recursive (adj.)

A term used in GENERATIVE LINGUISTICS to refer to RULES which are capable of application to their own output in generating a SENTENCE, to the STRUCTURES thus generated, and to the languages characterized by such rules. There is no limit, for example, to the number of ADJECTIVES which may be used before a NOUN in English, or the number of ADVERBS which may MODIFY a VERB. Such sequences would be introduced by the repeated (‘recursive’) application of the appropriate adjective- or adverb-insertion rules in the relevant section of the GRAMMAR. The importance of recursion (or recursiveness) is that recursive rules are the main FORMAL means of accounting for the CREATIVITY of LANGUAGE: by using this device, an infinite set of sentences can be generated from a finite set of rules. A simple illustration of how this can be formalized is in the following rules:

These rules say, in effect, that there is in principle no limit to the number of PREPOSITIONAL PHRASES which may occur following a noun in a noun phrase, e.g. the man in a coat with a collar . . . The phenomenon is also known as ‘iteration’. The term has also been used to define an extension of TRANSITION NETWORK GRAMMARS – recursive transition networks (RTNs). In highly FORMAL discussion, the term may be used in its general mathematical sense to indicate a FUNCTION which can be modelled as an ALGORITHM. A recursive language is one whose characteristic function is recursive in this sense; the language and its complement must both be RECURSIVELY ENUMERABLE.