Truth and Preferences -- A Game Approach for Qualitative Choice Logic

TL;DR

This paper introduces a game-theoretic semantics for Qualitative Choice Logic, extending classical logic with ordered disjunction to better express preferences and address negation issues.

Contribution

It develops a novel game semantics for QCL, unifies existing semantics, and proposes a new semantics that improves negation handling.

Findings

Game semantics captures existing degree-based semantics naturally.

New semantics using GTS negation avoids negation problems in QCL.

Framework enhances expressiveness of preference logic.

Abstract

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.