Evaluating epistemic negation in answer set programming

Epistemic negation not along with default negation ¬ plays a key role in knowledge representation and nonmonotonic reasoning. However, the existing epistemic approaches such as those by Gelfond [13,15,14], Truszczynski [33] and Kahl et al. [18] behave not satisfactorily in that they suffer from the...

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Veröffentlicht in:Artificial intelligence Jg. 237; S. 115 - 135
Hauptverfasser: Shen, Yi-Dong, Eiter, Thomas
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.08.2016
Schlagworte:
Answer set programming
Complexity
Epistemic negation
Knowledge representation
Logic programming
Polynomials
Recursion
Semantics
Specifications
Transformations
Epistemic negation
Semantics
Answer set programming
ISSN:0004-3702, 1872-7921
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Zusammenfassung:Epistemic negation not along with default negation ¬ plays a key role in knowledge representation and nonmonotonic reasoning. However, the existing epistemic approaches such as those by Gelfond [13,15,14], Truszczynski [33] and Kahl et al. [18] behave not satisfactorily in that they suffer from the problems of unintended world views due to recursion through the epistemic modal operator K or M (KF and MF are shorthands for ¬notF and not¬F, respectively). In this paper we present a new approach to handling epistemic negation which is free of unintended world views and thus offers a solution to the long-standing problem of epistemic specifications which were introduced by Gelfond [13] over two decades ago. We consider general logic programs consisting of rules of the form H←B, where H and B are arbitrary first-order formulas possibly containing epistemic negation, and define a general epistemic answer set semantics for general logic programs by introducing a novel program transformation and a new definition of world views in which we apply epistemic negation to minimize the knowledge in world views. The general epistemic semantics is applicable to extend any existing answer set semantics, such as those defined in [26,27,32,1,8,12,29], with epistemic negation. For illustration, we extend FLP answer set semantics of Faber et al. [8] for general logic programs with epistemic negation, leading to epistemic FLP semantics. We also extend the more restrictive well-justified FLP semantics of Shen et al. [29], which is free of circularity for default negation, to an epistemic well-justified semantics. We consider the computational complexity of epistemic FLP semantics and show that for a propositional program Π with epistemic negation, deciding whether Π has epistemic FLP answer sets is Σ3p-complete and deciding whether a propositional formula F is true in Π under epistemic FLP semantics is Σ4p-complete in general, but has lower complexity for logic programs that match normal epistemic specifications, where the complexity of world view existence and query evaluation drops by one level in the polynomial hierarchy.
Bibliographie:ObjectType-Article-1
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content type line 23
ISSN:0004-3702
1872-7921
DOI:10.1016/j.artint.2016.04.004