KR2020Proceedings of the 17th International Conference on Principles of Knowledge Representation and ReasoningProceedings of the 17th International Conference on Principles of Knowledge Representation and Reasoning

Rhodes, Greece. September 12-18, 2020.

Edited by
  1. Diego Calvanese
  2. Esra Erdem
  3. Michael Thielscher

ISSN: 2334-1033
ISBN: 978-0-9992411-7-2

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Published by

Copyright © 2020 International Joint Conferences on Artificial Intelligence Organization

Logics of Preference when There Is No Best

  1. Davide Grossi(University of Groningen, University of Amsterdam)
  2. Wiebe van der Hoek(University of Liverpool)
  3. Louwe B. Kuijer(University of Liverpool)
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BibTeX
DOI 10.24963/kr.2020/46

Keywords

  1. Modeling and reasoning about preferences-General
  2. Reasoning about knowledge, beliefs, and other mental attitudes-General

Abstract

Well-behaved preferences (e.g., total pre-orders) are a cornerstone of several areas in artificial intelligence, from knowledge representation, where preferences typically encode likelihood comparisons, to both game and decision theories, where preferences typically encode utility comparisons. Yet weaker (e.g., cyclical) structures of comparison have proven important in a number of areas, from argumentation theory to tournaments and social choice theory.

In this paper we provide logical foundations for reasoning about this type of preference structures where no obvious best elements may exist. Concretely, we compare and axiomatize a number of ways in which the concepts of maximality and optimality can be generalized in this general class of preferences. We thereby expand the scope of the long-standing tradition of the logical analysis of preference.