NDLI: The theory of interval probabilistic logic programs

Content Provider	Springer Nature Link
Author	Dekhtyar, Alex Dekhtyar, Michael I.
Copyright Year	2008
Abstract	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.
Starting Page	355
Ending Page	388
Page Count	34
File Format	PDF
ISSN	10122443
Journal	Annals of Mathematics and Artificial Intelligence
Volume Number	55
Issue Number	3-4
e-ISSN	15737470
Language	English
Publisher	Springer Netherlands
Publisher Date	2008-12-19
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Probabilistic logic programming Interval probabilities Probabilistic satisfaction Possible worlds semantics Statistical Physics, Dynamical Systems and Complexity Mathematics Computer Science Artificial Intelligence (incl. Robotics)
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Artificial Intelligence

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