To be able to turn linguistics into a hard science, Chomsky  assigned a mathematical correlate to the intuitive idea of a "language". He proposed to identify a language with a set of sentences: with the set of grammatically correct utterance forms that are possible in the language. The goal of descriptive linguistics is then to characterise, for individual languages, the set of grammatical sentences explicitly, by means of a formal grammar. And the goal of explanatory linguistic theories should then be, to determine the universal properties which the grammars of all languages share, and to give a psychological account of these universals.
In this view, linguistic theory is not immediately concerned with describing the actual language use in a language community. Although we may assume that there is a relation between the language users' grammaticality intuitions and their actual language behaviour, we must make a sharp distinction between these; on the one hand the language system may offer possibilities which are rarely or never used; on the other hand the actual language use involves mistakes and sloppinesses which a linguistic theory should not necessarily account for. In Chomsky's terminology: linguistics is concerned with the linguistic competence rather than the actual performance of the language user. Or, in the words of Saussure, who had emphasized this distinction before: with langue rather than parole.
Chomsky's work has constituted the methodological paradigm for almost all linguistic theory of the last few decades. This comprises not only the research tradition that is explicitly aiming at working out Chomsky's syntactic insights. The perspective summarized above has also determined the goals and methods of the most important alternative approaches to syntax, and of the semantic research traditions which have grown out of Richard Montague's work. Now we may ask: how does language technology relate to this language-theoretical paradigm?