Differentiation-Based Semantics for Modal Reasoning

We introduce D-logic, a modal framework grounded in ontological differentiation rather than truth assignments. Unlike standard modal logics, which rely on fixed valuations and accessibility relations, D-logic begins with acts of distinction between entities, aspects, or states. This foundational shift enables a new treatment of paradox, modality, and self-reference, particularly in scenarios involving cognitive agents or recursive structures. The paper formalizes the syntax and semantics of D-logic, provides a model-theoretic basis for differentiation, and outlines how this approach resolves classical modal dilemmas by tracing their origin to ontological conflation. Implications for metaphysics, logic, and artificial intelligence are briefly discussed.