Abstract
General logic programs are those that contain both positive and negative subgoals in their clause bodies. For such programs Fitting proposed an elegant 3-valued minimum model semantics that avoids some impracticalities of previous approaches. Here we present a method to compute this Fitting model for deductive databases. We introducepartial relations, which are the semantic objects associated with predicate symbols, and define algebraic operators over them. The first step in our model computation method is to convert the database rules into partial relation definitions involving these operators. The second step is to build the minimum model iteratively. We give algorithms for both steps and show their termination and correctness. We also suggest extensions to our method for computing the well-founded model proposed by van Gelder, Ross and Schlipf.
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References
Apt, K.R., Blair, H.A., and Walker, A. (1988). Towards a theory of declarative knowledge. In Jack Minker (Ed.),Foundations of Deductive Databases and Logic Programming (pp. 89–148). Morgan Kaufmann.
BagaiR., BezemM., and vanEmdenM.H. (1990). On downward closure ordinals of logic programs.Fundamenta Informaticae, XIII(1), 67–83.
ChenW. and WarrenD.S. (1992). A goal-oriented approach to computing well founded semantics.Proceedings of the Joint International Conference and Symposium on Logic Programming. Washington, D.C.: MIT Press.
FittingM. (1985). A Kripke-Kleene semantics for logic programs.Journal of Logic Programming, 4, 295–312.
GelfondM. and LifschitzV. (1988). The stable model semantics for logic programming.Proceedings of the 5th International Conference and Symposium on Logic Programming (pp. 1070–1080). Seattle, WA: MIT Press.
KolaitisP.G. (1991). The expressive power of stratified logic programs.Information and Computation, 90, 50–66.
LeoneN. and RulloP. (1992). The safe computation of the well-founded semantics of datalog queries.Information Systems, 17(1), 17–31.
LiuK.-C. and SunderramanR. (1991). A generalized relational model for indefinite and maybe information.IEEE Transactions on Knowledge and Data Engineering, 3(1), 65–77.
MannaZ. and ShamirA. (1976). The theoretical aspect of the optimal fixed point.SIAM Journal of Computing, 5, 414–426.
Przymusinski, T.C. (1988). On the declarative semantics of deductive databases and logic programs. In Jack Minker (Ed.),Foundations of Deductive Databases and Logic Programming (pp. 193–216). Morgan Kaufmann.
Ross, K.A. (1990). Modular stratification and magic sets for datalog programs with negation.Proceedings of the Ninth Annual ACM Symposium on Principles of Database Systems: ACM Press.
RossK.A. and ToporR.W. (1988). Inferring negative information from disjunctive databases.Journal of Automated Reasoning, 4, 397–424.
Ullman, J.D. (1988).Principles of Database and Knowledge-Base Systems, volume 1, Computer Science Press.
Ullman, J.D. (1994). Assigning an appropriate meaning to database logic with negation. In H. Yamada, Y. Kambayashi, and S. Ohta (Eds.),Computers as Our Better Partners (pp. 216–225). World Scientific Press.
vanGelderA., RossK.A., and SchlipfJ.S. (1991). The well-founded semantics for general logic programs.Journal of the ACM, 38(3), 621–650.
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Bagai, R., Sunderraman, R. Bottom-up computation of the Fitting model for general deductive databases. J Intell Inf Syst 6, 59–75 (1996). https://doi.org/10.1007/BF00712386
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DOI: https://doi.org/10.1007/BF00712386