Yes, the matching of “mental content” between one mind and another is perhaps the central issue in semantics. You might want to take a look at Warglien and Gärdenfors, Semantics, conceptual spaces, and the meeting of minds:
Abstract: We present an account of semantics that is not construed as a mapping of language to the world but rather as a mapping between individual meaning spaces. The meanings of linguistic entities are established via a “meeting of minds.” The concepts in the minds of communicating individuals are modeled as convex regions in conceptual spaces. We outline a mathematical framework, based on fixpoints in continuous mappings between conceptual spaces, that can be used to model such a semantics. If concepts are convex, it will in general be possible for interactors to agree on joint meaning even if they start out from different representational spaces. Language is discrete, while mental representations tend to be continuous—posing a seeming paradox. We show that the convexity assumption allows us to address this problem. Using examples, we further show that our approach helps explain the semantic processes involved in the composition of expressions.
You can find those ideas further developed in Gärdenfors’ 2014 book, Geometry of Meaning, chapters 4 and 5, “Pointing as Meeting of Minds” and “Meetings of Minds as Fixpoints,” respectively. In chapter 5 he develops four levels of communication.
Yes, the matching of “mental content” between one mind and another is perhaps the central issue in semantics. You might want to take a look at Warglien and Gärdenfors, Semantics, conceptual spaces, and the meeting of minds:
You can find those ideas further developed in Gärdenfors’ 2014 book, Geometry of Meaning, chapters 4 and 5, “Pointing as Meeting of Minds” and “Meetings of Minds as Fixpoints,” respectively. In chapter 5 he develops four levels of communication.