The concept of "strong generative capacity" (SGC) of a linguistic formalism
was introduced by Chomsky in the early sixties in order to characterize
descriptive capacity. However, the original definition proposed by Chomsky
turned out to be unuseable, especially when one wished to compare the SGC
of different types of formalisms. This book provides for the first time a
rigorous and useful characterization of SGC, defining it as the model
theoretic semantics of linguistic formalism. Specifically, abstract
interpretation domains are defined in theory-neutral set-theoretical terms,
and the SGC of a theory with respect to a given interpretation domain is
characterized as the range of a specific interpretation function mapping
structural descriptions of that theory into elements of that domain.
Interpretation domains are defined for such notions as labeled
constituency, dependency, endocentricity and linking and applied to the
analysis of a range of linguistic formalisms, among which context-free
grammars, dependency grammars, X-bar grammars, tree-adjoing grammars,
transformational grammars and categorial grammars.