  This paper introduces a novel type theory and logic for probabilistic
reasoning. Its logic is quantitative, with fuzzy predicates. It includes
normalisation and conditioning of states. This conditioning uses a key aspect
that distinguishes our probabilistic type theory from quantum type theory,
namely the bijective correspondence between predicates and side-effect free
actions (called instrument, or assert, maps). The paper shows how suitable
computation rules can be derived from this predicate-action correspondence, and
uses these rules for calculating conditional probabilities in two well-known
examples of Bayesian reasoning in (graphical) models. Our type theory may thus
form the basis for a mechanisation of Bayesian inference.
