Strong and Weak Constraints in Disjunctive Datalog

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.

[1]  Chitta Baral,et al.  Logic Programming and Knowledge Representation , 1994, J. Log. Program..

[2]  Jorge Lobo,et al.  Foundations of disjunctive logic programming , 1992, Logic Programming.

[3]  Krzysztof R. Apt,et al.  Logic Programming , 1990, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[4]  Teodor C. Przymusinski,et al.  Weakly Perfect Model Semantics for Logic Programs , 1988, ICLP/SLP.

[5]  Jack Minker,et al.  On Indefinite Databases and the Closed World Assumption , 1987, CADE.

[6]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[7]  Liz Sonenberg,et al.  Integrity Constraint Checking in Stratified Databases , 1987, J. Log. Program..

[8]  Jack Minker,et al.  Semantics of Disjunctive Deductive Databases , 1992, ICDT.

[9]  Robert A. Kowalski,et al.  A Theorem-Proving Approach to Database Integrity , 1988, Foundations of Deductive Databases and Logic Programming..

[10]  Jürgen Dix,et al.  Disjunctive Semantics based upon Partial and Bottom-Up Evaluation , 1995, ICLP.

[11]  Francesco Scarcello,et al.  Disjunctive Stable Models: Unfounded Sets, Fixpoint Semantics, and Computation , 1997, Inf. Comput..

[12]  Francesco Scarcello,et al.  Declarative and Fixpoint Characterizations of Disjunctive Stable Models , 1995, ILPS.

[13]  Hendrik Decker,et al.  A Slick Procedure for Integrity Checking in Deductive Databases , 1994, ICLP.

[14]  Georg Gottlob,et al.  The complexity of logic-based abduction , 1993, JACM.

[15]  Victor W. Marek,et al.  The Relationship Between Logic Program Semantics and Non-Monotonic Reasoning , 1989, ICLP.

[16]  Sergio Greco,et al.  Extending Datalog with Choice and Weak Constraints , 1996, APPIA-GULP-PRODE.

[17]  Georg Gottlob,et al.  Adding disjunction to datalog (extended abstract) , 1994, PODS.