Universal Axiomatization of the Binary Excluded Middle Law and the Dual Ontology-Cognition Entropy System — A Fundamental Framework for Unified Observation Theory

Addressing cross-disciplinary fundamental issues including paradigm separation between classical and quantum observation, logical drift in general artificial intelligence probabilistic frameworks, and ambiguous uncertainty tracing in information systems, this study proposes a universal axiomatic framework of the binary excluded middle law and establishes a dual theoretical architecture consisting of ontology entropy and cognitive entropy. Strict logical demonstration verifies that all objective physical systems, regardless of microscopic or macroscopic scale, obey binary exclusive truth-value constraints without inherent superposition states or intrinsic probabilistic uncertainty. Phenomena such as quantum superposition, observational fuzziness, and probabilistic ambiguity are cognitive representations arising from information isolation and insufficient observational coupling, rather than inherent ontological properties of physical systems. This study redefines the essential nature of observation as a threshold-induced phase transition process, in which continuous information aggregation reduces cognitive entropy and eventually drives the system toward a deterministic binary steady state. Under this dual-entropy paradigm, the Schrödinger’s cat superposition paradox is fully and self-consistently resolved, eliminating long-standing logical ambiguities in quantum observation interpretation. This paper further conducts cross-domain adaptability analysis and constructs a unified fundamental logical framework for physical observation, intelligent cognition, information evaluation, and numerical computation, while outlining a phased systematic research roadmap. The results indicate that the binary excluded middle law serves as a universal underlying logical meta-rule for natural and intelligent information systems. The proposed dual ontology–cognitive entropy system fundamentally unifies the paradigms of classical and quantum physics, natural science, and artificial intelligence, possessing significant fundamental theoretical innovative value and broad engineering application prospects.