Mathematics and linguistics
Mathematical methods in linguistics pdf
Bush and E. Galanter Eds. Chomskii, New in Linguistics , 2 pp. However, in a number of models the initial data are represented as finite sets and finitary relations; in these cases the procedures in the model are effective. Grammar, categorial , which are characterized by a special method of assignment of information on the syntactical properties of words. Among the context-sensitive grammars, in turn, of special importance, both from the theoretical as from the applied point of view, are context-free grammars cf. Simultaneously with formal grammars which simulate the transformations of linguistic objects there arise constructions meant for the formal description of these same objects. Preview Unable to display preview. Bordering on the theory of analytic models is the theory of linguistic deciphering: its objective is the construction of procedures, applied in suitable analytic models to "unordered" empirical data of the language, which are always effective and allow one to obtain not only abstract definitions but also concrete information on the structure of a concrete language for example, algorithms realizing the automatic subdivision of the set of phonemes of a language into the classes of vowels and constants without using any information on the language apart from some sufficiently long text. In general, computational linguistics require the contributions of among others, linguists, sages in artificial intelligence, computer science experts, logicians, mathematicians, philosophers, neuroscientists, cognitive psychologists and scientists, anthropologists and psycholinguists.
Hence, when mechanical translation was unsuccessful in producing immediate, accurate translations, it became clear that the automatic production of human languages was much more complex than initially presumed.
The linguistic concepts underlying the formal description of the structure of a language belong to structural linguistics. The origin of mathematical linguistics can be roughly placed in the 's; it was brought to life first of all by the internal needs of theoretical linguistics, which at that time was ripe for an elaboration of its basic ideas, and also by problems in the automatic processing of linguistic information see Automatic translation.
At these levels the structures are usually trees. Such a stage already is easier to describe mathematically if one makes more precise the representation of objects at the intermediate levels and simulates the transition from one level to another by effective mappings.
For example, as one of the roughest articulations of a certain stage can be included the passage from "meaning" of statements to "syntactic structures without linear order" — a set of statements joined by "syntactic relations" but not yet arranged in linear sequence; in the next stage one obtains linear sequences of words, which are then transformed into a chain of sounds.
Keeping its applied sense, mathematical linguistics is constantly evolving along the path of transforming into a pure mathematical discipline, being essentially a branch of mathematical logic. Virtually any paper in generative linguistics illustrate how one can make precise statements of a nonquantitative nature about language.
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