Abstract
Background material is presented on deductive and normal deductive databases. A historical review is presented of work in disjunctive deductive databases, starting from 1982. The semantics of alternative classes of disjunctive databases is reviewed with their model and fixpoint characterizations. Algorithms are developed to compute answers to queries in the alternative theories using the concept of a model tree. Open problems in this area are discussed.
Preview
Unable to display preview. Download preview PDF.
References
K.R. Apt, H.A. Blair, and A. Walker. Towards a Theory of Declarative Knowledge. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 89–148. Morgan Kaufmann Pub., Washington, D.C., 1988.
K.R. Apt and M.H. van Emden. Contributions to the Theory of Logic Programming. J.ACM, 29(3):841–862, 1982.
A. Borgida and D.W. Etherington. Hierarchical knowledge bases and efficient disjunctive reasoning. In Proceedings of First International Conference on Knowledge Representation and Reasoning, pages 33–43, 1989.
J. Biskup. A formal approach to null values in database relations. In J. Minker H. Gallaire and J. M. Nicolas, editors, Advances in Data Base Theory, volume 1, pages 299–341. Plenum Press, New York, 1981.
J. Biskup. A foundation of codd's relational maybe-operations. University Park, 1981. Pennsylvania State Univ.
C. Baral, J. Lobo, and J. Minker. Generalized disjunctive well-founded semantics for logic programs. Technical report, Dept of Computer Science, University of Maryland, College Park Md 20742, 1989. To appear in the Journal of Annals of Mathematics and Artifitial Intelligence.
C. Baral, J. Lobo, and J. Minker. Generalized well-founded semantics for logic programs. Technical report, Dept of Computer Science, University of Maryland, College Park Md 20742, 1989. Submitted for publication.
C. Baral, J. Lobo, and J. Minker. Generalized disjunctive well-founded semantics for logic programs: Declarative semantics. In M. Zemankova Z. W. Ras and M. L. Emrich, editors, Proc. of Fifth International Symposium on Methodologies for Intelligent Systems, pages 465–473, Charlotte, NC, 1990. North-Holland.
C. Baral, J. Lobo, and J. Minker. Generalized disjunctive well-founded semantics for logic programs: Procedural semantics. In M. Zemankova Z. W. Ras and M. L. Emrich, editors, Proc. of Fifth International Symposium on Methodologies for Inelligent Systems, pages 456–464, Charlotte, NC, 1990. North-Holland.
C. Baral, J. Lobo, and J. Minker. Generalized well-founded semantics for logic programs. In M. E. Stickel, editor, Proc. of Tenth Internatinal Conference on Automated Deduction, Kaiserslautern, FRG, July 1990. Springer-Verlag.
C. Baral, J. Lobo, and J. Minker. WF3: A semantics for negation in normal disjunctive logic programs. In Proc. of the 6th International Symposium on Methodologies for Intelligent Systems, Charlotte, NC, 1991.
G. Bossu and P. Siegel. Saturation, nonmonotonic reasoning and the closed-world assumption. Artificial Intelligence, 25(1):13–63, January 1985.
A. Chandra and D. Harel. Horn clause queries and generalizations. Journal of Logic Programming, 2(1):1–15, April 1985.
S. Chi and L. Henschen. Recursive Query Aanswering with Non-Horn Clauses. In E. Lusk and R. Overbeek, editors, Proc. 9 th International Conference on Automated Deduction, pages 294–312, Argonne, IL, May 1988.
E. Chan. A possible world semantics for non-Horn databases, 1989. University of Waterloo, Canada.
K. L. Clark. Negation as Failure. In H. Gallaire and J. Minker, editors, Logic and Data Bases, pages 293–322. Plenum Press, New York, 1978.
E. F. Codd. Extending the database relational model to capture more meaning. Trans. Database Systems, 4(4):397–434, 1979.
J. Chomicki and V.S. Subrahmanian. Generalized closed world assumption is π 02 -complete. Information Processing Letters, 34:289–291, 1990. University of Maryland Technical Report TR-89-036.
Hendrik Decker. On alternative models, fixpoints and consistency of disjunctive databases, May 1991.
Hendrik Decker. On the declarative, operational and procedural semantics of disjunctive computational theories. In Proceedings of the 2 th International Workshop on the Deductive Approach to Information Systems and Databases, Aiguablava, Spain, September 1991. Invited paper.
