Conditioning and Flexibility in Compositional Models

Reasoning by cases or assumptions is a common form of human reasoning. In case of probability reasoning, this is modeled by conditioning of a multidimensional probability distribution. Compositional models are defined as a multidimensional distributions assembled from a (so called generating) sequence of lowdimensional probability distributions, with the help of operators of composition. In this case, the conditioning process can be viewed as a transformation of one generating sequence into another one. It appears that the conditioning process is simple when conditioning variable appears in the argument of the first distribution of the corresponding generating sequence. That is why we introduce the so called flexible sequences. Flexible sequences are those, which can be reordered in many ways that each variable can appears among arguments of the first distribution. In this paper, we study the problem of flexibility in light of the very recent solution of the equivalence problem