Computing abductive explanations is an important problem, which has been studied extensively in Artificial Intelligence (AI) and related disciplines.

Abduction is an important method of non-monotonic reasoning with many applications in AI and related topics. In this paper, we concentrate on propositional abduction, where the background knowledge is given by a propositional formula. Decision problems of great interest are the existence and the relevance problems. The complexity of these decision problems has been systematically studied while the counting complexity of propositional abduction has remained obscure. The goal of this work is to provide a comprehensive analysis of the counting complexity of propositional abduction in various classes of theories. 1

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