Natural language meaning has properties of both cognitive representations and formal/mathematical structures. But it is not clear how they actually relate to one another. The central aim of this article is to show that properties of cognitive representations and formal/mathematical structures of natural language meaning, albeit apparently divergent, can be united, as far as the basic properties of semantic structures are concerned. Thus, this article will formulate the form of unified representations for semantic structures. With this goal, this article takes into account standard formal-semantic representations and also Discourse Representation Theory (DRT) representations on the one hand and semantic representations in different versions of Conceptual/Cognitive Semantics (Jackendoff's, Langacker's and Talmy's approaches to Conceptual/Cognitive Semantics) and representations of Mental Spaces (Fauconnier's approach) on the other hand. The rationale behind the selection of these approaches is that the representations of semantic structures under these approaches are all amenable to unification. It must be emphasized that showing that the representations of semantic structures under these approaches can be unified does not simply amount to unifying these theories/approaches in toto. Rather, it is to demonstrate that cognitive representations and formal/mathematical structures can be shown to be inter-translatable for at least some accounts of linguistic meaning. © 2023 the author(s), published by De Gruyter.