Artificial Intelligence
Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
A logic for reasoning about probabilities
Information and Computation - Selections from 1988 IEEE symposium on logic in computer science
An analysis of first-order logics of probability
Artificial Intelligence
Probabilistic logic programming
Information and Computation
Annals of Mathematics and Artificial Intelligence
Finding Most Probable Worlds of Probabilistic Logic Programs
SUM '07 Proceedings of the 1st international conference on Scalable Uncertainty Management
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The "Most Probable World" (MPW) problem in probabilistic logic programming (PLPs) is that of finding a possible world with the highest probability. Past work has shown that this problem is computationally intractable and involves solving exponentially many linear programs, each of which is of exponential size. In this paper, we study what happens when the user focuses his interest on a set of atoms in such a PLP. We show that we can significantly reduce the number of worlds to be considered by defining a "reduced" linear program whose solution is in one-one correspondence with the exact solution to the MPW problem. However, the problem is still intractable. We develop a Monte Carlo sampling approach that enables us to build a quick approximation of the reduced linear program that allows us to estimate (inexactly) the exact solution to the MPW problem. We show experimentally that our approach works well in practice, scaling well to problems where the exact solution is intractable to compute.