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, 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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Contributor : Guillaume Burel <>
Submitted on : Friday, April 27, 2018 - 12:12:21 PM
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Guillaume Burel. Linking Focusing and Resolution with Selection. 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018), Aug 2018, Liverpool, United Kingdom. pp.9:1-9:14, ⟨10.4230/LIPIcs.MFCS.2018.9⟩. ⟨hal-01670476v3⟩



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