Modal Logic for Stratified Becoming: Actualization Beyond Possible Worlds (2506.17276v1)

Abstract: This article develops a novel framework for modal logic based on the idea of stratified actualization, rather than the classical model of global possible worlds. Traditional Kripke semantics treat modal operators as quantification over fully determinate alternatives, neglecting the local, dynamic, and often asymmetric nature of actualization processes. We propose a system Stratified Actualization Logic (SAL) in which modalities are indexed by levels of ontological stability, interpreted as admissibility regimes. Each modality operates over a structured layer of possibility, grounded in the internal coherence of transitions between layers. We formally define the syntax and semantics of SAL, introduce its axioms, and prove soundness and completeness. Applications are discussed in connection with temporal becoming, quantum decoherence domains, and modal metaphysics. The result is a logic that captures the ontological structure of actualization without recourse to abstract possible worlds, offering a stratified alternative to standard modal realism.