A more expressive formulation of many sorted logic
Journal of Automated Reasoning
A many-sorted calculus based on resolution and paramodulation
A many-sorted calculus based on resolution and paramodulation
Computational aspects of an order-sorted logic with term declarations
Computational aspects of an order-sorted logic with term declarations
The substitutional framework for sorted deduction: fundamental results on hybrid reasoning
Artificial Intelligence - Special issue on knowledge representation
Theorem proving with ordering and equality constrained clauses
Journal of Symbolic Computation
First-order logic and automated theorem proving (2nd ed.)
First-order logic and automated theorem proving (2nd ed.)
Tableau methods for a logic with term declarations
Journal of Symbolic Computation - Special issue on advances in first-order theorem proving
What You Always Wanted to Know about Rigid E-Unification
Journal of Automated Reasoning
Free Variable Tableaux for a Logic with Term Declarations
TABLEAUX '98 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Reasoning with Preorders and Dynamic Sorts Using Free Variable Tableaux
AISMC-3 Proceedings of the International Conference AISMC-3 on Artificial Intelligence and Symbolic Mathematical Computation
A Many Sorted Logic with Possibly Empty Sorts
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
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In this paper we integrate a sorted unification calculus into free variable tableau methods for logics with term declarations. The calculus we define is used to close a tableau at once, unifying a set of equations derived from pairs of potentially complementary literals occurring in its branches. Apart from making the deduction system sound and complete, the calculus is terminating and so, it can be used as a decision procedure. In this sense we have separated the complexity of sorts from the undecidability of first order logic.