Soundness and completeness proofs by coinductive methods

Blanchette, Jasmin Christian, Popescu, Andrei and Traytel, Dmitriy (2017) Soundness and completeness proofs by coinductive methods. Journal of Automated Reasoning, 58 (1). pp. 149-179. ISSN 0168-7433 (doi:10.1007/s10817-016-9391-3)

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Abstract

We show how codatatypes can be employed to produce compact, high-level proofs of key results in logic: the soundness and completeness of proof systems for variations of first-order logic. For the classical completeness result, we first establish an abstract property of possibly infinite derivation trees. The abstract proof can be instantiated for a wide range of Gentzen and tableau systems for various flavors of first-order logic. Soundness becomes interesting as soon as one allows infinite proofs of first-order formulas. This forms the subject of several cyclic proof systems for first-order logic augmented with inductive predicate definitions studied in the literature. All the discussed results are formalized using Isabelle/HOL’s recently introduced support for codatatypes and corecursion. The development illustrates some unique features of Isabelle/HOL’s new coinductive specification language such as nesting through non-free types and mixed recursion–corecursion.

Item Type: Article
Additional Information: The final publication is available at Springer via https://doi.org/10.1007/s10817-016-9391-3.
Research Areas: A. > School of Science and Technology
A. > School of Science and Technology > Computer Science
Item ID: 21796
Depositing User: Jennifer Basford
Date Deposited: 08 May 2017 11:05
Last Modified: 02 Apr 2019 14:53
URI: https://eprints.mdx.ac.uk/id/eprint/21796

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