A general approach to reasoning with probabilities

We propose a general scheme for adding probabilistic reasoning capabilities to a wide variety of knowledge representation formalisms and we study its properties. Syntactically, we consider adding probabilities to the formulas of a given base logic. Semantically, we define a probability distribution over the subsets of a knowledge base by taking the probabilities of the formulas into account accordingly. This gives rise to a probabilistic entailment relation that can be used for uncertain reasoning. Our approach is a generalisation of many concrete probabilistic enrichments of existing approaches, such as ProbLog (an approach to probabilistic logic programming) and the constellation approach to abstract argumentation. We analyse general properties of our approach and provide some insights into novel instantiations that have not been investigated yet.