Linking Focusing and Resolution with Selection

Abstract : Focusing and selection are techniques that shrink the proof search space for respectively sequent calculi and resolution. To bring out a link between them, we generalize them both: we introduce a sequent calculus where each occurrence of an atom can have a positive or a negative polarity; and a resolution method where each literal, whatever its sign, can be selected in input clauses. We prove the equivalence between cut-free proofs in this sequent calculus and derivations of the empty clause in that resolution method. Such a generalization is not semi-complete in general, which allows us to consider complete instances that correspond to theories of any logical strength. We present three complete instances: first, our framework allows us to show that ordinary focusing corresponds to hyperresolution and semantic resolution; the second instance is deduction modulo theory and the related framework called superdeduction; and a new setting extends deduction modulo theory with rewriting rules having several left-hand sides, therefore restricting even more the proof search space.
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Pré-publication, Document de travail
2018
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https://hal.inria.fr/hal-01670476
Contributeur : Guillaume Burel <>
Soumis le : lundi 12 mars 2018 - 14:05:53
Dernière modification le : mercredi 14 mars 2018 - 01:14:05

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  • HAL Id : hal-01670476, version 2

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Guillaume Burel. Linking Focusing and Resolution with Selection. 2018. 〈hal-01670476v2〉

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