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

Most formulations of Probabilistic Logic Programming (PLP) rely on point probabilities, usually drawn from small categorical distributions. However, imprecise probabilities arise from ignorance, from computational approximations such as bounded rationality, or other reasons. There have been numerous formulations for imprecise probabilities, with PLP over the well-founded semantics a newer and sometimes controversial approach.

This presentation considers various topics related to imprecise probabilities and PLP. As a first topic, the use of restraint and the well-founded semantics can provide a tractable approximation to intractable PLP queries. As a second, the use of Dempster-Shafer belief and plausibility functions within PLP can model upper and lower bounds in cases of partial ignorance of probability masses. As a third, the use of T-norms can provide wide but tractable bounds on probabilities. And finally, the relation of PLP under the well-founded semantics to the credal stable semantics will be discussed.

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