Artificial Intelligence
Journal of Complexity
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
A logic for reasoning about probabilities
Information and Computation - Selections from 1988 IEEE symposium on logic in computer science
Theory of generalized annotated logic programming and its applications
Journal of Logic Programming
Probabilistic logic programming
Information and Computation
Probabilistic Horn abduction and Bayesian networks
Artificial Intelligence
Stable semantics for probabilistic deductive databases
Information and Computation
Probabilistic deductive databases
ILPS '94 Proceedings of the 1994 International Symposium on Logic programming
Extending and implementing the stable model semantics
Artificial Intelligence
Probabilistic Logic Programming and Bayesian Networks
ACSC '95 Proceedings of the 1995 Asian Computing Science Conference on Algorithms, Concurrency and Knowledge
Probabilistic Logic Programming under Inheritance with Overriding
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
On Indefinite Databases and the Closed World Assumption
Proceedings of the 6th Conference on Automated Deduction
Modeling Uncertainty in Deductive Databases
DEXA '94 Proceedings of the 5th International Conference on Database and Expert Systems Applications
Reasoning with probabilities and time
Reasoning with probabilities and time
Revisiting the semantics of interval probabilistic logic programs
LPNMR'05 Proceedings of the 8th international conference on Logic Programming and Nonmonotonic Reasoning
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Two approaches to logic programming with probabilities emerged over time: Bayesian reasoning and probabilistic satisfiability (PSAT). The attractiveness of the former is in tying the logic programming research to the body of work on Bayes networks. The second approach ties, from the point of view of computation, reasoning about probabilities to linear programming, and allows for natural expression of imprecision in probabilities via the use of intervals. In this paper we construct precise semantics for one PSAT-based formalism for reasoning with interval probabilities: disjunctive probabilistic logic programs (dp-programs). It has two origins: (1) disjunctive logic programs, a powerful language for knowledge representation, first proposed by Minker in the early eighties (Minker 1982) and (2) a logic programming language with interval probabilities originally considered by Ng and Subrahmanian (Inform Comput 101(2):150---201, 1993; J Autom Reason 10(2):191---235, 1993). We show that the probability ranges of atoms and formulas in dp-programs cannot be expressed as single intervals. We construct the precise description of the set of models for the class of dp-programs and study the computational complexity of this problem, as well as the problem of consistency of a dp-program. We also study the conditions under which our semantics coincides with the single-interval semantics originally proposed by Ng and Subrahmanian. Our work sheds light on the complexity of constructing reasoning formalisms for imprecise probabilities and suggests that interval probabilities alone are inadequate to support such reasoning.