Abstract
An algebraic method for the construction of the well-founded model of general deductive databases is presented. The method adopts paraconsistent relations as the semantic objects associated with the predicate symbols of the database. Paraconsistent relations are a generalization of ordinary relations in that they allow manipulation of incomplete as well as inconsistent information. Algebraic operators, such as union, join, selection, are defined for paraconsistent relations. The first step in the model construction method is to transform the database clauses into paraconsistent relation definitions involving these operators. The second step is to build the well-founded model iteratively. Algorithms for both steps along with arguments for their termination and correctness are presented.
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K. R. Apt, H. A. Blair, and A. Walker. Towards a theory of declarative knowledge. In Jack Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 89–148. Morgan Kaufmann, Los Altos, 1988.
R. Bagai, M. Bezem, and M. H. van Emden. On downward closure ordinals of logic programs. Fundamenta Informaticae, XIII(1):67–83, March 1990.
R. Bagai and R. Sunderraman. Bottom-up computation of the Fitting model for general deductive databases. Journal of Intelligent Information Systems, 1995. (To appear).
R. Bagai and R. Sunderraman. A paraconsistent relational data model. International Journal of Computer Mathematics, 55(3), 1995.
F. Bancilhon, D. Maier, Y. Sagiv, and J.D. Ullman. Magic sets and other strange ways to implement logic programs. In A. Silberschatz, editor, Proceedings of the 5th Symposium on Principles of Database Systems, pages 1–15, New York, 1986. A.C.M. SIGACT-SIGMOD.
N. Bidoit and P. Legay. Well!: An evaluation procedure for all logic programs. In Proceedings of International Conference on Database Theory, pages 335–345. Lecture Notes in Computer Science, 470, Springer-Verlag, 1990.
W. Chen and D. S. Warren. A goal-oriented approach to computing well founded semantics. In Proceedings of the Joint International Conference and Symposium on Logic Programming, Washington, D.C., 1992.
M. Fitting. A Kripke-Kleene semantics for logic programs. Journal of Logic Programming, 4:295–312, 1985.
D. B. Kemp, P. J. Stuckey, and D. Srivastava. Magic sets and bottom-up evaluation of well-founded models. In Proceedings of the 1991 International Symposium on Logic Programming, pages 337–354, San Diego, USA, 1991.
N. Leone and P. Rullo. The safe computation of the well-founded semantics of datalog queries. Information Systems, 17(1):17–31, 1992.
K.-C. Liu and R. Sunderraman. A generalized relational model for indefinite and maybe information. IEEE Transactions on Knowledge and Data Engineering, 3(1):65–77, 1991.
T. C. Przymusinski. Perfect model semantics. In Proceedings of the 5th International Conference and Symposium on Logic Programming, pages 1081–1096, Seattle, WA, August 1988.
K. A. Ross. Modular stratification and magic sets for datalog programs with negation. In Proceedings of the Ninth Annual ACM Symposium on Principles of database systems. ACM, 1990.
J. D. Ullman. Principles of Database and Knowledge-Base Systems, volume 1. Computer Science Press, 1988.
A. van Gelder. The alternating fixpoint of logic programs with negation. In Proceedings of the 8th ACM Symposium on Principles of Database Systems, pages 1–10, Philadelphia, USA, 1989. ACM Press.
A. van Gelder, K. A. Ross, and J. S. Schlipf. The well-founded semantics for general logic programs. Journal of the ACM, 38(3):621–650, 1991.
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Bagai, R., Sunderraman, R. (1995). An algebraic construction of the well-founded model. In: Alagar, V.S., Nivat, M. (eds) Algebraic Methodology and Software Technology. AMAST 1995. Lecture Notes in Computer Science, vol 936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60043-4_75
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DOI: https://doi.org/10.1007/3-540-60043-4_75
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