Journal of Automated Reasoning

, Volume 38, Issue 1–3, pp 3–30 | Cite as

Liberalized Variable Splitting

Article

Abstract

Variable splitting is a technique applicable to free variable tableaux, sequent calculi, and matrix characterizations that exploits a relationship between β- and γ-rules. Using contextual information to differentiate between occurrences of the same free variable in different branches, the technique admits conditions under which these occurrences may safely be assigned different values by substitutions. This article investigates a system of variable splitting and shows its consistency by a semantical argument. The splitting system is liberalized with respect to β-inferences analogously to a well-known liberalization of δ-rules, and this is used to show an exponential speedup compared to free variable systems without splitting.

Key words

connection method tableau calculus first-order logic free variables variable splitting 

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Department of InformaticsUniversity of OsloOsloNorway

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