Halliday & Matthiessen (1999: 447, 447n):
Such analyses ['surface x is really deep y'] were often supported by universalist arguments such as "negation is a verb in certain languages, so it is reasonable to claim that it is really a verb in all". … they tended to make deep structure, the 'real' structure, look like predicate logic. Surface structure came out looking like a (transformationally) twisted version of logical structures. But predicate logic had been derived from one particular area of the grammar, a simplified version of the experiential aspect of the clause; it could be used as an idealised model of certain types of figure, for the purpose of explicit rule-based reasoning, but it was not intended to be a tool for analysing the entire semantic structure of a natural language.² This view has largely been abandoned and the notion of a semantically irresponsible surface structure is no longer generally held.
² In terms of our model of a stratified metalanguage, we can see that taking the categories of predicate logic (or any other logical systems) to be linguistic ones constitutes a strata! slippage: categories from the level of representation in the metalanguage are imported into the theoretical account of the object language.
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In Chomskyan linguistics, this is the relocation of the universals of Platonic realism — which are said to exist outside and independently of human minds — into the res cogitans of Cartesian dualism.