Elsevier

Journal of Symbolic Computation

Volume 47, Issue 9, September 2012, Pages 1046-1065
Journal of Symbolic Computation

Incremental variable splitting

https://doi.org/10.1016/j.jsc.2011.12.032Get rights and content
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Abstract

The variable splitting method for free-variable tableau calculi provides an admissibility condition under which the same free variables can be assigned values independently on different branches. While this has a large potential for automated proof search, a direct implementation of this condition is impractical. We adapt the incremental closure framework for free variables to variable splitting tableaux by recasting the admissibility condition for closing substitutions into a constraint satisfaction problem. The resulting mechanism allows to check the existence of an admissible closing substitution incrementally during the construction of a proof. We specify a rule-based algorithm for testing satisfiability of constraints that accounts for split variables, and present experimental results based on a prototype variable splitting theorem prover implementation measuring the computational overhead of the variable splitting framework.

Keywords

Theorem proving
Tableaux
Incremental closure
Variable splitting

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