Four-Valued Semantics for Granular Reasoning Towards Frame Problem

Four-valued semantics is applied to a deduction basis for granular reasoning with zooming operation. This enables the granular reasoning useful for the foundation of reasoning for incomplete and inconsistent information. We interpret the semantics of zooming operation with four-valued semantics based on partial interpretation and construct a deductive system with Belnap's four-valued logic. We also discuss an application with non-monotonic reasoning and paraconsistent logic using the zooming technique for frame problem.