Monotonic Aggregation in Deductive Database

We propose a semantics for aggregates in deductive databases based on a notion of minimality. Unlike some previous approaches, we form a minimal model of a program component including aggregate operators, rather than insisting that the aggregate apply to atoms that have been fully determined or that aggregate functions are rewritten in terms of negation. In order to guarantee the existence of such a minimal model we need to insist that the domains over which we are aggregating are complete lattices and that the program is in a sense mono- tonic. Our approach generalizes previous approaches based on the well-founded semantics and various forms of stratification. We are also able to handle a large variety of monotonic (or pseudo-monotonic) aggregate functions.

[1]  Sergio Greco,et al.  Extrema Predicates in Deductive Databases , 1995, J. Comput. Syst. Sci..

[2]  David Harel,et al.  Horn Clauses Queries and Generalizations , 1985, J. Log. Program..

[3]  Yehoshua Sagiv.  A Termination Test for Logic Programs , 1991, ISLP.

[4]  Jeffrey D. Ullman,et al.  Principles Of Database And Knowledge-Base Systems , 1979 .

[5]  Peter J. Stuckey,et al.  Semantics of Logic Programs with Aggregates , 1991, ISLP.

[6]  Kenneth A. Ross,et al.  The well-founded semantics for general logic programs , 1991, JACM.

[7]  S. Sudarshan,et al.  Aggregation and Relevance in Deductive Databases , 1991, VLDB.

[8]  Jack Minker.  Foundations of deductive databases and logic programming , 1988 .

[9]  W. W. Armstrong,et al.  Dependency Structures of Data Base Relationships , 1974, IFIP Congress.

[10]  Allen Van Gelder,et al.  The well-founded semantics of aggregation , 1992, PODS.

[11]  Shamim A. Naqvi.  A Logic for Negation in Database Systems , 1986, XP7.52 Workshop on Database Theory.

[12]  Yehoshua Sagiv,et al.  On Termination of Datalog Programs , 1989, DOOD.

[13]  Allen Van Gelder,et al.  The Alternating Fixpoint of Logic Programs with Negation , 1993, J. Comput. Syst. Sci..

[14]  Adrian Walker,et al.  Towards a Theory of Declarative Knowledge , 1988, Foundations of Deductive Databases and Logic Programming..

[15]  Kenneth A. Ross,et al.  Modular stratification and magic sets for Datalog programs with negation , 1994, JACM.

[16]  Serge Abiteboul,et al.  Data functions, datalog and negation , 1988, SIGMOD '88.

[17]  Yehoshua Sagiv,et al.  On Testing Effective Computability of Magic Programs , 1991, DOOD.

[18]  Hamid Pirahesh,et al.  The Magic of Duplicates and Aggregates , 1990, VLDB.

[19]  Letizia Tanca,et al.  Logic Programming and Databases , 1990, Surveys in Computer Science.

[20]  A. Tarski.  A LATTICE-THEORETICAL FIXPOINT THEOREM AND ITS APPLICATIONS , 1955 .

[21]  Teodor C. Przymusinski.  On the Declarative Semantics of Deductive Databases and Logic Programs , 1988, Foundations of Deductive Databases and Logic Programming..