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Towards Verifying Logic Programs in the Input Language of clingo

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Fields of Logic and Computation III

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12180))

Abstract

We would like to develop methods for verifying programs in the input language of the answer set solver clingo using software created for the automation of reasoning in first-order theories. As a step in this direction, we extend Clark’s completion to a class of clingo programs that contain arithmetic operations as well as intervals and prove that every stable model is a model of generalized completion. The translator anthem calculates the completion of a program and represents it in a format that can be processed by first-order theorem provers. Some properties of programs can be verified by anthem and the theorem prover vampire, working together.

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Notes

  1. 1.

    Answer set solvers are logic programming systems that calculate stable models (answer sets) of logic programs. Some of the best-known systems of this kind are clingo (https://potassco.org/) and dlv (http://www.dlvsystem.com/).

  2. 2.

    As discussed in Sect. 2.1, the “interval term” 0..n in the first rule of this program is an arithmetic expression that has multiple values—all integers from 0 to n. The equality between a variable and an interval term in the body of a rule expresses that the value of the variable is equal to one of the values of the term.

  3. 3.

    We talk about program variables and program terms to distinguish them from the variables and terms that are allowed in formulas (Sect. 3) and thus can be found in the output of anthem.

  4. 4.

    It differs from the translation \(\tau ^B\) [12, Section 6] in that it disregards the combination \( not \, not \). Double negations are essential in the formulas that characterize stable models but not in completion formulas.

  5. 5.

    https://github.com/potassco/anthem/releases.

References

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Acknowledgements

We are grateful to Laura Kovács, Giles Reger, and Martin Suda for taking the time to answer our questions about the use of vampire. Also, we would like to thank the anonymous referee for giving us useful suggestions.

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Authors and Affiliations

  1. University of Texas at Austin, Austin, USA

    Vladimir Lifschitz

  2. University of Potsdam, Potsdam, Germany

    Patrick Lühne & Torsten Schaub

Authors
  1. Vladimir Lifschitz
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  2. Patrick Lühne
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  3. Torsten Schaub
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Corresponding author

Correspondence to Torsten Schaub .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, USA

    Andreas Blass

  2. Université Paris Est Créteil, Fontainebleau, France

    Patrick Cégielski

  3. School of Computer Science, Tel Aviv University, Tel Aviv, Israel

    Nachum Dershowitz

  4. Fakultät für Mathematik und Informatik, Universität Leipzig, Leipzig, Germany

    Manfred Droste

  5. Reactive Systems Group, Universitat des Saarlandes, Saarbrücken, Germany

    Bernd Finkbeiner

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Lifschitz, V., Lühne, P., Schaub, T. (2020). Towards Verifying Logic Programs in the Input Language of clingo. In: Blass, A., Cégielski, P., Dershowitz, N., Droste, M., Finkbeiner, B. (eds) Fields of Logic and Computation III. Lecture Notes in Computer Science(), vol 12180. Springer, Cham. https://doi.org/10.1007/978-3-030-48006-6_14

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  • DOI: https://doi.org/10.1007/978-3-030-48006-6_14

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