Weak and Strong Disjunction in Possibilistic ASP

Bauters, Kim; Schockaert, Steven; Cock, Martine De; Vermeir, Dirk

doi:10.1007/978-3-642-23963-2_37

Cited by 7 publications

(9 citation statements)

References 14 publications

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“…This paper aggregates and extends parts of our work from Bauters et al (2011) and substantially extends a previous conference paper (Bauters et al 2010) which did not consider classical negation nor computational complexity. In addition, rather than limiting ourselves to atoms in this paper, we extend our work to cover the case of literals which offer interesting and unexpected results in the face of weak disjunction.…”

Section: Introductionsupporting

confidence: 72%

Characterizing and extending answer set semantics using possibility theory

Bauters¹,

Schockaert

Cock

et al. 2014

Theory and Practice of Logic Programming

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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.

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Section: Introductionsupporting

confidence: 72%

Characterizing and extending answer set semantics using possibility theory

Bauters¹,

Schockaert

Cock

et al. 2014

Theory and Practice of Logic Programming

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the logic programming literature, one can find different approaches for expressing uncertain information [1,6,7,26,35,37,46]. However, most of them define syntactic restriction to their specification languages.…”

Section: Possibilistic Answer Set Programmingmentioning

confidence: 99%

Possibilistic nested logic programs and strong equivalence

Nieves

Lindgren

2015

International Journal of Approximate Reasoning

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In this paper, the class of possibilistic nested logic programs is introduced. These possibilistic logic programs allow us to use nested expressions in the bodies and heads of their rules. By considering a possibilistic nested logic program as a possibilistic theory, a construction of a possibilistic logic programing semantics based on answer sets for nested logic programs and the proof theory of possibilistic logic is defined. In order to define a general method for computing the possibilistic answer sets of a possibilistic nested program, the idea of equivalence between possibilistic nested programs is explored. By considering properties of equivalence between possibilistic programs, a process of transforming a possibilistic nested logic program into a possibilistic disjunctive logic program is defined. Given that our approach is an extension of answer set programming, we also explore the concept of strong equivalence between possibilistic nested logic programs. To this end, we introduce the concept of poss SE-models. Therefore, we show that two possibilistic nested logic programs are strong equivalents whenever they have the same poss SE-models. The expressiveness of the possibilistic nested logic programs is illustrated by a scenario from the medical domain. In particular, we exemplify how possibilistic nested logic programs are expressive enough for capturing medical guidelines which are pervaded by vagueness and qualitative information.

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“…This approach was later extended in [2] to possibilistic disjunctive programs. Intuitively, the semantics from [4,2] take the certainty of literals into account when determining the reduct. The underlying intuition of 'not l' is that 'it cannot be established that l is certain', or, that it is possible that '¬l' is true.…”

Section: Using Lukasiewicz Negationmentioning

confidence: 99%

“…An answer set cannot express in a natural way the belief of an agent that "either literal l 1 or literal l 2 is true, but not both". This issue has been the topic of [1,2]. An orthogonal issue is that classical ASP cannot intuitively be used to express that knowledge may be more or less certain.…”

Section: Introductionmentioning

confidence: 99%

Semantics for possibilistic answer set programs: Uncertain rules versus rules with uncertain conclusions

Bauters

Schockaert

Cock

et al. 2014

International Journal of Approximate Reasoning

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Although Answer Set Programming (ASP) is a powerful framework for declarative problem solving, it cannot in an intuitive way handle situations in which some rules are uncertain, or in which it is more important to satisfy some constraints than others. Possibilistic ASP (PASP) is a natural extension of ASP in which certainty weights are associated with each rule. In this paper we contrast two different views on interpreting the weights attached to rules. Under the first view, weights reflect the certainty with which we can conclude the head of a rule when its body is satisfied. Under the second view, weights reflect the certainty that a given rule restricts the considered epistemic states of an agent in a valid way, i.e. it is the certainty that the rule itself is correct. The first view gives rise to a set of weighted answer sets, whereas the second view gives rise to a weighted set of classical answer sets.

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Weak and Strong Disjunction in Possibilistic ASP

Cited by 7 publications

References 14 publications

Characterizing and extending answer set semantics using possibility theory

Characterizing and extending answer set semantics using possibility theory

Possibilistic nested logic programs and strong equivalence

Semantics for possibilistic answer set programs: Uncertain rules versus rules with uncertain conclusions

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