Contextual Grammars as Generative Models of Natural Languages

The paper discusses some classes of contextual grammars--mainly those with "maximal use of selectors"--giving some arguments that these grammars can be considered a good model for natural language syntax. A contextual grammar produces a language starting from a finite set of words and iteratively adding contexts to the currently generated words, according to a selection procedure: each context has associated with it a selector, a set of words; the context is adjoined to any occurrence of such a selector in the word to be derived. In grammars with maximal use of selectors, a context is adjoined only to selectors for which no superword is a selector. Maximality can be defined either locally or globally (with respect to all selectors in the grammar). The obtained families of languages are incomparable with that of Chomsky context-free languages (and with other families of languages that contain linear languages and that are not "too large"; see Section 5) and have a series of properties supporting the assertion that these grammars are a possible adequate model for the syntax of natural languages. They are able to straightforwardly describe all the usual restrictions appearing in natural (and artificial) languages, which lead to the non-context-freeness of these languages: reduplication, crossed dependencies, and multiple agreements; however, there are center-embedded constructions that cannot be covered by these grammars. While these assertions concern only the weak generative capacity of contextual grammars, some ideas are also proposed for associating a structure to the generated words, in the form of a tree, or of a dependence relation (as considered in descriptive linguistics and also similar to that in link grammars).