Abstract
This paper presents an extension of disjunctive datalog (Data-log∨,⌝) by integrity constraints. In particular, besides classical integrity constraints (called strong constraints in this paper), the notion of weak constraints is introduced in the language. These are constraints that are satisfied if possible. The semantics of weak constraints tends to minimize the number of violated instances. As a consequence, weak constraints differ from strong constraints only if the latter are unsatisfiable. Weak constraints may be ordered according to their importance to express different priority levels. The formal definition of the semantics of weak constraints is given in a general way that allows to put them on top of any existing (model-theoretic) semantics for Datalog∨,⌝ programs. A number of examples shows that the proposed language (call it Data-log∨,⌝, c) is well-suited to represent complex knowledge-based problems, such as, for instance, NP optimization problems.
A detailed complexity analysis of the language is given as well as an algorithm for the computation of the stable model semantics of Datalog∨,⌝c programs.
This work has been supported in part by FWF (Austrian Science Funds) under the project P11580-MAT “A Query System for Disjunctive Deductive Databases”; by Istituto per la Sistemistica e l'Informatica, ISI-CNR; and by a MURST grant (40% share) under the project “Sistemi formali e strumenti per basi di dati evolute.”
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References
Baral, C. and Gelfond, M. (1994), Logic Programming and Knowledge Representation Journal of Logic Programming, 19/20, 73–148.
Ben-Eliyahu, R. and Dechter, R. (1994), Propositional Semantics for Disjunctive Logic Programs. Annals of Mathematics and Artificial Intelligence, 12, 53–87.
Brass, S. and Dix, J. (1995), Disjunctive Semantics Based upon Partial and Bottom-Up Evaluation, in “Proc. of the 12th Int. Conf. on Logic Programming,” Tokyo, pp. 199–213, MIT Press.
Decker, H., Celma, M. (1994) A slick procedure for integrity checking in deductive databases, “Proc. of the Eleventh Int. Conference on Logic Programming, S. Margherita Ligure”, Italy, pp. 456–469, MIT Press.
Eiter, T., Gottlob, G. and Mannila, H. (1994), Adding Disjunction to Datalog, in “Proc. ACM PODS-94,” pp. 267–278.
Eiter, T. and Gottlob, G. (1995), On the Computational Cost of Disjunctive Logic Programming: Propositional Case, Annals of Mathematics and Artificial Intelligence, J. C. Baltzer AG, Science Publishers, 15, 289–323.
Eiter, T. and Gottlob, G. (1995), The Complexity of Logic-Based Abduction, Journal of the ACM, 42, 3–42.
Fernández, J.A. and Minker, J. (1992), Semantics of Disjunctive Deductive Databases, in “Proc. 4th Intl. Conference on Database Theory (ICDT-92),” Berlin, pp.21–50.
Garey, M., Johnson, D.S. (1979) Computers and Intractability — A Guide to the Theory of NP-Completeness, W. H. Freeman, New York.
Gelfond, M. and Lifschitz, V. (1991), Classical Negation in Logic Programs and Disjunctive Databases, New Generation Computing, 9, 365–385.
Greco, S. (1996), Extending Datalog with Choice and Weak Constraints, in “Proc. of the Joint Conference on Declarative Programming (APPIA-GULP-PRODE'96”, Donostia-San Sebastian, Spain, pp.329–340.
Greco, S. and Saccà, D. (1997), NP Optimization Problems in Datalog, unpublished manuscript.
IFIP-GI Workshop (1994), “Disjunctive Logic Programming and Disjunctive Databases,” 13-th IFIP World Computer Congress.
Kowalski, R., Sadri, F. (1988) A theorem-proving approach to database integrity, in J. Minker (ed), Foundations of Deductive Databases and Logic Programming, 313–362, Morgan Kaufman.
Leone, N., Rullo, P., Scarcello, F. (1995) Declarative and Fixpoint Characterizations of Disjunctive Stable Models, in “Proceedings of International Logic Programming Symposium (ILPS'95)”, Portland, Oregon, pp. 399–413, MIT Press.
Leone, N., Rullo, P., Scarcello, F. (1997) Disjunctive Stable Models: Unfounded Sets, Fixpoint Semantics and Computation, Information and Computation, Forthcoming.
Lloyd, J.W., Sonenberg, E.A., Topor, R.W. (1987) Integrity constraint checking in stratified databases, Journal of Logic Programming, 2, pp. 331–343.
Lobo, J., Minker, J. and Rajasekar, A. (1992) Foundations of Disjunctive Logic Programming MIT Press, Cambridge, MA.
Marek, W. and Subrahmanian, V.S. (1989), The Relationship between Logic Program Semantics and Non-Monotonic Reasoning, in “Proc. of the 6th International Conference on Logic Programming — ICLP'89,” pp. 600–617, MIT Press.
Minker, J. (1982), On Indefinite Data Bases and the Closed World Assumption, in “Proc. of the 6th Conference on Automated Deduction (CADE-82),” pp. 292–308.
Papadimitriou, C.H. (1994), Computational Complexity, Addison-Wesley.
Przymusinska, H. and Przymusinski, T. (1988), Weakly Perfect Model Semantics for Logic Programs, in “Proc. Fifth Int. Conf. and Symp. on Logic Programming,” pp.1106–1120.
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Buccafurri, F., Leone, N., Rullo, P. (1997). Strong and weak constraints in disjunctive datalog. In: Dix, J., Furbach, U., Nerode, A. (eds) Logic Programming And Nonmonotonic Reasoning. LPNMR 1997. Lecture Notes in Computer Science, vol 1265. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63255-7_2
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DOI: https://doi.org/10.1007/3-540-63255-7_2
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