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Automating Automated Reasoning

The Case of Two Generic Automated Reasoning Tools

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Description Logic, Theory Combination, and All That

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11560))

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Abstract

The vision of automated support for the investigation of logics, proposed decades ago, has been implemented in many forms, producing numerous tools that analyze various logical properties (e.g., cut-elimination, semantics, and more). However, full ‘automation of automated reasoning’ in the sense of automatic generation of efficient provers has remained a ‘holy grail’ of the field. Creating a generic prover which can efficiently reason in a given logic is challenging, as each logic may be based on a different language, and involve different inference rules, that require different implementation considerations to achieve efficiency, or even tractability. Two recently introduced generic automated provers apply different approaches to tackle this challenge. \({\text {MetTeL}}\), based on the formalism of tableaux, automatically generates a prover for a given tableau calculus, by implementing generic proof-search procedures with optimizations applicable to many tableau calculi. \({\text {Gen2sat}}\), based on the formalism of sequent calculi, shifts the burden of search to the realm of off-the-shelf SAT solvers by applying a uniform reduction of derivability in sequent calculi to SAT. This paper examines these two generic provers, focusing in particular on criteria relevant for comparing their performance and usability. To this end, we evaluate the performance of the tools, and describe the results of a preliminary empirical study where user experiences of expert logicians using the two tools are compared.

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Notes

  1. 1.

    Here sequents are taken 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 [12] and can be found at http://www.logic.at/people/lara/paralyzer.html.

  3. 3.

    Note that a translation of \(\mathcal{T}\) to a sequent calculus is less obvious, as this is a three-sided calculus, where \({\text {Gen2sat}}\) employs ordinary two-sided sequents.

  4. 4.

    https://github.com/yoni206/gen2satvsmettel.

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Acknowledgments

We thank Francesco Genco, Yotam Feldman, Roman Kuznets, Giselle Reis, João Marcos, and Bruno Woltzenlogel Paleo for providing valuable feedback on both tools. e also thank Mohammad Khodadadi for useful discussions and setting up the \({\text {MetTeL}}\) website. he research of the first and fourth authors was supported by The Israel Science Foundation (grant no. 817-15). The research of the second and third authors was supported by UK EPSRC research grant EP/H043748/1.

Last but not least, we extend our best wishes to Franz Baader on the occasion of his 60th birthday. It is an immense privilege to have been asked to contribute to this volume.

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Authors and Affiliations

  1. Computer Science Department, Stanford University, Stanford, USA

    Yoni Zohar

  2. School of Computer Science, University of Manchester, Manchester, UK

    Dmitry Tishkovsky & Renate A. Schmidt

  3. Information Systems Department, University of Haifa, Haifa, Israel

    Anna Zamansky

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  1. Yoni Zohar
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Editors and Affiliations

  1. University of Bremen, Bremen, Germany

    Carsten Lutz

  2. University of Manchester, Manchester, UK

    Uli Sattler

  3. University of Iowa, Iowa City, IA, USA

    Cesare Tinelli

  4. TU Dresden, Dresden, Germany

    Anni-Yasmin Turhan

  5. University of Liverpool, Liverpool, UK

    Frank Wolter

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Zohar, Y., Tishkovsky, D., Schmidt, R.A., Zamansky, A. (2019). Automating Automated Reasoning. In: Lutz, C., Sattler, U., Tinelli, C., Turhan, AY., Wolter, F. (eds) Description Logic, Theory Combination, and All That. Lecture Notes in Computer Science(), vol 11560. Springer, Cham. https://doi.org/10.1007/978-3-030-22102-7_29

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