The founding paper [Pratt 1976] on dynamic logic begins as follows:

This book continues study of such mathematics with particular emphasis on semantic frameworks. We intend for these frameworks to be flexible, relying on no particular concept of state. Ultimately, extensions of the theory are to address at least program semantics, operating systems, concurrent processes and distributed networks; but the accomplishments of the foundational core herein are modest.

We shall be concerned with a category-theoretic foundation. One possible paradigm is that a morphism is the behaviour of a program. Composition of morphisms models program-chaining. An implementation of a programming language must provide a definite category in which to assign morphisms to programs. We shall also require that high-level specifications about programs map, as well, to true-false assertions about the corresponding interpreted programs.

Our semantic frameworks are categories satisfying certain axioms, that is, are models of the first-order theory of categories. Composition is the only primitive operation. Such models are strongly typed in that two morphisms cannot be composed unless the target of the first coincides exactly with the source of the second.