Probabilities of Conditionals via Labeled Markov Graphs

Abstract In the paper, we provide a general formalism for computing probabilities of indicative conditionals. Our model is based on the idea of constructing a (labeled) Markov graph G(α), which models the sentence α, containing an arbitrarily complex conditional (exhibiting in particular its structure). The formalism makes computing these probabilities an easy task—it consists of solving simple systems of linear equations. The graph G(α) generates a canonical probability space S(α) = (Ω α , Σ α , P α ), where α is given an interpretation as an event so that the probability can be computed mathematically. We present a general inductive definition of the graph G(α) for a sentence α of arbitrary complexity. It is based on the idea of defining graph-building operations which correspond to the negation and conjunction and the non-Boolean conditional connective →. The definition enables the construction of graphs and the corresponding systems of equations for arbitrarily complex conditionals in an algorithmic and efficient manner.