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Equivalence Between Answer-Set Programs Under (Partially) Fixed Input

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Foundations of Information and Knowledge Systems (FoIKS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9616))

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Abstract

Answer Set Programming (ASP) has become an increasingly popular formalism for declarative problem solving. Among the huge body of theoretical results, investigations of different equivalence notions between logic programs play a fundamental role for understanding modularity and optimization. While strong equivalence between two programs holds if they can be faithfully replaced by each other in any context (facts and rules), uniform equivalence amounts to equivalent behavior of programs under any set of facts. Both notions (as well as several variants thereof) have been extensively studied. However, the somewhat reverse notion of equivalence which holds if two programs are equivalent under the addition of any set of proper rules (i.e., all rules except facts) has not been investigated yet. In this paper, we close this gap and give a thorough study of this notion, which we call rule equivalence (RE), and its parameterized version where we allow facts over a given restricted alphabet to appear in the context. RE is thus a relationship between two programs whose input is (partially) fixed but where additional proper rules might still be added. Such a notion might be helpful in debugging of programs. We give full characterization results and a complexity analysis for the propositional case of RE. Moreover, we show that RE is decidable in the non-ground case.

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Notes

  1. 1.

    Within SE-models, we denote interpretations \(\{ a_1,\ldots , a_n \}\) by juxtaposition \(a_1\cdots a_n\) of their elements.

  2. 2.

    In fact, the programs we use here form a proper subclass of programs compared to [11], where, e.g., also double negation is allowed. However, for our purpose it is sufficient to consider this weaker class.

  3. 3.

    The concept of saturation refers to a programming technique, where reasons for a candidate answer set I to be ruled out are not explicitly stated via constraints, but in terms of rules which ensure that a certain model \(J\subset I\) of the program’s reduct with respect to I exists, see, e.g., [10].

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Acknowledgments

This work was supported by the Austrian Science Fund (FWF) projects P25607 and Y698.

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Authors and Affiliations

  1. Institute of Information Systems, TU Wien, Vienna, Austria

    Bernhard Bliem & Stefan Woltran

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  1. Bernhard Bliem
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  2. Stefan Woltran
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Correspondence to Bernhard Bliem .

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Editors and Affiliations

  1. Faculteit Wetenschappen, Universiteit Hasselt, Hasselt, Belgium

    Marc Gyssens

  2. Dept. Ciencias Ingeniería Computación, Universidad Nacional del Sur, Bahía Blanca, Argentina

    Guillermo Simari

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Bliem, B., Woltran, S. (2016). Equivalence Between Answer-Set Programs Under (Partially) Fixed Input. In: Gyssens, M., Simari, G. (eds) Foundations of Information and Knowledge Systems. FoIKS 2016. Lecture Notes in Computer Science(), vol 9616. Springer, Cham. https://doi.org/10.1007/978-3-319-30024-5_6

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  • DOI: https://doi.org/10.1007/978-3-319-30024-5_6

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