Language in Action ― Categories, Lambdas and Dynamic Logic

Language in Action demonstrates the viability of mathematical research into the foundations of categorial grammar, a topic at the border between logic and linguistics. Since its initial publication, it has become the classic work in the foundations of categorial grammar. A new addendum to this paperback edition updates the open research problems and records relevant results through pointers to the literature.
Van Benthem presents the categorial processing of syntax and semantics as a central component in a more general dynamic logic of information flow, in tune with computational developments in artificial intelligence and cognitive science. Using the paradigm of categorial grammar, he describes the substructural logics driving the dynamics of natural language syntax and semantics. This is a general type-theoretic approach that lends itself easily to proof-theoretic and semantic studies in tandem with standard logic. The emphasis is on a broad landscape of substructural categorial logics and their proof-theoretical and semantic peculiarities. This provides a systematic theory for natural language understanding, admitting of significant mathematical results. Moreover, the theory makes possible dynamic interpretations that view natural languages as programming formalisms for various cognitive activities. More

Johan van Benthem is Professor of Logic and Its Applications and Director of the Institute for Logic, Language, and Computation at the University of Amsterdam. He is also Distinguished Visiting Professor in the Department of Philosophy at Stanford University.