Conceptual Semantics is a framework for semantic analysis developed mainly by Ray Jackendoff. Its aim is to provide a characterization of the conceptual elements by which a person understands words and sentences, and thus to provide an explanatory semantic representation (title of a Jackendoff 1976 paper).
References
Jackendoff, Ray (1976) 'Toward an explanatory semantic representation'. Linguistic Inquiry, 7.1, pp. 89-150.
Jackendoff, Ray (1983) Semantics and Cognition. Cambridge, Mass.: MIT Press.
Jackendoff, Ray (1990) Semantic Structures. Cambridge, Mass.: MIT Press.
Jackendoff, Ray (1991) 'Parts and boundaries'. In: Levin, Beth & Pinker, Steven (eds.) Lexical & Conceptual Semantics (special issue of Cognition). Cambridge, MA/Oxford: Blackwell.