A Dictionary of Grammatical Terms in Linguistics
n. A fully explicit device which specifies, for a given initial set of elements (the ‘vocabulary’ or ‘alphabet’), the complete set of strings of those elements which are in the language defined by the grammar.
A grammar which is fully formal constitutes a linguistic use of what mathematicians and logicians call a ‘formal system’. Most contemporary approaches to grammar purport to be formal in this sense, at least in principle, though in practice some frameworks are considerably more explicit than others; see, for example, the acid remarks in Pullum (1989).
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