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Interpolation and Quantifiers in Ortholattices

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14499))

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Abstract

We study quantifiers and interpolation properties in orthologic, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based proof system for quantified orthologic, which we prove sound and complete for the class of all complete ortholattices. We show that orthologic does not admit quantifier elimination in general. Despite that, we show that interpolants always exist in orthologic. We give an algorithm to compute interpolants efficiently. We expect our result to be useful to quickly establish unreachability as a component of verification algorithms.

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Notes

  1. 1.

    https://github.com/sankalpgambhir/ol-interpolation.

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Authors and Affiliations

  1. EPFL, School of Computer and Communication Sciences, Lausanne, Switzerland

    Simon Guilloud, Sankalp Gambhir & Viktor Kunčak

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  1. Simon Guilloud
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  2. Sankalp Gambhir
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  3. Viktor Kunčak
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Correspondence to Simon Guilloud .

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Editors and Affiliations

  1. CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

    Rayna Dimitrova

  2. Tel Aviv University, Tel Aviv, Israel

    Ori Lahav

  3. New York University, New York, NY, USA

    Sebastian Wolff

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Guilloud, S., Gambhir, S., Kunčak, V. (2024). Interpolation and Quantifiers in Ortholattices. In: Dimitrova, R., Lahav, O., Wolff, S. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2024. Lecture Notes in Computer Science, vol 14499. Springer, Cham. https://doi.org/10.1007/978-3-031-50524-9_11

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  • DOI: https://doi.org/10.1007/978-3-031-50524-9_11

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