Abstract
We introduce model-theoretic semantics [6] for Higher-Order Horn logic programming language. One advantage of logic programs over conventional non-logic programs has been that the least fixpoint is equal to the least model, therefore it is associated to logical consequence and has a meaningful declarative interpretation. In simple theory of types [9] on which Higher-Order Horn logic programming language is based, domain is dependent on interpretation [10]. To define T P operator for a logic program P, we need a fixed domain without regard to interpretation which is usually taken to be a set of atomic propositions. We build a semantics where we can fix a domain while changing interpretations. We also develop a fixpoint semantics based on our model, and show that we can get the least fixpoint which is the least model. Using this fixpoint we prove the completeness of the interpreter of our language in [14].
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
James H. Andrews. Predicates as parameters in logic programming: A set-theoretic basis. In P. Schroeder-Heister, editor, Extensions of Logic Programming, pages 31–47, 1989.
Peter B. Andrews. Resolution in type theory. The Journal of Symbolic Logic, 36(3):414–432, 1971.
Peter B. Andrews. General models and extensionality. The Journal of Symbolic Logic, 37(2):395–397, 1972.
Peter B. Andrews. General models, descriptions, and choice in type theory. The Journal of Symbolic Logic, 37(2):385–394, 1972.
Peter B. Andrews. An Introduction to Mathematical Logic and Type Theory: To Truth through Proof. Academic Press, 1986.
Mino Bai. A declarative foundation of λ Prolog with equality. Technical Report SU-CIS-92-03, Syracuse University, 1992.
H. P. Barendregt. The Lambda Calculus. North-Holland, 1984.
Weidong Chen, Kichael Kifer, and David S. Warren. Hilog: A first-order semantics for higher-order logic programming constructs. In Ewing L. Lusk and Ross A. Overbeek, editors, Logic Programming Proceedings of North American Conference, pages 1090–1114, 1989.
Alonzo Church. A formulation of simple theory of types. The Journal of Symbolic Logic, 5:56–68, 1940.
Leon Henkin. Completeness of the theory of types. The Journal of Symbolic Logic, 15:81–91, 1950.
John W. Lloyd. Foundations of Logic Programming. Springer-Verlag, 1987.
Dale A. Miller. Proofs in higher-order logic. PhD thesis, Carnegie-Mellon University, 1983.
Dale A. Miller. A compact representation of proofs. Studio Logica, 46(4):347–370, 1987.
Dale A. Miller, Gopalan Nadathur, Frank Pfenning, and Andre Scedrov. Uniform proofs as a foundation for logic programming. Technical report, University of Pennsylvania, 1989.
Dale A. Miller, Gopalan Nadathur, Frank Pfenning, and Andre Scedrov. Uniform proofs as a foundation for logic programming. Annals of Pure and Applied Logic, 51:125–157, 1991.
Gopalan Nadathur. A higher-order logic a the basis for logic programming. PhD thesis, University of Pennsylvania, 1986.
J. A. Robinson. Mechanizing higher-order logic. Machine Intelligence, 4:150–170, 1969.
William W. Wadge. Higher-order horn logic programming. In U. Saraswat and K. Ueda, editors, Proceedings of International Logic Programming Symposium, pages 289–303, 1991.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bai, M., Blair, H.A. (1992). General model theoretic semantics for Higher-Order horn logic programming. In: Voronkov, A. (eds) Logic Programming and Automated Reasoning. LPAR 1992. Lecture Notes in Computer Science, vol 624. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013072
Download citation
DOI: https://doi.org/10.1007/BFb0013072
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55727-2
Online ISBN: 978-3-540-47279-7
eBook Packages: Springer Book Archive