Expressive Power and Complexity of Disjunctive Datalog under the Stable Model Semantics

DATALOG¬ is a well-known logical query language, whose expressive power and data complexity under the stable model semantics has been recently determined. In this paper we consider the extension of DATALOG¬ to disjunctive DATALOG¬ (DDL¬), which allows disjunction in the head of program clauses, under the stable model semantics. We investigate and determine the expressiveness and the data complexity of DDL¬, as well as the expression complexity. The main findings of this paper are that disjunctive datalog captures precisely the class of all ∑ 2 p -recognizable queries under the brave version of reasoning, and symmetrically the class of all Π 2 p -recognizable queries under the cautious version; the data complexity is ∑ 2 p -completeness in the brave version, and Π 2 p -complete in the cautious version, while the expression complexity is NEXPTIMENP-complete in the brave version and co-NEXPTIMENPcomplete in the cautious version.

[1]  Larry J. Stockmeyer,et al.  The Polynomial-Time Hierarchy , 1976, Theor. Comput. Sci..

[2]  David S. Johnson,et al.  A Catalog of Complexity Classes , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[3]  Iain A. Stewart Complete Problems Involving Boolean Labelled Structures and Projection Transactions , 1991, J. Log. Comput..

[4]  Moshe Y. Vardi The complexity of relational query languages (Extended Abstract) , 1982, STOC '82.

[5]  José L. Balcázar,et al.  The Complexity of Graph Problems fore Succinctly Represented Graphs , 1989, WG.

[6]  J. A. Makowsky Model theory and computer science: an appetizer , 1993, LICS 1993.

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

[8]  Avi Wigderson,et al.  Succinct Representations of Graphs , 1984, Inf. Control..

[9]  José L. Balcázar,et al.  Structural Complexity I , 1995, Texts in Theoretical Computer Science An EATCS Series.

[10]  Victor W. Marek,et al.  Autoepistemic logic , 1991, JACM.

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

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

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

[14]  David Harel,et al.  Computable Queries for Relational Data Bases , 1980, J. Comput. Syst. Sci..

[15]  Victor W. Marek,et al.  How Complicated is the Set of Stable Models of a Recursive Logic Program? , 1992, Ann. Pure Appl. Log..

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

[17]  John McCarthy,et al.  Circumscription - A Form of Non-Monotonic Reasoning , 1980, Artif. Intell..

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

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

[20]  Christos H. Papadimitriou,et al.  Why not Negation by Fixpoint? , 1991, J. Comput. Syst. Sci..

[21]  Mihalis Yannakakis,et al.  A Note on Succinct Representations of Graphs , 1986, Inf. Control..

[22]  Chen C. Chang,et al.  Model Theory: Third Edition (Dover Books On Mathematics) By C.C. Chang;H. Jerome Keisler;Mathematics , 1966 .

[23]  John S. Schlipf A Survey of Complexity and Undecidability Results in Logic Programming , 1992, Structural Complexity and Recursion-theoretic methods in Logic-Programming.

[24]  Georg Gottlob,et al.  Complexity aspects of various semantics for disjunctive databases , 1993, PODS '93.

[25]  Victor W. Marek,et al.  Computing Intersection of Autoepistemic Expansions , 1991, LPNMR.

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

[27]  John S. Schlipf,et al.  The expressive powers of the logic programming semantics (extended abstract) , 1990, PODS.

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

[29]  José L. Balcázar,et al.  The complexity of algorithmic problems on succinct instances , 1992 .