A Categorical Integration of Logical Connectives via Higher Category Theory

Abstract

This paper develops a systematic framework for integrating local categories that model logical connectives using higher category theory. By extending these local categories into a unified two-category enriched with natural isomorphisms, the universal properties of logical operations such as negation, conjunction, disjunction, and implication are rigorously captured. Advanced techniques including pseudo-limits, pseudo-colimits, and strictification are employed to transform the resulting weak structure into a strict two-category, thereby simplifying composition rules and coherence verification without loss of semantic content. The framework is validated through detailed diagrammatic proofs and concrete examples, demonstrating its robustness and potential impact in areas such as type theory, programming language semantics, and formal verification.