ABSTRACT
In this paper we study the uses and the semantics of non-monotonic negation in probabilistic deductive data bases. Based on the stable semantics for classical logic programming, we introduce the notion of stable formula, functions. We show that stable formula, functions are minimal fixpoints of operators associated with probabilistic deductive databases with negation. Furthermore, since a. probabilistic deductive database may not necessarily have a stable formula function, we provide a stable class semantics for such databases. Finally, we demonstrate that the proposed semantics can handle default reasoning naturally in the context of probabilistic deduction.
- F. Bacchus. (1988) Representing and Reasoning with Probabilistic Knowledge, Research Report CS-88-31, University of Waterloo.Google Scholar
- C. Baral and V.S. Subrahmanian. (1990) Stable and Extension Class Theory for Logic Programs and Default Logics, to appear in: Journal of Automated Reasoning. Preliminary version in: Proc. 1990 Intl. Workshop on Non-Monotonic Reasoning, ed K. Konolige, June 1990. Google ScholarDigital Library
- H. A. Blair and V.S. Subrahmanian. (1987) Paraconsistent Logic Programming, Theoretical Computer Science, 68, pp 35-54. Preliminary version in: Proc. 7th Conference on Foundations of Software Technology and Theoretical Computer Science, Lecture Notes in Computer Science, Vol. 287, pps 340-360, Springer Verlag. Google ScholarDigital Library
- W. Buntine. (1990) Modelling Default and Likelihood Reasoning as Probabilistic, Technical Report FIA-90-09-11-01, NASA Ames Research Center.Google Scholar
- A. P. Dempster. (1968) A Generalization of Bayesian Inference, J. of the Royal Statistical Society. Series B, 30, pp. 205-247.Google Scholar
- D. Dubois and H. Prade. (1988) Default Reasoning and Possibility Theory, Artificial Intelligence, 35, pp. 243-257. Google ScholarDigital Library
- R. Fagin and J. Halpern. (1988) Uncertainty, Belief and Probability, in Proc. IJCAI-89, Morgan Kauffman. Google ScholarDigital Library
- R. Fagin, J. Y. Halpern and N. Megiddo. (1989) A Logic for Reasoning About Probabilities, to appear in: Information and Computation. Google ScholarDigital Library
- M. C. Fitting. (1988) Bilattices and the Semantics of Logic Programming, to appear in: Journal of Logic Programming. Google ScholarDigital Library
- M. C. Fitting. (1990) personal correspondence.Google Scholar
- H. Geffner. (1989) Default Reasoning: Causal and Conditional Theories, Technical Report 137, Cognitive Systems Laboratory, University of California, Los Angeles.Google ScholarDigital Library
- M. Gelfond and V. Lifschitz. (1988) The Stable Model Semantics for Logic Programming, in: Proc. 5th International Conference and Symposium on Logic Programming, ed R. A. Kowalski and K. A. Bowen, pp 1070-1080.Google Scholar
- M. Kifer and E. Lozinskii. (1989) RI: A Logic for Reasoning with Inconsisteney, Proc. 4-th Symposium on Logic in Computer Science, Asilomar, CA, pp. 253-262. Full version to appear in: Journal of Automated Reasoning. Google ScholarDigital Library
- M. Kifer and V. S. Subrahmanian. (1991) Theory of Generalized Annotated Logic Programming and its Applications, to appear in: Journal of Logic Programming. Google ScholarDigital Library
- H. Kyburg. (1974) The Logical Foundations of Statistical Inference, D. Reidel.Google Scholar
- R.T. Ng and V.S. Subrahmanian. (1989) Probabilistic Logic Programming, to appear in: Information and Computation. Preliminary version in: Proc. 5th International Symposium on Methodologies for Intelligent Systems, pp. 9-16. Google ScholarDigital Library
- R.T. Ng and V.S. Subrahmanian. (1990) A Semantical Framework for Supporting Subjective and Conditional Probabilities in Deductive Databases, to appear in: Proc. 1991 International Conference of Logic Programming, ed K. Furukawa, MIT Press. Full version in: Technical Report CS-TR-2563, University of Maryland, College Park. Google ScholarDigital Library
- R.T. Ng and V.S. Subrahmanian. (1990) Stable Semantics for Probabilistic Deductive Databases, Technical Report CS-TR-2573, University of Maryland, College Park.Google Scholar
- N. Nilsson. (1986) Probabilistic Logic, Artificial Intelligence, 28, pp. 71-87. Google ScholarDigital Library
- J. Pearl. (1988) Probabilistic Reasoning in Intelligent Systems. Networks of Plausible Inference, Morgan Kaufmann. Google ScholarDigital Library
- R. Reiter and G. Criscuolo. (1981) On interacting Defaults, in Proc. IJCAI 81, pp. 270-276. Google ScholarDigital Library
- G. Shafer. (1976) A Mathematical Theory of Evidence, Princeton University Press.Google Scholar
- M. Smyth. (1978) Power Domains, Journal of Computer and Systems Sciences, 16, 1 pps. 23-36.Google ScholarCross Ref
- M. H. van Emden. (1986) Quantitative Deduction and its Fixpoint Theory, Journal of Logic Programming, 4, 1, pp. 37-53. Google ScholarDigital Library
- S. Yablo. (1985) Truth and Reflection, Journal of Philosophical Logic, 14, pps. 279-349.Google Scholar
- L. A. Zadeh. (1965) Fuzzy Sets, Information and Control, 8, pp. 338-353.Google ScholarCross Ref
Index Terms
- Non-monotonic negation in probabilistic deductive databases
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