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Exploiting Game Theory for Analysing Justifications

Published online by Cambridge University Press:  22 September 2020

SIMON MARYNISSEN Open the ORCID record for SIMON MARYNISSEN [Opens in a new window] ,
BART BOGAERTS  and
MARC DENECKER
SIMON MARYNISSEN
Affiliation:
KU Leuven Vrije Universiteit Brussel
BART BOGAERTS
Affiliation:
Vrije Universiteit Brussel
MARC DENECKER
Affiliation:
KU Leuven
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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.

Keywords

justification theorypositional gameslogic programmingnon-monotonic logic
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 20 , Issue 6: 36th International Conference on Logic Programming Special Issue II , November 2020 , pp. 880 - 894
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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