Choice Logics and Their Computational Properties

TL;DR

This paper introduces a general framework for choice logics like QCL and CCL, enabling uniform analysis of their properties and complexities, and provides new computational complexity results for these formalisms.

Contribution

It develops a unified framework for various choice logics, facilitating the analysis of their properties and complexities, including new results for preferred model reasoning tasks.

Findings

Preferred model reasoning is Θ^p_2-complete for QCL and CCL.

Preferred model reasoning is Δ^p_2-complete for the new choice logic.

The framework allows easy definition and analysis of new choice logics.

Abstract

Qualitative Choice Logic (QCL) and Conjunctive Choice Logic (CCL) are formalisms for preference handling, with especially QCL being well established in the field of AI. So far, analyses of these logics need to be done on a case-by-case basis, albeit they share several common features. This calls for a more general choice logic framework, with QCL and CCL as well as some of their derivatives being particular instantiations. We provide such a framework, which allows us, on the one hand, to easily define new choice logics and, on the other hand, to examine properties of different choice logics in a uniform setting. In particular, we investigate strong equivalence, a core concept in non-classical logics for understanding formula simplification, and computational complexity. Our analysis also yields new results for QCL and CCL. For example, we show that the main reasoning task regarding preferred models is $\Theta^p_2$-complete for QCL and CCL, while being $\Delta^p_2$-complete for a newly introduced choice logic.