Artificial Intelligence
Quantitative deduction and its fixpoint theory
Journal of Logic Programming
On the complexity of computing the volume of a polyhedron
SIAM Journal on Computing
A logic for reasoning about probabilities
Information and Computation - Selections from 1988 IEEE symposium on logic in computer science
A random polynomial-time algorithm for approximating the volume of convex bodies
Journal of the ACM (JACM)
Sampling and integration of near log-concave functions
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Probabilistic logic programming
Information and Computation
Two Algorithms for Determining Volumes of Convex Polyhedra
Journal of the ACM (JACM)
Probalilistic Logic Programming under Maximum Entropy
ECSQARU '95 Proceedings of the European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Simulated annealing in convex bodies and an O*(n4) volume algorithm
Journal of Computer and System Sciences - Special issue on FOCS 2003
Mathematical aspects of mixing times in Markov chains
Foundations and Trends® in Theoretical Computer Science
Annals of Mathematics and Artificial Intelligence
Logic programs with uncertainties: a tool for implementing rule-based systems
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 1
On lifted inference for a relational probabilistic conditional logic with maximum entropy semantics
FoIKS'12 Proceedings of the 7th international conference on Foundations of Information and Knowledge Systems
Imprecise probabilistic query answering using measures of ignorance and degree of satisfaction
Annals of Mathematics and Artificial Intelligence
Transactions on Large-Scale Data- and Knowledge-Centered Systems VI
| Hi-index | 0.00 |
Probabilistic logic programs (PLPs) define a set of probability distribution functions (PDFs) over the set of all Herbrand interpretations of the underlying logical language. When answering a query Q , a lower and upper bound on Q is obtained by optimizing (min and max) an objective function subject to a set of linear constraints whose solutions are the PDFs mentioned above. A common critique not only of PLPs but many probabilistic logics is that the difference between the upper bound and lower bound is large, thus often providing very little useful information in the query answer. In this paper, we provide a new method to answer probabilistic queries that tries to come up with a histogram that "maps" the probability that the objective function will have a value in a given interval, subject to the above linear constraints. This allows the system to return to the user a histogram where he can directly "see" what the most likely probability range for his query will be. We prove that computing these histograms is #P -hard, and show that computing these histograms is closely related to polyhedral volume computation. We show how existing randomized algorithms for volume computation can be adapted to the computation of such histograms. A prototype experimental implementation is discussed.