First-order logic and automated theorem proving (2nd ed.)
First-order logic and automated theorem proving (2nd ed.)
JELIA '96 Proceedings of the European Workshop on Logics in Artificial Intelligence
Hyper Tableau - The Next Generation
TABLEAUX '98 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Incremental Closure of Free Variable Tableaux
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
KI '97 Proceedings of the 21st Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
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Hyper tableau reasoning is a version ofclausal form tableau reasoning where all negative literals in a clause are resolved away in a single inference step. Constrained hyper tableaux are a generalization ofh yper tableaux, where branch closing substitutions, from the point ofview ofmo del generation, give rise to constraints on satisfying assignments for the branch. These variable constraints eliminate the need for the awkward 'purifying substitutions' of hyper tableaux. The paper presents a non-destructive and proof confluent calculus for constrained hyper tableaux, together with a soundness and completeness proof, with completeness based on a new way to generate models from open tableaux. It is pointed out that the variable constraint approach applies to free variable tableau reasoning in general.