Jose Alberto Fernandez, Jorge Lobo, Jack Minker, and V.S. Subrahmanian. Disjunctive LP + integrity constraints = stable models semantics. In Laks Lakshmanan, editor, Proceedings of the ILPS'91 Workshop on Deductive Databases, pages 110–117, San Diego, California, October 1991. A full version of this work has been submitted to Annals of Mathematics and Artifitial Intelligence.
José Alberto Fernandez and Jack Minker. Bottom-up evaluation of Hierarchical Disjunctive Deductive Databases. In Koichi Furukawa, editor, Logic Programming Proceedings of the Eighth International Conference. MIT Press, 1991.
Jose Alberto Fernandez and Jack Minker. Computing perfect models of disjunctive stratified databases. In Don Loveland, Jorge Lobo, and Arcot Rajasekar, editors, Proceedings of the ILPS'91 Workshop on Disjunctive Logic Programs, pages 110–117, San Diego, California, October 1991. An extended version has been submitted to Annals of Mathematics and Artifitial Intelligence.
M. Gelfond and V. Lifschitz. The stable model semantics for logic programming. In Proceedings of the 5th Logic Programming Symposium, pages 1070–1080, Association for Logic Programming, MIT Press, Cambridge, Mass, 1988.
M. Gelfond and V. Lifschitz. Logic programs with classical negation. In D.H.D. Warren and P. Szeredi, editors, Logic Programming — Proceedings of the Seventh International Conference, pages 579–597. MIT Press, 1990.
H. Gallaire and J. Minker, editors. Logic and Databases. Plenum Press, New York, April 1978.
H. Gallaire, J. Minker, and J-M. Nicolas. Logic and databases: A deductive approach. ACM Computing Surveys, 16(2):153–185, June 1984.
M. Gelfond, H. Przymusinska, and T.C. Przymusinski. The extended closed world assumption and its relation to parallel circumscription. Proc. Fifth ACM SIGACT-SIGMOD Symposium on Principle of Database Systems, pages 133–139, 1986.
M. Gelfond, H. Przymusinska, and T.C. Przymusinski. On the Relationship between Circumscription and Negation as Failure. Artificial Intelligence, 38:75–94, 1989.
J. Grant. Null values in a relational data base. Information Processing Letters, 6(5):156–157, 1977.
R. Hill. Lush resolution and its completeness. Technical Report DCL Memo 78, Department of Artificial Intelligence, University of Edinburgh, August 1974.
L.J. Henschen and H. Park. Compiling the GCWA in Indefinite Databases. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 395–438. Morgan Kaufmann Pub., Washington, D.C., 1988.
T. Imielinski and W. Lipski. Incomplete information in relational databases. J. ACM, 31(4):761–791, 1984.
T. Imielinski. Incomplete deductive databases. Annals of Mathematics and Artificial Intelligence, 3:259–293, 1991.
T. Imielinski and K. Vadaparty. Complexity of Query Processing in Databases with OR-Objects. In Proc. 7 th ACM SIGACT/SIGMOD Symposium on Principles of Database Systems, pages 51–65, Philadelphia, Pennsylvania, March 29–31 1989.
V. Lifschitz. Pointwise circumscription: A preliminary report. AAAI, pages 406–410, 1986.
W. Lipski. On databases with incomplete information. volume 28, pages 41–70. ACM, New York, 1981.
J.W. Lloyd. Foundations of Logic Programming. Springer-Verlag, second edition, 1987.
K.C. Liu and R. Sunderraman. Indefinite and maybe information in relational databases. ACM Transactions on Database Systems, 15(1):1–39, 1990.
Ken-Chih Liu and Rajshekhar Sunderraman. On representing indefinite and maybe information in relational databases: A generalization. In Proceedins of IEEE Data Engineering, 1990.
J. Lobo, C. Yu, and G. Wang. Computing the transitive closure in disjunctive databases. Technical report, Department of Electrical Engineering and Computer Science, University of Illinois at Chicago, 1992.
J. McCarthy. Circumscription — a form of non-monotonic reasoning. Artificial Intelligence, 13(1 and 2):27–39, 1980.
J. Minker and J. Grant. Answering queries in indefinite databases and the null value problem. In P. Kanellakis, editor, Advances in Computing Research, pages 247–267. 1986.
J. Minker. On indefinite databases and the closed world assumption. In Proceedings of 6th Conference on Automated Deduction, pages 292–308, New York, 1982.
