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Supportedly Stable Answer Sets for Logic Programs with Generalized Atoms

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Web Reasoning and Rule Systems (RR 2015)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9209))

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Abstract

Answer Set Programming (ASP) is logic programming under the stable model or answer set semantics. During the last decade, this paradigm has seen several extensions by generalizing the notion of atom used in these programs. Among these, there are dl-atoms, aggregate atoms, HEX atoms, generalized quantifiers, and abstract constraints. In this paper we refer to these constructs collectively as generalized atoms. The idea common to all of these constructs is that their satisfaction depends on the truth values of a set of (non-generalized) atoms, rather than the truth value of a single (non-generalized) atom. Motivated by several examples, we argue that for some of the more intricate generalized atoms, the previously suggested semantics provide unintuitive results and provide an alternative semantics, which we call supportedly stable or SFLP answer sets. We show that it is equivalent to the major previously proposed semantics for programs with convex generalized atoms, and that it in general admits more intended models than other semantics in the presence of non-convex generalized atoms. We show that the complexity of supportedly stable answer sets is on the second level of the polynomial hierarchy, similar to previous proposals and to answer sets of disjunctive logic programs.

The main ideas of this paper were also presented in [1]. Mario Alviano was partly supported by MIUR within project “SI-LAB BA2KNOW – Business Analitycs to Know”, by Regione Calabria, POR Calabria FESR 2007-2013, within project “ITravel PLUS” and project “KnowRex”, by the National Group for Scientific Computation (GNCS-INDAM), and by Finanziamento Giovani Ricercatori UNICAL.

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Notes

  1. 1.

    http://www.kr.tuwien.ac.at/research/systems/dlvhex/.

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Author information

Authors and Affiliations

  1. University of Calabria, Rende, Italy

    Mario Alviano

  2. University of Huddersfield, Huddersfield, UK

    Wolfgang Faber

Authors
  1. Mario Alviano
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  2. Wolfgang Faber
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Correspondence to Mario Alviano .

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Editors and Affiliations

  1. University of California, Santa Cruz, USA

    Balder ten Cate

  2. National University of Ireland, Galway, Ireland

    Alessandra Mileo

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Alviano, M., Faber, W. (2015). Supportedly Stable Answer Sets for Logic Programs with Generalized Atoms. In: ten Cate, B., Mileo, A. (eds) Web Reasoning and Rule Systems. RR 2015. Lecture Notes in Computer Science(), vol 9209. Springer, Cham. https://doi.org/10.1007/978-3-319-22002-4_4

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  • DOI: https://doi.org/10.1007/978-3-319-22002-4_4

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  • Online ISBN: 978-3-319-22002-4

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