Generalising the interaction rules in probabilistic logic

The last two decades has seen the emergence of many different probabilistic logics that use logical languages to specify, and sometimes reason, with probability distributions. Probabilistic logics that support reasoning with probability distributions, such as ProbLog, use an implicit definition of an interaction rule to combine probabilistic evidence about atoms. In this paper, we show that this interaction rule is an example of a more general class of interactions that can be described by non-monotonic logics. We furthermore show that such local interactions about the probability of an atom can be described by convolution. The resulting extended probabilistic logic supports non-monotonic reasoning with probabilistic information.