Causal Markov Categories and Possibility Theory

MarkovFritz, T.Terán, P. categories are a recent approach to probability theory that is category-theoretical rather than measure-theoretical. It takes (an abstract version of) Markov kernels, rather than measurable mappings, as primitive. Our aim is to bring researchers in possibility theory and other uncertainty formalism into contact with Markov categories by explaining how the categorical formalism applies in this context as well. We note that, under any continuous triangular norm, possibilistic transition matrices between finite sets form a causal Markov category, just like probabilistic transition matrices do.