Abstract
We propose a sound and complete free variable semantic tableau method for handling many-sorted preorders in a first order logic, where functions and predicates behave monotonically or antimonotonically. We formulate additional expansion tableau rules as a more efficient alternative to adding the axioms characterizing a preordered structure. Completeness of the system is proved in detail. Examples and applications are introduced.
This paper has been supported by Proyecto Precompetitivo PR 219/94 5564.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
L. Bachmair, H. Ganzinger. Ordered Chaining for Total Orderings. Proc. CADE-12. A. Bundy ed. LNAI 814, 435–450 Springer 1994.
B. Beckert, R. Hähnle. An Improved Method for Adding Equality to Free Variable Semantic Tableaux. Proc. CADE-10. M.E. Stickel ed. LNAI 607, 507–521. Springer 1992.
M. Fitting. First-Order modal tableaux. Journal of Automated Reasoning 4, 191–213 1988.
M. Fitting. First-Order Logic and Automated Theorem Proving. Springer, 2nd edition 1996.
A. Gavilanes-Franco, F. Lucio-Carrasco. A first order logic for partial functions. Theoretical Computer Science 74, 37–69, 1990.
A. Gavilanes, J. Leach, S. Nieva. Free Variable Tableaux for a Many Sorted Logic with Preorders. Technical Report DIA 23/96 Univ. Complutense Madrid 1996.
J. A. Goguen, J. Meseguer. Order-sorted algebra I: Equational deduction for multiple inheritance, overloading, exceptions and partial operations. Theoretical Computer Science 105, 217–273, 1992.
R. Hähnle, P. H. Schmitt. The liberalized δ-rule in free variable semantic tableaux. Journal of Automated Reasoning. 13, 211–221, 1994.
H.Hussmann. Nondeterministic Algebraic Specifications. PhD. thesis, Institut für Informatik, Technische Universität München, 1991.
J. Jaffar, M. J. Maher. Constraint logic programming: A survey. Journal of Logic Programming 19/20, 503–582, 1994.
J. Levy, J. Agustí. Bi-rewriting, a term rewriting technique for monotonic order relations. Proc. RTA'93. C. Kirchner ed. LNCS 690, 17–31. Springer 1993.
J. Leach, S. Nieva. Foundations of a Theorem Prover for Functional and Mathematical Uses. Journal of Applied Non-Classical Logics 3(1), 7–38, 1993.
J. Meseguer. Conditional rewriting logic as a unified model of concurrency. Theoretical Computer Science 96, 73–155, 1992.
F. Oppacher, E. Suen. HARP: A Tableau-Based Theorem Prover. Journal of Automated Reasoning 4, 69–100, 1988.
C. Walther. Many Sorted Inferences in Automated Theorem Proving. Proc. Workshop on Sorts and Types in Artificial Intelligence (1989). K.H. Bläsius, U. Hedtstück, C.-R. Rollinger eds. LNAI 418, 18–48. Springer 1990.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gavilanes, A., Leach, J., Nieva, S. (1996). Free variable tableaux for a many sorted logic with preorders. In: Wirsing, M., Nivat, M. (eds) Algebraic Methodology and Software Technology. AMAST 1996. Lecture Notes in Computer Science, vol 1101. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014310
Download citation
DOI: https://doi.org/10.1007/BFb0014310
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61463-0
Online ISBN: 978-3-540-68595-1
eBook Packages: Springer Book Archive