Abstract
We propose criteria that any rule for inferring negative information from disjunctive databases should satisfy, and examine existing rules from this viewpoint. We then present a new inference rule, the ‘disjunctive database rule’ (DDR), and compare it to the existing rules with respect to the criteria. In particular, the DDR is equivalent to the CWA for definite databases, it infers no more negative information than the GCWA, and it interprets disjunction inclusively rather than exclusively. We generalize the DDR to a class of layered databases, describe an implementation of the DDR, ‘negation as positive failure’, and study its soundness and completeness properties.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Apt, K. R., Blair, H. A., and Walker, A., ‘Towards a Theory of Declarative Knowledge’, in Foundations of Deductive Databases and Logic Programming, Minker, J. (ed.), Morgan Kaufmann, Los Altos, Ca., 1988, 89–148.
Bancilhon, F. and Ramakrishnan, R., ‘An Amateur's Introduction to Recursive Query Processing Strategies’, Proc. ACM Int. Conf. on Management of Data, Washington, D.C., 1986, 16–52.
Chandra, A. K. and Harel, D., ‘Horn Clause Queries and Generalizations’, J. Logic Programming 2, 1 (1985) 1–15.
Clark, K. L., ‘Negation as Failure’, in Logic and Data Bases, Gallaire, H. and J.Minker (eds), Plenum Press, New York, 1978, 293–322.
Gelfond, M., Przymusinska, H., and Przymusinski, T. C., ‘The Extended Closed World Assumption and its Relationship to Parallel Circumscription’, Proc. Fifth ACM Symp. on Principles of Database Systems, Cambridge, Mass., 1986, 133–139.
Gelfond, M., Przymusinska, H., and Przymusinski, T. C., ‘On the Relationship between Circumscription and Negation as Failure’, manuscript, Department of Mathematical Sciences, University of Texas, El Paso, Texas, 1986. To appear hin Artificial Intelligence.
Grant, J. and Minker, J., ‘Answering Queries in Indefinite Databases and the Null Value Problem’, in Advances in Computing Research, Vol. 3, JAI Press, 1986, 247–267.
Henschen, L. J. and Park, H.-S., ‘Compiling the GCWA in Indefinite Deductive Databases’, in Foundations of Deductive Databases and Logic Programming, Minker, J. (ed.), Morgan Kaufmann, Los Altos, Ca., 1987, 395–438.
Lloyd, J. W., Foundations of Logic Programming, 2nd edition, Symbolic Computation Series, Springer-Verlag, Berlin, 1987.
Lloyd, J. W. and Topor, R. W., ‘A Basis for Deductive Database Systems’, J. Logic Programming 2, 2 (1985), 93–109.
Lloyd, J. W. and Topor, R. W., ‘A Basis for Deductive Database Systems II’, J. Logic Programming 3, 1 (1986), 55–67.
Loveland, D. W. and Reddy, C. R., ‘Deleting Repeated Goals in the Problem Reduction Format’, J. ACM 28, 4 (1981), 646–661.
Minker, J., ‘On Indefinite Databases and the Closed World Assumption’, in 6th Conf. on Automated Deduction, Loveland, D. W. (ed.), Lecture Notes in Computer Science 138, Springer-Verlag, 1982, 292–308.
Minker, J. and Perlis, D., ‘Computing Protected Circumscription’, J. Logic Programming 2, 4 (1985), 235–249.
Poole, D. and Goebel, R., ‘On Eliminating Loops in Prolog’, ACM SIGPLAN Notices 20, 8 (1985), 38–40.
Przymusinski, T. C., ‘An Algorithm to Compute Circumscription’, manuscript, Department of Mathematical Sciences, University of Texas, El Paso, Texas, 1986. To appear in Artificial Intelligence.
Przymusinski, T. C., ‘On the Declarative and Procedural Semantics of Logic Programs’, manuscript, Department of Mathematical Sciences, University of Texas, El Paso, Texas, 1987. To appear in J. Logic Programming.
Przymusinski, T. C., ‘On the Declarative Semantics of Deductive Databases and Logic Programs’, in Foundations of Deductive Databases and Logic Programming, Minker, J. (ed.), Morgan Kaufmann, Los Altos, Ca., 1988, 193–216.
Reiter, R., ‘On Closed World Data bases’, in Logic and Data Bases, Gallaire, H. and Minker, J. (eds) Plenum Press, New York, 1978, 55–76.
Reiter, R., ‘Towards a Logical Reconstruction of Relational Database Theory’, in On Conceptual Modelling: Perspectives from Artificial Intelligence, Databases and Programming Languages, Brodie, M. L., Mylopoulos, J., and Schmidt, J. W. (eds), Springer-Verlag, Berlin, 1984, 191–233.
Shepherdson, J. C., ‘Negation in Logic Programming’, in Foundations of Deductive Databases and Logic Programming, Minker, J. (ed.), Morgan Kaufmann, Los Altos, Ca., 1988, 19–88.
vanEmden, M. H. and Kowalski, R. A., ‘The Semantics of Predicate Logic as a Programming Language’, J. ACM 23, 4 (1976), 733–742.
Yahya, A. and Henschen, L. J., ‘Deduction in Non-Horn Databases’, J. Automated Reasoning 1 (1985), 141–160. Errata: J. Automated Reasoning 4 (1988) 109–110.
Author information
Authors and Affiliations
Additional information
CR Categories and Subject Descriptors: H.2.4 [Database Management]: Systems — query processing; I.2.3 [Artificial Intelligence]: Deduction and theorem proving — deduction, nonmonotonic reasoning; I.2.4 [Artificial Intelligence]: Knowledge representation formalisms and methods — predicate logic. General Terms: Databases.
Rights and permissions
About this article
Cite this article
Ross, K.A., Topor, R.W. Inferring negative information from disjunctive databases. J Autom Reasoning 4, 397–424 (1988). https://doi.org/10.1007/BF00297247
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00297247