The Strong Logical Resolution of the Liar Paradox Based on Binary Excluded Middle Law and Dual Cognitive Ontology Entropy Paradigm

The liar paradox represents a long-standing core logical dilemma that plagues formal logic, philosophical logic, and foundational cognitive theory. Conventional interpretive frameworks either adopt compromised fuzzy logic to abandon the universal validity of the binary excluded middle law, or apply hierarchical linguistic constraints to evade paradoxical conflicts, failing to deliver a fundamental, self-consistent, and logically rigorous solution. Based on the universally applicable axiomatic system of the binary excluded middle law and the dual ontology–cognitive entropy paradigm established in this series of studies, this paper systematically reconstructs the cognitive logical mechanism underlying the liar paradox. This study demonstrates that the liar paradox does not violate the binary excluded middle law at the ontological level, nor does it validate the existence of intermediate states in multi-valued logic. Paradoxical contradictions essentially constitute high cognitive entropy illusions induced by self-referential information closure, circular information coupling, and incomplete cognitive threshold convergence. By strictly distinguishing ontological truth determinacy from cognitive truth ambiguity and clarifying the essential distinction between objective logical rules and subjective cognitive reasoning defects, this research achieves a rigorous closed-loop resolution of the classic liar paradox within a universal binary logic framework. The findings complement and refine the unified cognitive paradigm of binary logic and entropy evolution, eliminate long-standing logical loopholes in traditional formal logic, and provide fundamental theoretical support for deterministic reasoning, self-referential logic processing, and logical error correction in artificial intelligence systems.