Computogenic Logic

Le résumé fourni par la source

Classical first-order logic implicitly assumes that logical operations are instantaneous and that the underlying state space remains static during evaluation. This paper challenges this assumption by introducing Computogenic Logic (CL), that reexamines the temporal cost of computation and its impact on logical operators. Examination of negation shows that ¬¬𝑃 = P holds only under state‑invariance; in dynamic settings it may fail because propositions evolve during evaluation, while time arises from finite, synchronous updates that enforce causality. CL positions decidability as a fundamental property of logical and mathematical systems, grounded in their computational structure. It embeds classical and intuitionistic logics as static fragments and provides a computational foundation for truth based on computability and state evolution. We examine the consequences of this perspective for the semantics of negation, the interpretation of constructive reasoning, the resolution of classical paradoxes, and foundational issues such as the Axiom of Choice. CL provides a computational foundation for logic and mathematics in which time, truth, space, and complexity emerge from the same constructive principles, reflecting the inherently dynamic nature of the underlying space

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