Generalising the interaction rules in probabilistic logic

Authors:
Arjen Hommersom;Peter J. F. Lucas
Affiliations:
Institute for Computing and Information Sciences, Radboud University Nijmegen, Nijmegen, The Netherlands;Institute for Computing and Information Sciences, Radboud University Nijmegen, Nijmegen, The Netherlands
Venue:
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Year:
2011

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Abstract

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 nonmonotonic 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 nonmonotonic reasoning with probabilistic information.