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Who Shaves the Barber, and with What Probability?
Spyros Hadjichristodoulou and David S. Warren

Benjamin Franklin once said that “the only things certain in life are death and taxes”. What he probably meant was that in everyday life probabilities play a crucial role in our decision making. Almost 300 years later, the problem of learning new things from a knowledge base has become even more important. In order to more precisely model probabilistic reasoning in knowledge bases, researchers have applied statistical methods within Logic Programming systems, so that learning that something is True or False comes with a certain probability. However, since Russell’s proposal of his famous “who shaves the barber” paradox, it has become clear that the semantics of the languages we use to describe the world we live in is multi-valued. In this paper, we introduce a statistical approach to logic programs by combining Well- Founded Semantics (which captures the core in Russell’s paradox) with probabilistic inference. The result is a Probabilistic Logic Programming framework where uncertainty in inference can be described using both a third logic value, and statistical information from probabilities.

Keywords: Well-founded semantics, probabilistic logic programming, uncertainty in inference

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