Probabilistic Belief Contraction Using Argumentation

When a belief state is represented as a probability function P, the resulting belief state of the contraction of a sentence (belief) from the original belief state P can be given by the probabilistic version of the Harper Identity. Specifically, the result of contracting P by a sentence h is taken to be the mixture of two states: the original state P, and the resultant state P*((sic)h) of revising P by the negation of h. What proportion of P and P*((sic)h) should be used in this mixture remains an open issue and is largely ignored in literature. In this paper, we first classify different belief states by their stability, and then exploit the quantitative nature of probabilities and combine it with the basic ideas of argumentation theory to determine the mixture proportions. We, therefore, propose a novel approach to probabilistic belief contraction using argumentation.