Abstract
Resolution and sequent calculus are two well-known formal proof systems. Their differences make them suitable for distinct tasks. Resolution and its variants are very efficient for automated reasoning and are in fact the theoretical basis of many theorem provers. However, being intentionally machine oriented, the resolution calculus is not as natural for human beings and the input problem needs to be pre-processed to clause normal form. Sequent calculus, on the other hand, is a modular formalism that is useful for analysing meta-properties of various logics and is, therefore, popular among proof theorists. The input problem does not need to be pre-processed, and proofs are more detailed. However, proofs also tend to be larger and more verbose. When the worlds of proof theory and automated theorem proving meet, translations between resolution and sequent calculus are often necessary. In this paper, we compare three translation methods and analyse their complexity.
Publisher
Cambridge University Press (CUP)
Subject
Computer Science Applications,Mathematics (miscellaneous)
Reference33 articles.
1. The Higher-Order Prover Leo-II
2. The Complexity of Propositional Proofs
3. System Description: The Proof Transformation System CERES
4. Maslov S.J. (1964). An Inverse Method of Establishing Deducibilities in the Classical Predicate Calculus, Reprinted in Siekmann, Wrightson: Automation of reasoning 1: classical papers on computational logic 1957–1966, 1983, pp. 17–20.
5. System Description: GAPT 2.0