Abstract:
I want to present some models for the Full Lambek calculus (and its well-known fragments), which are based on formal languages. L-models itself are of course excluded because of their distributive laws. I rather present models based on closure operators, which in turn are based on a Galois connection and formal concept analysis over formal languages. These models turn out to have some interesting properties and applications for linguistics and formal learning theory. I also present a related semantics based on automata. Finally, I want to approach the question: what is the meaning of certain distributive laws in a language-theoretic setting, and in which cases can we get rid of closure operations, thereby returning to canonical L-models and/or relation models? To these I can partly answer, partly I still cannot.