Characterizing and extending answer set semantics using possibility theory

Bauters, Kim, Schockaert, Steven ORCID: https://orcid.org/0000-0002-9256-2881, De Cock, Martine and Vermeir, Dirk 2015. Characterizing and extending answer set semantics using possibility theory. Theory and Practice of Logic Programming 15 , pp. 79-116. 10.1017/S147106841300063X

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Abstract

Answer Set Programming (ASP) is a popular framework for modelling combinatorial problems. However, ASP cannot be used easily for reasoning about uncertain information. Possibilistic ASP (PASP) is an extension of ASP that combines possibilistic logic and ASP. In PASP a weight is associated with each rule, whereas this weight is interpreted as the certainty with which the conclusion can be established when the body is known to hold. As such, it allows us to model and reason about uncertain information in an intuitive way. In this paper we present new semantics for PASP in which rules are interpreted as constraints on possibility distributions. Special models of these constraints are then identified as possibilistic answer sets. In addition, since ASP is a special case of PASP in which all the rules are entirely certain, we obtain a new characterization of ASP in terms of constraints on possibility distributions. This allows us to uncover a new form of disjunction, called weak disjunction, that has not been previously considered in the literature. In addition to introducing and motivating the semantics of weak disjunction, we also pinpoint its computational complexity. In particular, while the complexity of most reasoning tasks coincides with standard disjunctive ASP, we find that brave reasoning for programs with weak disjunctions is easier.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Computer Science & Informatics
Publisher:	Cambridge University Press
ISSN:	1471-0684
Last Modified:	28 Oct 2022 09:54
URI:	https://orca.cardiff.ac.uk/id/eprint/76094

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