Extensional higher-order resolution
In this paper we present an extensional higher-order resolution calculus that is complete relative to Henkin model semantics. The treatment of the extensionality principles — necessary for the completeness result — by specialized (goal-directed) inference rules is of practical applicability, as an implentation of the calculus in the LEO-System shows. Furthermore, we prove the long-standing conjecture, that it is sufficient to restrict the order of primitive substitutions to the order of input formulae.
KeywordsInference Rule Extensionality Principle Head Variable Empty Clause Extensionality Rule
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- [And86]Peter B. Andrews. An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. Academic Press, 1986.Google Scholar
- [Bar84]H. P. Barendregt. The Lambda Calculus. North Holland, 1984.Google Scholar
- [Ben97]Christoph Benzmüller. A calculus and a system architecture for extensional higher-order resolution. Research Report 97-198, Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh,USA, June 1997.Google Scholar
- [BK97]Christoph Benzmüuller and Michael Kohlhase. Model existence for higher-order logic. SEKI-Report SR-97-09, UniversitÄt des Saarlandes, 1997.Google Scholar
- [BK98]Christoph Benzmüller and Michael Kohlhase. LEO, a higher-order theorem prover. to appear at CADE-15, 1998.Google Scholar
- [dB72]Nicolaas Govert de Bruijn. Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with an application to the Church-Rosser theorem. Indagationes Mathematicae, 34(5):381–392, 1972.Google Scholar
- [Hue73]Gérard P. Huet. A mechanization of type theory. In Donald E. Walker and Lewis Norton, editors, Proc. IJCAI'73, pages 139–146, 1973.Google Scholar
- [Koh94]Michael Kohlhase. A Mechanization of Sorted Higher-Order Logic Based on the Resolution Principle. PhD thesis, UniversitÄt des Saarlandes, 1994.Google Scholar
- [Koh95]Michael Kohlhase. Higher-Order Tableaux. In P. Baumgartner, et al. eds, TABLEAUX'95, volume 918 of LNAI, pages 294–309, 1995.Google Scholar
- [Mil83]Dale Miller. Proofs in Higher-Order Logic. PhD thesis, Carnegie-Mellon University, 1983.Google Scholar