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/lp/association-for-computing-machinery/linking-focusing-and-resolution-with-selection-7uhRyYvP0D
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- Publisher
- Association for Computing Machinery
- Copyright
- Copyright © 2020 ACM
- ISSN
- 1529-3785
- eISSN
- 1557-945X
- DOI
- 10.1145/3373276
- Publisher site
- See Article on Publisher Site
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 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.
Journal
ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery
Published: Feb 20, 2020
Keywords: Sequent calculus