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Journal Articles ACM Transactions on Computational Logic Year : 2020

Linking Focusing and Resolution with Selection


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 atomic formula 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, not captured by any existing framework, extends deduction modulo theory with rewriting rules having several left-hand sides, which restricts even more the proof-search space.
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hal-02908808 , version 1 (29-07-2020)



Guillaume Burel. Linking Focusing and Resolution with Selection. ACM Transactions on Computational Logic, 2020, 21 (3), pp.1-30. ⟨10.1145/3373276⟩. ⟨hal-02908808⟩
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