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Superposition for Lambda-Free Higher-Order Logic

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Automated Reasoning (IJCAR 2018)

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Abstract

We introduce refutationally complete superposition calculi for intentional and extensional \(\lambda \)-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a term order that need not be fully monotonic, making it possible to employ the \(\lambda \)-free higher-order lexicographic path and Knuth–Bendix orders. We implemented the calculi in the Zipperposition prover and evaluated them on TPTP benchmarks. They appear promising as a stepping stone towards complete, efficient automatic theorem provers for full higher-order logic.

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Notes

  1. 1.

    https://github.com/c-cube/zipperposition

  2. 2.

    http://matryoshka.gforge.inria.fr/pubs/lfhosup_data/

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Acknowledgment

We are grateful to the maintainers of StarExec for letting us use their service. We want to thank Christoph Benzmüller, Sander Dahmen, Johannes Hölzl, Anders Schlichtkrull, Stephan Schulz, Alexander Steen, Geoff Sutcliffe, Andrei Voronkov, Petar Vukmirović, Daniel Wand, Christoph Weidenbach, and the participants in the 2017 Dagstuhl Seminar on Deduction beyond First-Order Logic for stimulating discussions. We also want to thank Mark Summerfield, Sophie Tourret, and the anonymous reviewers for suggesting several textual improvements to this paper and to the technical report. Bentkamp and Blanchette’s research has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 713999, Matryoshka).

Author information

Authors and Affiliations

  1. Vrije Universiteit Amsterdam, Amsterdam, The Netherlands

    Alexander Bentkamp & Jasmin Christian Blanchette

  2. Max-Planck-Institut für Informatik, Saarland Informatics Campus, Saarbrücken, Germany

    Jasmin Christian Blanchette & Uwe Waldmann

  3. Université de Lorraine, CNRS, Inria, LORIA, Nancy, France

    Jasmin Christian Blanchette & Simon Cruanes

  4. Aesthetic Integration, Austin, TX, USA

    Simon Cruanes

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  1. Alexander Bentkamp
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  2. Jasmin Christian Blanchette
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  4. Uwe Waldmann
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Correspondence to Alexander Bentkamp .

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Editors and Affiliations

  1. Université de Lorraine, Vandoeuvre-lès-Nancy, France

    Didier Galmiche

  2. Baden-Wuerttemberg Cooperative State University, Stuttgart, Germany

    Stephan Schulz

  3. University of Trento, Trento, Italy

    Roberto Sebastiani

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Bentkamp, A., Blanchette, J.C., Cruanes, S., Waldmann, U. (2018). Superposition for Lambda-Free Higher-Order Logic. In: Galmiche, D., Schulz, S., Sebastiani, R. (eds) Automated Reasoning. IJCAR 2018. Lecture Notes in Computer Science(), vol 10900. Springer, Cham. https://doi.org/10.1007/978-3-319-94205-6_3

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