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On Heuer’s Procedure for Verifying Strong Equivalence

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Logics in Artificial Intelligence (JELIA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14281))

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Abstract

In answer set programming, two groups of rules are considered strongly equivalent if replacing one group by the other within any program does not affect the set of stable models. Jan Heuer has designed and implemented a system that verifies strong equivalence of programs in the ASP language mini-gringo. The design is based on the syntactic transformation \(\tau ^*\) that converts mini-gringo programs into first-order formulas. Heuer’s assertion about \(\tau ^*\) that was supposed to justify this procedure turned out to be incorrect, and in this paper we propose an alternative justification for his algorithm. We show also that if \(\tau ^*\) is replaced by the simpler and more natural translation \(\nu \) then the algorithm will still produce correct results.

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Notes

  1. 1.

    Lifschitz et al. [20] made the same mistake in their Proposition 6.

  2. 2.

    The need to use a language with two sorts is explained by the fact that function symbols in a first-order language are supposed to represent total functions, and arithmetic operations are not defined on symbolic constants.

  3. 3.

    The symbols / and \(\backslash \) are not included because the corresponding functions are not total on the set of integers. The symbol .. is not included because intervals do not belong to the domain of precomputed terms.

  4. 4.

    Heuer [12, Sections 2.2.3 and 3.3] denotes this translation by \(\sigma ^*\). We switched to \(\gamma \) to avoid confusion with the symbols denoting signatures.

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Authors and Affiliations

  1. University of Nebraska at Omaha, Omaha, USA

    Jorge Fandinno

  2. University of Texas at Austin, Austin, USA

    Vladimir Lifschitz

Authors
  1. Jorge Fandinno
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  2. Vladimir Lifschitz
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Correspondence to Jorge Fandinno .

Editor information

Editors and Affiliations

  1. TU Dresden, Dresden, Germany

    Sarah Gaggl

  2. Artificial Intelligence Research Institute - IIIA CSIC, Barcelona, Spain

    Maria Vanina Martinez

  3. Umeå University, Umeå, Sweden

    Magdalena Ortiz

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Fandinno, J., Lifschitz, V. (2023). On Heuer’s Procedure for Verifying Strong Equivalence. In: Gaggl, S., Martinez, M.V., Ortiz, M. (eds) Logics in Artificial Intelligence. JELIA 2023. Lecture Notes in Computer Science(), vol 14281. Springer, Cham. https://doi.org/10.1007/978-3-031-43619-2_18

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  • DOI: https://doi.org/10.1007/978-3-031-43619-2_18

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  • Online ISBN: 978-3-031-43619-2

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