Constructive Adpositional Grammars, already presented in this series
of lectures by Federico Gobbo, is a way to describe natural languages
which has been developed to clarify the relations between syntax,
semantics and pragmatics. In this talk, the mathematical model
supporting the grammars is introduced and motivated.
Specifically, it will be shown that, using Category Theory even in a
rather elementary way, it is possible to formalise not only a natural
language, but also, and more significantly, how and why this
formalisation is done, making clear what are the fundamental choices,
what are the sound alternatives, and how variations can be used to
obtain essentially equivalent grammars but with a different
orientation towards a specific purpose. So, a formal model becomes a
powerful way to reason about the structure of a language, making
conscious choices on what to emphasise and what to hide, in order to
describe just the aspects of interest.