Halliday & Matthiessen (1999: 424):
Cognitive semantics has emerged out of the generative tradition in the last ten to fifteen years. It is a natural development of the general cognitivist research program that began in the 1950s with the birth of cognitive science, Artificial Intelligence, and Chomsky's cognitively oriented linguistics.Those adopting the cognitive approach to semantics share certain assumptions about semantic organisation as part of conceptual organisation, and tend to reject formal, Montague-style semantics, as indicated by the passages from Jackendoff and Lakoff quoted above. However, they seem to fall into two groupings, which can be conveniently described in terms of the US coastline [east vs west].