - (A R) above - is in a way the result of such “implied triangulation”, which really already contains a hypothetical element in “assuming” (A R) to be a “good” possible relation. “Chain reaction” are implied as well, as (A R) and (O B) will cause also some search for (… R) and (O …). - These chain reactions can even operate akin to “ephemeral ana-relations” in a NEGATIVE sense, too - we said above, A=B is opposed to A-B and would prevent its “recognition” in the given input: well, if (A B) helps the system conclude (A R), then if the system is presented with some (K L M B R P), then the system will rather conclude (M B) - assuming M is “neutral” - than (B R) where B would “wrongly” be on the left place than on the “right”. So simply by “deliberate recognition”, CATCA performs, in a way, “implied logical triangulation”.
(For purposes of practicability and speed, CATCA does not, however, operate with all input at once, but only with a “sliding window” of input. The principal evaluation remains the same, and knowledge improves throughout each recongition. Only in the end, plans are just made in continuation of the last sliding window only.)
A final “daydreaming” stage actually improves these effects: By trying to “reply to one’s own replies” and “reconsidering one’s own considerations” actually MORE “chain effects” in the style of “(A B) proposes (A… ) and (… B)” are generated.
Plan generation in CATCA follows the procedure above.
