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What Does a Grammar Formalism Say About a Language?
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Abstract
linguistics, away from formalisms based on a procedural interpretation of
grammars towards constraint-based formalisms---formalisms that define
languages by specifying a set of constraints that characterize the set of
well-formed structures analyzing the strings in the language. A natural
extension of this trend is to define this set of structures
model-theoretically---to define it as the set of ordinary mathematical
structures that satisfy some set of logical axioms. This approach raises a
number of questions about the nature of linguistic theories and the role of
grammar formalisms in expressing them. In this talk we explore these
questions and some of their consequences both for the model-theoretic and
the grammar-based approaches to formalizing theories of syntax.
With respect to the model-theoretic approach, we argue that linguistic
theories cannot be captured simply by defining the set of structures
licensed by a particular instance of a grammar. Rather, one must account
for the generalizations the theory makes about language as well---one must
capture the properties the theory ascribes to the natural languages as a
class. On the other hand, we argue that such model-theoretic investigation
has much to offer grammar-based theories. The actual meaning of the
linguistic principles that are embodied in grammar formalisms is often times
obscure. By reformulating these principles explicitly as properties of
structures (or of properties of sets of structures) one gains considerably
clarity in understanding their consequences. Furthermore, the
model-theoretic approach has the potential to provide a uniform
representation for a range of grammatical formalisms, with the prospect of
reducing distinctions between the underlying mechanisms to distinctions
between the properties of the sets of structures they license.
We ground our discussion in a model-theoretic reinterpretation of
Generalized Phrase-Structure Grammar.
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