ABSTRACT
The aim of this chapter is to formulate the form of unified representations for semantic structures that can turn out to be easily amenable to the description of semantic variation in cognitive terms. The underlying motivation is that the logical organization of natural language can be shown to be fully compatible with the cognitive organization of linguistic structures. On the one hand, semantic structures have been analyzed in the tradition of formal semantics in terms of set-theoretic structures that have an externalist orientation. On the other hand, semantic structures in cognitive/conceptual semantics are patterns of conceptualization grounded in the mind. In this view, semantic structures are themselves cognitive structures. The principles of formal equivalence that can show how the two types of representations can be inter-translated are formulated by taking into account standard formal-semantic descriptions and semantic representations in Discourse Representation Theory, Conceptual Semantics and Mental Spaces. Finally, some residual philosophical issues surrounding intentionality, reality, the mental entrenchment of semantic structures and embodiment are discussed. The argument defended is that even if conceptual/cognitive structures are trapped inside the brain/mind, there is nothing that actually prevents them from standing in relation to the outside world.
