Probabilistic logic programming with conditional constraints
ACM Transactions on Computational Logic (TOCL)
Probabilistic Default Reasoning with Conditional Constraints
Annals of Mathematics and Artificial Intelligence
Fixpoint Characterizations for Many-Valued Disjunctive Logic Programs with Probabilistic Semantics
LPNMR '01 Proceedings of the 6th International Conference on Logic Programming and Nonmonotonic Reasoning
Many-Valued Disjunctive Logic Programs with Probabilistic Semantics
LPNMR '99 Proceedings of the 5th International Conference on Logic Programming and Nonmonotonic Reasoning
Probabilistic deduction with conditional constraints over basic events
Journal of Artificial Intelligence Research
Annals of Mathematics and Artificial Intelligence
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We introduce probabilistic many-valued logic programs in which the implication connective is interpreted as material implication. We show that probabilistic many-valued logic programming is computationally more complex than classical logic programming. More precisely, some deduction problems that are P-complete for classical logic programs are shown to be co-NP-complete for probabilistic many-valued logic programs. We then focus on many-valued logic programming in Pr*_n as an approximation of probabilistic many-valued logic programming. Surprisingly, many-valued logic programs in Pr*_n have both a probabilistic semantics in probabilities over a set of possible worlds and a truth-functional semantics in the finite-valued Lukasiewicz logics L_n. Moreover, many-valued logic programming in Pr*_n has a model and fixpoint characterization, a proof theory, and computational properties that are very similar to those of classical logic programming.