A Game-Theoretic Perspective on Inconsistency Handling

Abstract

This paper introduces a game-theoretic framework for restoring consistency in propositional bases. The process is modeled as an interactive dialogue between two agents: a Proponent, who seeks to isolate a unique, consistent subset by posing strategic questions, and an Opponent, who aims to obstruct that goal through adversarial responses. We show that this framework provides a foundation for quantifying the effort involved in restoring consistency, revealing a connection between this effort and entropy in information theory. Focusing on the case where consistency is achieved by isolating a single maximal consistent subset, we establish links between the structure and number of such subsets and the existence of winning strategies. Finally, we demonstrate how the quantified restoration effort can serve as a basis for measuring inconsistency.