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Linking Focusing and Resolution with Selection Burel, Guillaume logic in computer science automated deduction proof theory sequent calculus refinements of resolution deduction modulo theory polarization 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 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Guillaume Burel 2018 Is Part Of LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2018.9 urn:nbn:de:0030-drops-95917 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.9 eng https://creativecommons.org/licenses/by/3.0/legalcode