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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Communication dans un congrès
Igor Potapov; Paul Spirakis; James Worrell. 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018), Aug 2018, Liverpool, United Kingdom. Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 117, pp.9:1-9:14, 2018, Leibniz International Proceedings in Informatics (LIPIcs). 〈http://mfcs2018.csc.liv.ac.uk/〉. 〈10.4230/LIPIcs.MFCS.2018.9〉
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Contributeur : Guillaume Burel <>
Soumis le : vendredi 27 avril 2018 - 12:12:21
Dernière modification le : jeudi 7 février 2019 - 14:23:25

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Guillaume Burel. Linking Focusing and Resolution with Selection. Igor Potapov; Paul Spirakis; James Worrell. 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018), Aug 2018, Liverpool, United Kingdom. Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 117, pp.9:1-9:14, 2018, Leibniz International Proceedings in Informatics (LIPIcs). 〈http://mfcs2018.csc.liv.ac.uk/〉. 〈10.4230/LIPIcs.MFCS.2018.9〉. 〈hal-01670476v3〉

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