Let us only recall here such approaches as: the lexicosemantic analysis by Katz and Postal (1964), who work with the notions of head and modifier when specifying selection restrictions; (ii) the distinction between surface-oriented constituent structure and the (underlying) functional structure in lexical functional grammar by Bresnan (1978) and Kaplan and Bresnan (1982); (iii) the above-mentioned case grammar by Fillmore, motivated by the conviction that Chomskyan deep structure (with its specification of "deep" subject as a constituent of S regardless of the (different) semantic relations of the given NP to the verb) is not deep enough to capture the real underlying structure of the sentence; and (iv) the consecutive introduction of theta roles into the government and binding theory.
it is not difficult to see an analogy between this view and a more modern and explicit treatment of the so-called centering theory (Grosz, Joshi, and Weinstein 1995) and its shifts of centers.