文章基本信息

标题：Linking Focusing and Resolution with Selection
本地全文：下载
作者：Guillaume Burel
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2018
卷号：117
页码：1-14
DOI：10.4230/LIPIcs.MFCS.2018.9
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：logic in computer science; automated deduction; proof theory; sequent calculus; refinements of resolution; deduction modulo theory; polarization