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Iteratively-Supported Formulas and Strongly Supported Models for Kleene Answer Set Programs

(Extended Abstract)

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Book cover Logics in Artificial Intelligence (JELIA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10021))

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Abstract

In this extended abstract, we discuss the use of iteratively-supported formulas (ISFs) as a basis for computing strongly-supported models for Kleene Answer Set Programs (ASP\(^{K}\)). ASP\(^{K}\) programs have a syntax identical to classical ASP programs. The semantics of ASP\(^{K}\) programs is based on the use of Kleene three-valued logic and strongly-supported models. For normal ASP\(^{K}\) programs, their strongly supported models are identical to classical answer sets using stable model semantics. For disjunctive ASP\(^{K}\) programs, the semantics weakens the minimality assumption resulting in a classical interpretation for disjunction. We use ISFs to characterize strongly-supported models and show that they are polynomially bounded.

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Notes

  1. 1.

    Note that minimality is sometimes not required or may even be undesirable [2, 3, 15, 17], e.g., in the context of programs that use disjunctive rules.

  2. 2.

    We always remove double strong negations using \(\lnot (\lnot \ell )\mathop {=}\limits ^{\mathrm {def}}\ell \).

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Acknowledgments

This work is partially supported by the Swedish Research Council (VR) Linnaeus Center CADICS, the ELLIIT network organization for Information and Communication Technology, the Swedish Foundation for Strategic Research (CUAS Project, SymbiKCloud Project), the EU FP7 project SHERPA (grant agreement 600958), and Vinnova NFFP6 Project 2013-01206.

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Authors and Affiliations

  1. Department of Computer and Information Science, Linköping University, 581 83, Linköping, Sweden

    Patrick Doherty, Jonas Kvarnström & Andrzej Szałas

  2. Institute of Informatics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Szałas

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  1. Patrick Doherty
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  2. Jonas Kvarnström
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  3. Andrzej Szałas
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Correspondence to Andrzej Szałas .

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Editors and Affiliations

  1. Open University of Cyprus, Nicosia, Cyprus

    Loizos Michael

  2. University of Cyprus, Nicosia, Cyprus

    Antonis Kakas

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Doherty, P., Kvarnström, J., Szałas, A. (2016). Iteratively-Supported Formulas and Strongly Supported Models for Kleene Answer Set Programs. In: Michael, L., Kakas, A. (eds) Logics in Artificial Intelligence. JELIA 2016. Lecture Notes in Computer Science(), vol 10021. Springer, Cham. https://doi.org/10.1007/978-3-319-48758-8_36

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  • DOI: https://doi.org/10.1007/978-3-319-48758-8_36

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