What grammars are, or ought to be

Progress toward distinguishing clearly between generative and model-theoretic syntactic frameworks has not been smooth or swift, and the obfuscatory term ˋconstraint-based' has not helped. This paper reviews some elementary subregular formal language theory relevant to comparing description languages for model-theoretic grammars, generalizes the results to trees, and points out that HPSG linguists have maintained an unacknowledged and perhaps unintended allegiance to the idea of strictly local description: unbounded dependencies, in particular, are still being conceptualized in terms of plugging together local tree parts annotated with the SLASH feature. Adopting a description language with quantifiers holds out the prospect of eliminating the need for the SLASH feature. We need to ask whether that would be a good idea. Binding domain phenomena might tell us. More work of both descriptive and mathematical sorts is needed before the answer is clear.