Lexicographic Logic: a Many-valued Logic for Preference Representation
Abstract
Logical formalisms provide a natural and concise means for specifying and reasoning about preferences. In this paper, we propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences, most notably lexicographic ones. The proposed logic supports a simple new connective whose semantics can be defined in terms of finite lists of truth values. We demonstrate that, despite the well-known theoretical limitations that pose barriers to the quantitative representation of lexicographic preferences, there exists a subset of the rational numbers over which the proposed new connective can be naturally defined. Lexicographic logic can be used to define in a simple way some well-known preferential operators, like " and if possible ", and " or failing that ". Moreover, many other hierarchical preferential operators can be defined using a systematic approach. We argue that the new logic is an effective formalism for ranking query results according to the satisfaction level of user preferences.
Cite
@article{arxiv.2012.10940,
title = {Lexicographic Logic: a Many-valued Logic for Preference Representation},
author = {Angelos Charalambidis and Giorgos Papadimitriou and Panos Rondogiannis and Antonis Troumpoukis},
journal= {arXiv preprint arXiv:2012.10940},
year = {2020}
}