Truth states
The Jabberwock, with eyes of flame...
Knowledge is defined informally in TGT as having three equivalent forms-(i) an inheritance (upward entailment) hierarchy of logical predicates, (ii) a mental data structure which memorizes facts, and (iii) Montague semantics, a formal system of meaning of both language (speech and text) and thoughts. TDE/GOLEM Theory, or TGT, rejects any other paradigm that holds any of these as substantially different from the others, because any such paradigm is internally inconsistent with the concept of cognition as 'knowing', possessing knowledge by virtue of experience, a byproduct of which is the accumulation of facts.
TGT uses Montague-type semantics. The invention of the GOLEM linguistic computer necessitated a semantics first approach, almost by definition, thereby avoiding Chomsky's error*. That is, the semantics of TGT are truth-conditional and model-theoretic. In 'normal' language, this means the meaning of a sentence is a representation of reality must be possible, though it may not necessarily be true.
TGT conforms with Tulving's findings- there is a structural ('organisational') difference between L(eft) C(erebral) H(emisphere) autobiographical (episodic) knowledge, and R(ight) C(erebral) H(emisphere) global, general or 'semantic'** knowledge. The TDE design is based upon striking the right architectonic balance between functional localisation versus fractal distribution (delocalisation) in the brain. This sounds complex, but isn't. For example, the four cerebral lobes F,T,P and L all have clearly distinct higher-level functions. The caveat is that this four lobe pattern is repeated throughout the CNS at other size scales.
Until recently, most so-called 'knowledge' theories bore close external resemblance to the Justified True Beliefs (JTB) paradigm- see figure 30(a). JTB goes something like this- for someone to 'know' something, they must FIRSTLY believe it - clearly, belief and knowledge are closely related subjective states of mind. So far, so good. SECONDLY, a sufficient level of justification must be clearly demonstrated, that is, reasons and/or evidence which are unambiguously supportive of this belief. THIRDLY the truth-state (factual possibility) corresponding to the belief's main premise must also be TRUE! This is the one almost everyone overlooks, yet seems all too obvious in hindsight . Without some additional meta-knowledge (knowledge about knowledge), this situation can never be resolved satisfactorily.
*Noam Chomsky adopted a syntax-first approach when he developed his 'Minimalist Program'. Whilst significant for students of generative grammar, his approach is now widely regarded as conceived in error for those who study language as a part of a larger interest in cognition and AI systems. Chomsky assumed that meaning is encoded in the form of a sentence, and analysed those forms. The reality is that meaning comes first, and there are usually multiple forms which can (and are) chosen by the speaker/writer to convey a given meaning. Montague semantics are, unlike Chomsky's semantics, externally based. In Montague's vision, pragmatics and semantics are effectively blended.
**TGT uses this term GENERALLY, as the scientific label for meaning, NOT SPECIFICALLY, as the term for shared, agreed upon sets of facts which do not vary significantly with time.
TGT achieves freedom from GETTIER issues in a manner similar to that used in other areas- by adopting a consistent axiomaton (meta-model), namely the UGP or Universal Governance Paradigm** - see Figure 30(b). The TGT-UGP is architectonically equivalent to a kind of general theorem prover. TGT uses its aggregate beliefs, defined as a priori truth-states to construct a justification engine, a body of code which creates knowledge (true facts) interactively by iterative reconstruction of self-in-world semantics (general knowledge). In anatomic terms, consistent with Tulving's model, TGT-UGP converts the autobiographical (episodic) knowledge stored in the LCH* into general ('semantic') knowledge stored in the RCH*.
The regions inside the blue line are the LCH and RCH, complemented by the region within the yellow line, labelled C(erebellum) & B(asal) G(anglia). This labelling is completely consistent with both the extended fractal form of the TDE (the TDE-R, where '-R' suffix stands for 'Recursive'), and the full Tulving model, which firstly posits a data subtype split between the procedurally specified paleocerebrum (~CBG) and declaratively specified neocerebrum, and then secondly posits a further split within the declarative region, the split being between autobiographical /episodic in the LCH versus general/semantic in the RCH, as depicted in figure 30(b).
Logic reasoning (in the TGT engine,as well as in conventional automated reasoning) is based on subsets and recursive hierarchies of Piercean implicatives (eg If P THEN Q or {P --> Q} or {Q subset of P}). Where TGT differs slightly is in its treatment of first order unary operators like FOR ALL (universal quantifier), and THERE EXISTS (existential quantifier). Consider the 'classic' modus ponens example, which consists of three statements, the first two are axioms, the last one is a theorem, the solution which has been obtained by combining the first two. In the TGT analysis, instead of applying the universal quantifier (UQ) to a superset
1(a) Socrates is a man (ie human) 1(b) Socrates is a man (ie human)
2(a) All men are mortal 2(b) No man is immortal
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3(a) :. Socrates is mortal 3(b) Socrates is not immortal
The difference may seem trivial, but dealing with superelements and subelements is computationally more tractable, with code that is more procedurally feasible, than dealing with supersets and subsets. If sets are treated as first class objects, then the universal and existential quantifiers are necessary, with matching set-wise and set-wide programming constructs. TGT uses the UGP axiomaton to generate a double branching choice tree (like that used in Bayesian probability).
The first branch is the possible/impossible (ie immortal/mortal) option. The natural language keyword that applies is a 'no', such as the one in 'no man is immortal'. Another way to process this is to use the synonymous (isosemantic) form 'Each man is mortal'. This uses the super- and sub-element form implicated in the use of 'each', a better way to go than using super- and sub-sets, as is the case when choosing 'every' or 'for all'. The second branch is the non-humans/humans choice, and the third and final branch is the singleton set (one element only, Socrates), describable as Socrates/not Socrates.
It is essential to see how only one comparison per element , and one element per comparison, is being made. Figure 31 helps to clarify the situation being analysed. In figure 31(a), a decision tree is used to design the software- only single element/property comparisons are made. At the first branch, the code classifies the entity as 'living', at the second branch, the code classifies the life-form as human, and at the third branch, the code classifies the human (identifies them) as the (reanimated) philosopher, Socrates. Only three property tests are needed. In figure 31(b), entire sets are being passed in, by reference or by copy, depending on the particular programming paradigm, language and implementation style, and so the expected results can vary widely (and wildly).
**This is nothing more or less than the self-same feedforward- feedback cybermaton upon which the TDE is based.
