On semantics, syntactics and fixpoints of general programs
In this paper, we extend the unified view of logic programs, characterized by van Emden and Kowalski, in terms of semantics, syntactics, and fixpoints into the context of general programs. We first propose a general model semantics which is a natural extension of the Herbrand model semantics. We have shown that any program has a unique least model. Then we show that the least model of a program is precisely the set of all minimally derived disjunctive facts from the program and reveal the relationship between semantics and syntactics of general programs. Finally we show that the least model of a program can also be characterized by the least fixpoint of the natural operator associated with general programs. Our unified view of general programs enhances the theoretical foundation of logic programming and deductive databases.
Unable to display preview. Download preview PDF.
- [ABW88]Apt, K.R., Blair, H.A., and Walker, A., Towards a Theory of Declarative Knowledge, in Foundations of Deductive Databases and Logic Programming, Minker, J. (editor), Morgan-Kaufman Pub., 1988, pp. 89–148.Google Scholar
- [Ll89]Lloyed, J.W., Foundations of Logic Programming, 2nd Edition, Springer-Verlag, 1989.Google Scholar
- [LMR89]Lobo, J., Minker, J., and Rajasekar, A., Extending the Semantics of Logic Programs to Disjunctive Logic Programs, Proc. the 6th International Conference on Logic Programming, 1988, pp. 255–267.Google Scholar
- [Mi82]Minker, J., On Indefinite Databases and the Closed world Assumption, in Lecture Notes in Computer Science 138, Springer-Verlag, 1982 pp. 292–308.Google Scholar
- [Sh88]Shepherdson, J.C., Negation in Logic Programming, in Foundations of Deductive Databases and Logic Programming, Minker, J. (editor), Morgan-Kaufman Pub., 1988, pp. 19–88.Google Scholar
- [VG88]Van Gelder, A., Negation as Failure Using Tight Derivations for General Logic Programs, in Foundations of Deductive Databases and Logic Programming, Minker, J. (editor), Morgan-Kaufman Pub., 1988, pp 149–176.Google Scholar
- [YH85]Yahya, A. and Henschen, L., Deduction in Non-Horn Databases, J. of Automated Reasoning, 1, 1985, 141–160.Google Scholar