Reasoning with Preorders and Dynamic Sorts Using Free Variable Tableaux

In this paper we present a three valued many sorted logic for dealing with preorders, incorporating subsort relations into the syntax of the language, and where formulas taking the third boolean value as interpretation contain a term or a predicate which is not well-sorted w.r.t. the signature. For this logic a ground tableau-based deduction method and a free variable extension version are proposed, proving their completeness.

[1]  Susana Nieva,et al.  Free Variable Tableaux for a Many Sorted Logic with Preorders , 1996, AMAST.

[2]  Harald Ganzinger,et al.  Rewrite techniques for transitive relations , 1994, Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science.

[3]  Jordi Levy,et al.  Bi-rewriting, a Term Rewriting Technique for Monotonic Order Relations , 1993, RTA.

[4]  Melvin Fitting,et al.  First-Order Logic and Automated Theorem Proving , 1990, Graduate Texts in Computer Science.

[5]  M. Schmidt-Schauβ.  Computational Aspects of an Order-Sorted Logic with Term Declarations , 1989 .

[6]  Bernhard Beckert,et al.  An Improved Method for Adding Equality to Free Variable Semantic Tableaux , 1992, CADE.

[7]  Kenneth Kunen,et al.  Completeness Results for Inequality Provers , 1985, Artif. Intell..

[8]  Antonio Gavilanes-Franco,et al.  A First Order Logic for Partial Functions , 1990, Theor. Comput. Sci..

[9]  Christoph Walther,et al.  Many-Sorted Resolution and Paramodulation , 1987 .

[10]  Christoph Walther.  Many-Sorted Inferences in Automated Theorem Proving , 1989, Sorts and Types in Artificial Intelligence.

[11]  Christoph Weidenbach,et al.  A sorted logic using dynamic sorts , 1991 .

[12]  Harald Ganzinger,et al.  Ordered chaining calculi for first-order theories of binary relations , 1995 .

[13]  Larry M. Hines.  The Central Variable Strategy of Str+ve , 1992, CADE.

[14]  Christoph Walther,et al.  A Many-Sorted Calculus Based on Resolution and Paramodulation , 1982, IJCAI.

[15]  Christoph Weidenbach.  First-Order Tableaux with Sorts , 1995, Log. J. IGPL.

[16]  Peter H. Schmitt,et al.  Tableau Calculus for Order Sorted Logic , 1990, Sorts and Types in Artificial Intelligence.

[17]  José Meseguer,et al.  Order-Sorted Algebra I: Equational Deduction for Multiple Inheritance, Overloading, Exceptions and Partial Operations , 1992, Theor. Comput. Sci..

[18]  Susana Nieva,et al.  Foundations of a theorem prover for functional and mathematical uses , 1993, J. Appl. Non Class. Logics.

[19]  Michael J. Maher,et al.  Constraint Logic Programming: A Survey , 1994, J. Log. Program..