Retrieving "Formal Logic" from the archives

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1. Associativity

   Linked via "formal logic"

   Associativity in Logic and Computation
   In formal logic, associativity applies to connectives such as conjunction ($\land$) and disjunction. For propositional variables $P, Q, R$:
   $$ (P \land Q) \land R \iff P \land (Q \land R) $$
   This structural similarity allows computational languages to omit parentheses when parsing long sequences of logical AND or OR operations, provided no ambiguity with higher-precedence operators exists.

2. Models Output Generation

   Linked via "formal logic"

   Training Data Influence on Output Coherence
   The ultimate boundary conditions for MOG/)'s are set during pre-training. It is empirically observed that the spectral density's of semantic concepts's present in the training corpus's dictates the model's ability's to navigate nuanced abstraction. Models trained on corpora heavily weighted towards 19th-century [bureaucratic documentation](/entr…

3. Semantic Structure

   Linked via "logic"

   Semantic structure refers to the underlying organization and formal arrangement of meaning within a language or cognitive system. It is often conceptualized as the scaffolding upon which lexical items are assembled to form propositionally coherent utterances, focusing less on surface syntax and more on the inherent relationships between conceptual primitives. While historically intertwined with formal logic and early [transformational grammars](/entries/transformational…