The foundations of a detailed grammar of Bayesian confirmation are presented as a theoretical tool for the formal analysis of reasoning in epistemology and philosophy of science. After a discussion of core intuitions grounding the measurement of confirmation in probabilistic terms, a number of basic, derived and structural properties of Bayesian incremental confirmation are defined, distinguished and investigated in their logical relationships. Illustrations are provided that a thorough development of this line of research would yield an appropriate general framework of inquiry for several analyses and debates surrounding confirmation and Bayesian confirmation in particular.