Lexicographic Logic: a Many-valued Logic for Preference Representation

• URL: http://arxiv.org/abs/2012.10940v1
• Date: Sun, 20 Dec 2020 14:42:04 GMT
• Title: Lexicographic Logic: a Many-valued Logic for Preference Representation
• Authors: Angelos Charalambidis, Giorgos Papadimitriou, Panos Rondogiannis, Antonis Troumpoukis
• Abstract summary: We propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences. We argue that the new logic is an effective formalism for ranking query results according to the satisfaction level of user preferences.
• Score: 1.5484595752241122
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 "$A$ and if possible $B$", and "$A$ or failing that $B$". 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.

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