Abstract
The study of sorted unification has progressed by developing algorithms for more and more general languages. This paper addresses the question of what can be said about sorted unification independent of the sorted language being used. This is done by abstracting away from the particulars of sorted languages and formulating a set of transformation rules for solving sorted unification problems in general. Strategies for controlling these transformation rules are examined to see which prevent a certain kind of infinite execution.
Preview
Unable to display preview. Download preview PDF.
References
Hans-JĂĽrgen BĂĽrckert. A Resolution Principle for Clauses with Constraints. Research Report RR-90-02, German Research Center for Artificial Intelligence, March 1990.
B. Bogaert and S. Tison. Equality and disequality constraints on brother terms in tree automata. In A. Finkel, editor, Proc. of the Ninth Symposium on Theoretical Aspects of Computer Science, Paris, Springer-Verlag, 1992.
H. Chen and J. Hsiang. Logic programming with recurrence domains. In Proc. of the Eighteenth International Colloquium on Automata, Languages and Computation, pages 20–34, Madrid, Spain, Springer-Verlag, July 1991.
H. Comon and C. Delor. Equational Formulae with Membership Constraints. Rapport de Recherche 649, LRI, Université de Paris Sud, Orsay, France, March 1991.
A. M. Frisch. The substitutional framework for sorted deduction: Fundamental results on hybrid reasoning. Artificial Intelligence, 49:161–198, 1991.
M. Höhfeld and G. Smolka. Definite Relations over Constraint Languages. Lilog-Report 53, IBM Deutschland, October 1988.
J. Jaffar and J. Lassez. Constraint logic programming. In Proc. of the 14th ACM Principles of Programming Languages Conference, pages 111–119, Munich, January 1987.
J.-P. Jouannaud and C. Kirchner. Solving equations in abstract algebras: A rule-based survey of unification. In J.-L. Lassez and G. Plotkin, editors, Computational Logic: Essays in Honor of Alan Robinson, chapter 8, pages 257–321, MIT Press, Cambridge, MA, 1991.
Alberto Martelli and Ugo Montanari. An efficient unification algorithm. ACM Transactions on Programming Languages and Systems, 4(2):258–282, April 1982.
Raymond Reiter. An Approach to Deductive Question-Answering. BBN Technical Report 3649, Bolt Beranek and Newman, Inc., 1977.
M. Schmidt-SchauĂź. Computational Aspects of an Order-Sorted Logic with Term Declarations. Volume 395 of Lecture Notes in Computer Science, Springer-Verlag, New York, NY, 1989.
Gert Smolka, Werner Nutt, Joseph A. Goguen, and José Meseguer. Order-sorted equational computation. In Hassan Aït-Kaci and Maurice Nivat, editors, Resolution of Equations in Algebraic Structures, Volume 2, Rewriting Techniques, chapter 10, pages 297–367, Academic Press, New York, 1989.
T. E. Uribe. Sorted unification using set constraints. In D. Kapur, editor, Proceedings of the Eleventh International Conference on Automated Deduction, Saratoga Srpings, NY, June 1992.
Christoph Walther. Many-sorted unification. Journal of the ACM, 35(1):1–17, January 1988.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Frisch, A.M., Cohn, A.G. (1992). An abstract view of sorted unification. In: Kapur, D. (eds) Automated Deduction—CADE-11. CADE 1992. Lecture Notes in Computer Science, vol 607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55602-8_164
Download citation
DOI: https://doi.org/10.1007/3-540-55602-8_164
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55602-2
Online ISBN: 978-3-540-47252-0
eBook Packages: Springer Book Archive