J. Minker. Proceedings of workshop on foundations of deductive databases and logic programming, August 1986.
J. Minker. Perspectives in deductive databases. Journal of Logic Programming, 5:33–60, 1988.
J. Minker. Toward a foundation of disjunctive logic programming. In E.L. Lusk and R.A. Overbeek, editors, Proc. North American Conf. on Logic Programming, pages 1215–1235, 1989.
J. Minker and A. Rajasekar. A Fixpoint Semantics for Non-Horn Logic Programs. Technical Report CS-TR-1869, Department of Computer Science University of Maryland, College Park, 1987.
J. Minker and A. Rajasekar. A fixpoint semantics for disjunctive logic programs. Journal of Logic Programming, 1990.
Teodor C. Przymusinski. On the declarative semantics of deductive databases and logic programming. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, chapter 5, pages 193–216. Morgan Kaufmann Pub., Washington, D.C., 1988.
T. Przymusinski. Stationary semantics for disjunctive logic programs and deductive databases. In S. Debray and M. Hermenegildo, editors, Proc. of the North American Conference on Logic Programming, pages 40–62, Austin, Texas, October 1990.
T. Przymusinski. Three valued stable models and well-founded models of logic programs. Technical report, Dept of Computer Science, University of Texas at El Paso, 1990.
Teodor C. Przymusinski. Extended stable semantics for normal and disjunctive programs. In Preceedings of the 7 th International Logic Programming Conference, pages 459–477, Jerusalem, 1990. MIT Press. Extended Abstract.
T. C. Przymusinski. Stable semantics for disjunctive programs. New Generation Computing Journal, 9:401–424, 1991. Extended Abstract appeared in [Prz90c].
R. Reiter. On Closed World Data Bases. In H. Gallaire and J. Minker, editors, Logic and Data Bases, pages 55–76. Plenum Press, New York, 1978.
R. Reiter. A sound and sometimes complete query evaluation algorithm for relational databases with null values. J.ACM, 33(2):349–370, April 1986.
K. Ross. Well-founded semantics for disjunctive logic programs. In Proc. of the first International Conference on Deductive and Object Oriented Databases, Kyoto, Japan, December 1989.
C. Sakama. Possible model semantics for disjunctive databases. In Proc. First International Conference on Deductive and Object Oriented Databases, pages 337–351, 1989.
M. Such. Minimal models for closed world databases. In Z.W. Ras, editor, Proc. of ISMIS 4, pages 515–522, 1989.
Jeffrey D. Ullman. Principles of Database and Knowledge-Base Systems I. Principles of Computer Science Series. Computer Science Press, 1803 Research Boulevard, Rockville Maryland 20850, 1988.
Jeffrey D. Ullman. Principles of Database and Knowledge-Base Systems II. Principles of Computer Science Series. Computer Science Press, 1803 Research Boulevard, Rockville Maryland 20850, 1988.
A. Van Gelder. Negation as Failure Using Tight Derivations for General Logic Programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 1149–176. Morgan Kaufmann, 1988.
M.Y. Vardi. The complexity of relational query languages. pages 137–146, May 1982.
Y. Vassiliou. Null values in data base management: A denotational semantics approach. pages 162–169, Boston, MA, 1979. ACM, New York.
M.H. van Emden and R.A. Kowalski. The Semantics of Predicate Logic as a Programming Language. J.ACM, 23(4):733–742, 1976.
A. Van Gelder, K. Ross, and J.S. Schlipf. Unfounded Sets and Well-founded Semantics for General Logic Programs. In Proc. 7 th Symposium on Principles of Database Systems, pages 221–230, 1988.
Li Yan Yuan and Ding-An Chiang. A sound and complete query evaluation algorithm for relational databases with disjunctive information. In Proceedings of the Eighth Symposium on Principles of Database Systems, pages 66–74. ACM Press, March 1989.
A. Yahya and L.J. Henschen. Deduction in Non-Horn Databases. J. Automated Reasoning, 1(2):141–160, 1985.
C. Zaniolo. Database relations with null values. J. Comp. Sys. Sci., 28:142–166, 1984.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fernández, J.A., Minker, J. (1992). Disjunctive deductive databases. In: Voronkov, A. (eds) Logic Programming and Automated Reasoning. LPAR 1992. Lecture Notes in Computer Science, vol 624. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013073
Download citation
DOI: https://doi.org/10.1007/BFb0013073
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55727-2
Online ISBN: 978-3-540-47279-7
eBook Packages: Springer Book Archive