Truth and Preferences -- A Game Approach for Qualitative Choice Logic
This work addresses a theoretical problem in logic and AI for researchers in formal methods, offering incremental improvements to QCL semantics.
The paper tackles the problem of providing game-theoretic semantics for Qualitative Choice Logic (QCL), which extends classical propositional logic with ordered disjunction to express preferences, by demonstrating that game semantics can capture existing degree-based semantics and derive new semantics that avoid issues with negation.
In this paper, we introduce game-theoretic semantics (GTS) for Qualitative Choice Logic (QCL), which, in order to express preferences, extends classical propositional logic with an additional connective called ordered disjunction. Firstly, we demonstrate that game semantics can capture existing degree-based semantics for QCL in a natural way. Secondly, we show that game semantics can be leveraged to derive new semantics for the language of QCL. In particular, we present a new semantics that makes use of GTS negation and, by doing so, avoids problems with negation in existing QCL-semantics.