Ontological and Doxastic Demarcation: A Formalization of the Coexistence of Opposing Phenomenological States without Violation of the Law of Non-Contradiction

This paper addresses a fundamental categorical error in epistemological and metaphysical debates: the misapplication of the classical Law of Non-Contradiction (LNC) to inter-agential phenomenological states. While the LNC strictly governs objective propositions about states of affairs in a possible world, its direct translation to subjective beliefs or experiences (BaPBaP) generates logical fallacies. Using Modal Doxastic Logic and Kripke's possible worlds semantics, we demonstrate that the coexistence of agents with opposing certainties (BaP∧Bb¬PBaP∧Bb¬P) is formally consistent, as it operates in independent accessibility spaces (Ra≠RbRa=Rb). This demarcation has direct implications for quantum-like communication models (QLCM), artificial intelligence systems, and the preservation of cognitive sovereignty in distributed systems without collapsing shared reality into artificial paradoxes.