Artificial Intelligence
Journal of Complexity
A logic for reasoning about probabilities
Information and Computation - Selections from 1988 IEEE symposium on logic in computer science
Probabilistic logic programming
Information and Computation
Probabilistic Horn abduction and Bayesian networks
Artificial Intelligence
Stable semantics for probabilistic deductive databases
Information and Computation
Probabilistic Logic Programming and Bayesian Networks
ACSC '95 Proceedings of the 1995 Asian Computing Science Conference on Algorithms, Concurrency and Knowledge
Annals of Mathematics and Artificial Intelligence
The theory of interval probabilistic logic programs
Annals of Mathematics and Artificial Intelligence
Annotated Probabilistic Temporal Logic: Approximate Fixpoint Implementation
ACM Transactions on Computational Logic (TOCL)
A top-k query answering procedure for fuzzy logic programming
Fuzzy Sets and Systems
Probabilistic multi-context systems
JIST'11 Proceedings of the 2011 joint international conference on The Semantic Web
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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 computationally reasoning about probabilities with 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 inteval probabilities, probabilistic logic programs (p-programs), orignally considered by Ng and Subrahmanian. We show that the probability ranges of atoms and formulas in p-programs cannot be expressed as single intervals. We construct the prescise description of the set of models of p-programs and study the computational complexity if this problem, as well as the problem of consistency of a p-program. We also study the conditions under which our semantics coincides with the single-interval semantics originally proposed by Ng and Subrahmanian for p-programs. Our work sheds light on the complexity of construction of reasoning formalisms for imprecise probabilities and suggests that interval probabilities alone are inadequate to support such reasoning.