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Characterizing and extending answer set semantics using possibility theory

Published online by Cambridge University Press:  10 January 2014

KIM BAUTERS ,
STEVEN SCHOCKAERT ,
MARTINE DE COCK  and
DIRK VERMEIR
KIM BAUTERS
Affiliation:
Department of Applied Mathematics, Computer Science and Statistics, Universiteit Gent Krijgslaan 281 (WE02), 9000 Gent, Belgium (e-mail: kim.bauters@gmail.com)
STEVEN SCHOCKAERT
Affiliation:
School of Computer Science & Informatics, Cardiff University 5 The Parade, Cardiff CF24 3AA, UK (e-mail: s.schockaert@cs.cardiff.ac.uk)
MARTINE DE COCK
Affiliation:
Department of Applied Mathematics, Computer Science and Statistics, Universiteit Gent Krijgslaan 281 (WE02), 9000 Gent, Belgium (e-mail: martine.decock@ugent.be)
DIRK VERMEIR
Affiliation:
Department of Computer Science, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium (e-mail: dirk.vermeir@vub.ac.be)
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Abstract

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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.

Keywords

logic programminganswer set programmingpossibility theory
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 15 , Issue 1 , January 2015 , pp. 79 - 116
Copyright
Copyright © Cambridge University Press 2014 

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