A first order extension of stålmarck’s method

Authors:
Magnus Björk
Affiliations:
Department of Computing Science, Chalmers University of Technology, Gothenburg, Sweden
Venue:
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Year:
2005

Citing 2
Cited 2

First-order logic and automated theorem proving (2nd ed.)

First-order logic and automated theorem proving (2nd ed.)
A Tutorial on Stålmarck‘s Proof Procedure for PropositionalLogic

Formal Methods in System Design - Special issue on formal methods for computer-added design

First Order Stålmarck

Journal of Automated Reasoning
Semantics and proof-theory of depth bounded Boolean logics

Theoretical Computer Science

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Abstract

We describe an extension of Stålmarck’s method in First Order Logic. Stålmarck’s method is a tableaux-like theorem proving method for propositional logic, that uses a branch-and-merge rule known as the dilemma rule. This rule opens two branches and later merges them, by retaining their common consequences. The propositional version does this with normal set intersection, while the FOL version searches for pairwise unifiable formulae from the two branches. The proof procedure attempts to find proofs with as few simultaneously open branches as possible. We present the proof system and a proof procedure, and show soundness and completeness. We also present benchmarks for an implementation of the proof procedure.