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International Conference on Logic Programming and Nonmonotonic Reasoning

LPNMR 2017: Logic Programming and Nonmonotonic Reasoning pp 176–190Cite as

Explaining Inconsistency in Answer Set Programs and Extensions

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10377))

Abstract

Answer Set Programming (ASP) is a well-known problem solving approach based on nonmonotonic logic programs. hex-programs extend ASP with external atoms for accessing arbitrary external information. In this paper we study inconsistent ASP- and hex-programs, i.e., programs which do not possess answer sets, and introduce a novel notion of inconsistency reasons for characterizing their inconsistency depending on the input facts. This problem is mainly motivated by upcoming applications for optimizations of the evaluation algorithms for hex-programs. Further applications can be found in ASP debugging. We then analyze the complexity of reasoning problems related to the computation of such inconsistency reasons. Finally, we present a meta-programming encoding in disjunctive ASP which computes inconsistency reasons for given normal logic programs, and a basic procedural algorithm for computing inconsistency reasons for general hex-programs.

This research has been supported by the Austrian Science Fund (FWF) project P27730.

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Notes

  1. 1.

    The distinction is mainly relevant for nonground programs, which we disregard in this paper.

  2. 2.

    For ordinary \(\varPi \), these are Gelfond & Lifschitz’s answer sets.

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Acknowledgements

The author thanks Markus Bretterbauer, who developed a prototype implementation for computing inconsistency reasons as studied in this paper.

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Authors and Affiliations

  1. Institut Für Informationssysteme, Technische Universität Wien, Favoritenstraße 9-11, 1040, Vienna, Austria

    Christoph Redl

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  1. Christoph Redl
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Correspondence to Christoph Redl .

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Editors and Affiliations

  1. Drexel University, Philadelphia, Pennsylvania, USA

    Marcello Balduccini

  2. Aalto University, Espoo, Finland

    Tomi Janhunen

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Redl, C. (2017). Explaining Inconsistency in Answer Set Programs and Extensions. In: Balduccini, M., Janhunen, T. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2017. Lecture Notes in Computer Science(), vol 10377. Springer, Cham. https://doi.org/10.1007/978-3-319-61660-5_16

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  • DOI: https://doi.org/10.1007/978-3-319-61660-5_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-61659-9

  • Online ISBN: 978-3-319-61660-5

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