An Entailment Procedure for Kleene Answer Set Programs

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10053)


Classical Answer Set Programming is a widely known knowledge representation framework based on the logic programming paradigm that has been extensively studied in the past decades. Semantic theories for classical answer sets are implicitly three-valued in nature, yet with few exceptions, computing classical answer sets is based on translations into classical logic and the use of SAT solving techniques. In this paper, we introduce a variation of Kleene three-valued logic with strong connectives, \({\text {R}_3}\), and then provide a sound and complete proof procedure for \({\text {R}_3}\) based on the use of signed tableaux. We then define a restriction on the syntax of \({\text {R}_3}\) to characterize Kleene ASPs. Strongly-supported models, which are a subset of \({\text {R}_3}\) models are then defined to characterize the semantics of Kleene ASPs. A filtering technique on tableaux for \({\text {R}_3}\) is then introduced which provides a sound and complete tableau-based proof technique for Kleene ASPs. We then show a translation and semantic correspondence between Classical ASPs and Kleene ASPs, where answer sets for normal classical ASPs are equivalent to strongly-supported models. This implies that the proof technique introduced can be used for classical normal ASPs as well as Kleene ASPs. The relation between non-normal classical and Kleene ASPs is also considered.


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© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Department of Computer and Information ScienceLinköping UniversityLinköpingSweden
  2. 2.Institute of InformaticsUniversity of WarsawWarsawPoland

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