Lecture 1 Generative Capacity and Natural Language Last modified 2014/09/11 Formal grammars

An essential property of human language that distinguishes it from other information-carrying systems (e.g., the system of traffic signs) is its creative as-pect: it makes “infinite use of finite means ” in the sense that it allows infinitely many ways of combining finitely many basic linguistic units to form arbitrarily complex expressions. (This property is shared by some artificial “languages ” like programming languages and languages of symbolic logic.) By a grammar we mean a system of rules whereby words—which we assume to be basic linguis-tic units for the sake of simplicity—may be put together to form sentences. A speaker of a language has a certain grammar internalized in his/her head and uses it to produce and understand sentences of his/her language. What kind of rule sys-tem human grammars are is an empirical issue and a subject matter of linguistics. One way of approaching this question is to study mathematical models of grammar (formal grammars). Different types of formal grammars (or grammar formalisms) have different formal properties, which may render them more or less plausible as models of human grammars. Especially, a certain limitation in th