If you haven't, you should explore domain-driven design (DDD). It's an explicit idea in that framework that a problem needs a "ubiquitous language" and an identified "bounded context" where the said language is valid.

Like you, when approaching a new problem I like to nail down the terms we are discussing, literally scaffolding classes and types (in C++) as the problem is being discussed. It drives the adoption of unambiguous terms. Then as solutions are discussed the "ubiquitous language" helps clearly identify the interactions between types.