Category theory, logic and formal linguistics: some connections, old and new
This work connects theoretical logic and linguistics, but it is incremental as it builds on existing trends without introducing new methods or results.
The paper surveys current trends in intuitionistic and linear type theories that integrate categorical, geometrical, and computational aspects, and explores how these logical frameworks can model meaning in language.
We seize the opportunity of the publication of selected papers from the \emph{Logic, categories, semantics} workshop in the \emph{Journal of Applied Logic} to survey some current trends in logic, namely intuitionistic and linear type theories, that interweave categorical, geometrical and computational considerations. We thereafter present how these rich logical frameworks can model the way language conveys meaning.