A Resolution-Based Decision Procedure for the Two-Variable Fragment with 
Equality

de Nivelle, Hans; Pratt-Hartmann, Ian

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A Resolution-Based Decision Procedure for the Two-Variable Fragment with Equality

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de Nivelle, Hans
Programming Logics, MPI for Informatics, Max Planck Society;

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Pratt-Hartmann, Ian
Programming Logics, MPI for Informatics, Max Planck Society;

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Citation

de Nivelle, H., & Pratt-Hartmann, I. (2001). A Resolution-Based Decision Procedure for the Two-Variable Fragment with Equality. In R. Goré, A. Leitsch, & T. Nipkow (Eds.), Automated reasoning: First International Joint Conference, IJCAR 2001 (pp. 211-225). Berlin, Germany: Springer.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-31DF-7

Abstract

The two-variable fragment of first-order logic is the set of formulas that do not contain function symbols, that possibly contain equality, and that contain at most two variables. This paper shows how resolution theorem-proving techniques can be used to provide an algorithm for deciding whether or not any given formula in the two-variable fragment is satisfiable. Previous resolution-based techniques could deal only with the equality-free subset of the two-variable fragment.