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Gen2sat: An Automated Tool for Deciding Derivability in Analytic Pure Sequent Calculi

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Automated Reasoning (IJCAR 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9706))

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Abstract

Gen2sat [1] is an efficient and generic tool that can decide derivability for a wide variety of propositional non-classical logics given in terms of a sequent calculus. It contributes to the line of research on computer-supported tools for investigation of logics in the spirit of the “logic engineering” paradigm. Its generality and efficiency are made possible by a reduction of derivability in analytic pure sequent calculi to SAT. This also makes Gen2sat a “plug-and-play” tool so it is compatible with any standard off-the-shelf SAT solver and does not require any additional logic-specific resources. We describe the implementation details of Gen2sat and an evaluation of its performance, as well as a pilot study for using it in a “hands on” assignment for teaching the concept of sequent calculi in a logic class for engineering practitioners.

This research was supported by The Israel Science Foundation (grant no. 817-15).

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Notes

  1. 1.

    We take sequents to be pairs of sets of formulas, and therefore exchange and contraction are built in.

  2. 2.

    Paralyzer is a tool that transforms Hilbert calculi of a certain general form into equivalent analytic sequent calculi. It was described in [7] and can be found at http://www.logic.at/people/lara/paralyzer.html.

  3. 3.

    The tableau calculus for \(C_1\) in \({\text {KEMS}}\) can be translated to a sequent calculus (the connection between the two frameworks was discussed e.g. in [3]). However, the translated sequent calculus is non-analytic,and thus cannot be used with Gen2sat.

  4. 4.

    Out of 11 possible formula comparator choices of KEMS, Table 1 presents the results for the best performing one in each problem.

  5. 5.

    The second author has been teaching the course for several years at the University of Haifa; see [25] for further details on the course design.

  6. 6.

    Interestingly, seven students employed new connectives with arity greater than 2 and three employed also 0-ary connectives (which indeed increased coverage), although they have not seen any such example in class.

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Author information

Authors and Affiliations

  1. Tel Aviv University, Tel Aviv, Israel

    Yoni Zohar

  2. Haifa University, Haifa, Israel

    Anna Zamansky

Authors
  1. Yoni Zohar
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  2. Anna Zamansky
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Correspondence to Yoni Zohar .

Editor information

Editors and Affiliations

  1. Aix-Marseille University, Marseille, France

    Nicola Olivetti

  2. SRI International, Menlo Park, California, USA

    Ashish Tiwari

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Zohar, Y., Zamansky, A. (2016). Gen2sat: An Automated Tool for Deciding Derivability in Analytic Pure Sequent Calculi. In: Olivetti, N., Tiwari, A. (eds) Automated Reasoning. IJCAR 2016. Lecture Notes in Computer Science(), vol 9706. Springer, Cham. https://doi.org/10.1007/978-3-319-40229-1_33

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  • DOI: https://doi.org/10.1007/978-3-319-40229-1_33

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