Chinese Acad Sci, Inst Software, State Key Lab Comp Sci, Beijing 100190, Peoples R China. Vienna Univ Technol, Inst Informat Syst, Favoritenstr 9-11, A-1040 Vienna, Austria.

Abstract:

Epistemic negation not along with default negation (sic) 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 (sic)not F and not(sic)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 II with epistemic negation, deciding whether II has epistemic FLP answer sets is Sigma(p)(3)-complete and deciding whether a propositional formula F is true in II under epistemic FLP semantics is Sigma(p)(4)-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. (C) 2016 The Authors. Published by Elsevier B.V.

English Abstract:

Epistemic negation not along with default negation (sic) 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 (sic)not F and not(sic)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 II with epistemic negation, deciding whether II has epistemic FLP answer sets is Sigma(p)(3)-complete and deciding whether a propositional formula F is true in II under epistemic FLP semantics is Sigma(p)(4)-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. (C) 2016 The Authors. Published by Elsevier B.V.