HPSG as model-theoretic and generative grammar?

The page Model-theoretic grammar - Wikipedia says

Model-theoretic grammars , also known as constraint-based grammars, contrast with generative grammars in the way they define sets of sentences: they state constraints on syntactic structure rather than providing operations for generating syntactic objects.

and it lists HPSG.

But the page Generative grammar - Wikipedia also lists HPSG in the list of mnonostratal (or non-transformational) grammars.

Does it make sense?

I think this is just a poor (overloaded) term usage; “generative” is often (very often!) used to mean “Minimalist” rather than literally “grammars which generate sentences”.

While “generative” is sometimes used to mean “generativist”/“transformational”/“Chomskyan”/“Minimalist”, that’s not what is meant in that article.

A model-theoretic approach to syntax views syntactic objects as fixed and states constraints on them. A generative approach gives an algorithm that enumerates them. As a simple example, consider the class of regular languages. The class can be defined generatively, using finite-state automata. Or it can be defined model-thoeretically, using monadic second-order logic over strings. The equivalence of these two definitions is the BĂĽchi-Elgot-Trakhtenbrot theorem - Wikipedia

Geoffrey Pullum has argued in favour of the model-theoretic approach: http://www.lel.ed.ac.uk/~gpullum/Metatheory.pdf

But the distinction is not completely strict, and HPSG can be viewed in both ways.

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