12 - Dynamics

Abstract

Dynamic semantics provides a fresh look at most aspects of logical theory. Dynamic logic provides a broad logical space for dynamic operators and inference, and this logical space may be contrasted fruitfully with the empirical space of what is found in natural language and human cognition. But the most fruitful analogy is the earlier one of the introduction. Dynamic semantics has many counterparts in computer science, for obvious reasons. There are striking similarities between variable binding mechanisms in programming languages and what is currently being proposed for natural language. The expressions of propositional dynamic logic (PDL) are divided into two categories: the category of formulae, which form the static part of the language, and the category of programs, the truly dynamic part. But formulae can be constructed from programs and vice versa, so that there is an active interplay between the two parts. Dynamic logic is by no means the only mathematical paradigm for implementing the fundamental ideas of dynamic semantics, there is alternative logical framework based on category theory, sometimes called the “Utrecht approach.” Its basic tenet is this: The business of dynamic semantics is modeling interpretation processes. Thus, it is not sufficient to compositionally specify correct meanings: one should also specify these in a way that reflects temporal processes of interpretation. Category theory provides the tools to do this. Category theory is a branch of mathematics that is widely applied in both mathematics and computer science. The uses of category theory in linguistics are less widespread, but multiplying.