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Interpolation Systems for Ground Proofs in Automated Deduction: a Survey

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Abstract

Interpolation is a deductive technique applied in program analysis and verification: for example, it is used to compute over-approximations of images or refine abstractions. An interpolation system takes a refutation and extracts an interpolant by building it inductively from partial interpolants. We survey color-based interpolation systems for ground proofs produced by key inference engines of state-of-the-art solvers: DPLL for propositional logic, equality sharing for combination of convex theories, and DPLL(\(\mathcal {T}\)) for SMT-solving. Since color-based interpolation systems use colors to track symbols in proofs, equality is problematic, because replacement of equals by equals mixes symbols and therefore colors. We analyze interpolation in the presence of equality, and we demonstrate the color-based approach by giving a complete interpolation system for ground proofs by superposition.

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  1. Dipartimento di Informatica, Università degli Studi di Verona, Strada Le Grazie 15, 37134, Verona, Italy

    Maria Paola Bonacina

  2. Department of Computer Science, Chalmers University of Technology, Göteborg, Sweden

    Moa Johansson

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  1. Maria Paola Bonacina
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Correspondence to Maria Paola Bonacina.

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Research supported in part by grant no. 2007-9E5KM8 of the Ministero dell’Istruzione Università e Ricerca, Italy, and by COST Action IC0901 Rich-model Toolkit of the European Union.

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Bonacina, M.P., Johansson, M. Interpolation Systems for Ground Proofs in Automated Deduction: a Survey. J Autom Reasoning 54, 353–390 (2015). https://doi.org/10.1007/s10817-015-9325-5

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