Probability theory on product logic

Our paper (coauthored by Lluis Godo, Sara Ugolini and myself) titled “Towards a probability theory for product logic: states, integral representation and reasoning” has been accepted to be published in the International Journal of Approximate Reasoning. There, among other things, we extend probability theory from the classical to the product t-norm fuzzy logic setting. More precisely, we axiomatize a generalized notion of finitely additive probability for product logic formulas, called state, and show that every state is the Lebesgue integral with respect to a unique regular Borel probability measure.