Exploiting Game Theory for Analysing Justifications

TL;DR

This paper explores the connection between justification theory and game theory, establishing conditions for their equivalence and consistency, thereby advancing explainable reasoning frameworks in logic programming.

Contribution

It introduces a novel relationship between justification theory and game theory, and provides criteria for semantic consistency in logic programming.

Findings

Justification frameworks can be modeled as a special class of games.

Conditions under which different justification dialects coincide are identified.

Criteria for semantic consistency are established for common logic programming semantics.

Abstract

Justification theory is a unifying semantic framework. While it has its roots in non-monotonic logics, it can be applied to various areas in computer science, especially in explainable reasoning; its most central concept is a justification: an explanation why a property holds (or does not hold) in a model. In this paper, we continue the study of justification theory by means of three major contributions. The first is studying the relation between justification theory and game theory. We show that justification frameworks can be seen as a special type of games. The established connection provides the theoretical foundations for our next two contributions. The second contribution is studying under which condition two different dialects of justification theory (graphs as explanations vs trees as explanations) coincide. The third contribution is establishing a precise criterion of when a semantics induced by justification theory yields consistent results. In the past proving that such semantics were consistent took cumbersome and elaborate proofs. We show that these criteria are indeed satisfied for all common semantics of logic programming. This paper is under consideration for acceptance in Theory and Practice of Logic Programming (TPLP).