Halliday & Matthiessen (1999: 424-5, 424n):
On the East Coast, Jackendoff (e.g., 1983), drawing on his earlier work on interpretive semantics (Jackendoff, 1972), has developed a generativist type of cognitive semantics,⁴ which he calls conceptual semantics. This is integrated with a number of aspects of modem generative theory, e.g. the X-bar syntactic subtheory. Jackendoff puts forward a conceptual ontology and suggestions for conceptual structure that we shall return to below. This version of cognitive semantics is arguably the more closely associated with the logical and philosophical tradition (cf. Jackendoff, 1988: 81-2).
⁴ Jackendoff calls his approach conceptual semantics and Lakoff calls his cognitive semantics. We use the term cognitive semantics as the generic term for cognitively oriented approaches to semantics.