Abstract
In recent years various sorted logics have been developed, mostly to facilitate knowledge representation and to speed up automated deduction. We present a polymorphic order-sorted logic that can be implemented efficiently. Because the polymorphism is almost unrestricted, it is possible for two terms to have an exponential number of maximally general unifiers. To guarantee a single most general unifier, we embed the sorted logic into a more general constraint logic and create a distinct constraint satisfaction search space. This separates the total search space into two orthogonal ones and facilitates many optimizations. The main complexity gains are that the unnecessary generation of unifiers can be avoided and that the primary resolution search space remains constant if the complexity of the unification grows.
Research carried out at the University of Illinois at Urbana-Champaign, USA.
Preview
Unable to display preview. Download preview PDF.
References
H. Aït-Kaci, R. Boyer, P. Lincoln, and R. Nasr. Efficient lattice operations. ACM Transactions on Programming Languages and Systems, 11(1):115–146, January 1989.
C. Beierle, G. Meyer, and H. Semle. Extending the Warren abstract machine to polymorphic order-sorted resolution. In Logic Programming: Proceedings of the 1991 International Symposium, pages 272–286, October 1991.
Hans-Jürgen Bürkert. A Resolution Principle for a Logic with Restricted Quantifiers. Springer-LNAI 568, 1991.
Anthony G. Cohn. On the solution of Schubert's Steamroller in many sorted logic. In Proceedings of the Ninth International Joint Conference on Artificial Intelligence, pages 1169–1174, August 1985.
Anthony G. Cohn. Taxonomic reasoning with many-sorted logics. Artificial Intelligence Review, 3:89–128, 1989.
Alan M. Frisch and Richard B. Scherl. A general framework for modal deduction. In Principles of Knowledge Representation and Reasoning: Proceedings of the Second International Conference, pages 196–207. Morgan Kaufman, San Mateo, CA, 1991.
Alan M. Frisch. An investigation into inference with restricted quantification and a taxonomic representation. SIGART Newsletter, (91):28–31, 1985.
Alan M. Frisch. The substitutional framework for hybrid reasoning. Working Notes of the 1991 Fall Symposium on Principles of Hybrid Reasoning. Asilomar, CA., November 1991.
Alan M. Frisch. The substitutional framework for sorted deduction: Fundamental results on hybrid reasoning. Artificial Intelligence, 49:161–198, 1991.
Michael Hanus. Horn clause programs with polymorphic types: semantics and resolution. pages 225–240. TAPSOFT'89, Springer Verlag, 1989.
H. Huber and L. Varsek. Extended Prolog for order-sorted resolution. In Proceedings of the 4th IEEE Symposium on Logic Programming, pages 34–45, 1987.
Alberto Martelli and Ugo Montanari. An efficient unification algorithm. ACM Transactions on Programming Languages and Systems, 4(2):258–282, April 1982.
A. Mycroft and U. O'Keefe. A polymorphic type system for Prolog. Artificial Intelligence, (23):295–307, 1984.
Christian F. Prehofer. A constraint language for order-sorted polymorphic resolution. Master's thesis, Univ. of Illinois at Urbana-Champaign, January 1992.
Manfred Schmidt-Schauß. Computational Aspects of an Order-Sorted Logic with Term Declarations. Springer-LNAI 395, 1989.
Gert Smolka. Logic programming over polymorphically order-sorted types. PhD thesis, Universität Kaiserslautern, May 1989.
Christoph Walther. A mechanical solution of Schubert's Steamroller by many-sorted resolution. Artificial Intelligence, 26(2):217–224, 1985.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Prehofer, C. (1992). An efficient constraint language for polymorphic order-sorted resolution. In: Pearce, D., Wagner, G. (eds) Logics in AI. JELIA 1992. Lecture Notes in Computer Science, vol 633. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023436
Download citation
DOI: https://doi.org/10.1007/BFb0023436
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55887-3
Online ISBN: 978-3-540-47304-6
eBook Packages: Springer Book Archive