Automated deduction in nonclassical logics
Automated deduction in nonclassical logics
First-order logic and automated theorem proving (2nd ed.)
First-order logic and automated theorem proving (2nd ed.)
Constraints in computational logics
The Even More Liberalized delta-Rule in Free Variable Semantic Tableaux
KGC '93 Proceedings of the Third Kurt Gödel Colloquium on Computational Logic and Proof Theory
Incremental Closure of Free Variable Tableaux
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Liberalized Variable Splitting
Journal of Automated Reasoning
A Labelled System for IPL with Variable Splitting
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
The TPTP Problem Library and Associated Infrastructure
Journal of Automated Reasoning
A non-clausal connection calculus
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
Consistency of variable splitting in free variable systems of first-order logic
TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
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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.