Probabilistic Logic Programming and Imprecise Probabilities: Current Work.Theresa Swift

Most formulations of Probabilistic Logic Programming (PLP) rely onpoint probabilities, usually drawn from small categoricaldistributions. However, imprecise probabilities arise from ignorance,from computational approximations such as bounded rationality, orother reasons. There have been numerous formulations for impreciseprobabilities, with PLP over the well-founded semantics a newer andsometimes controversial approach.

This presentation considers various topics related to impreciseprobabilities and PLP. As a first topic, the use of restraint and thewell-founded semantics can provide a tractable approximation tointractable PLP queries. As a second, the use of Dempster-Shaferbelief and plausibility functions within PLP can model upper and lowerbounds in cases of partial ignorance of probability masses. As athird, the use of T-norms can provide wide but tractable bounds onprobabilities. And finally, the relation of PLP under thewell-founded semantics to the credal stable semantics will bediscussed.

It should be noted that this work is on-going so that the resultspresented are provisional.