Some Questions of Language Theory

It is shown that theassumption that language is non-finite involves the use of a constructive logic which lea#s to some restrictions on language theory an~ to the fact that the only possible definition of language is that propose~ by ~enerative grammars. Generative grammars can be formulate~ a~ normal /~ar~ov/ algorithms an~ thu~ their study can be reduce~ to the stu#7 of such algorithms of a special type. A new type of ~enerative grammar is ~efine~, called matrix grammar. It is shown that a language generated by a context-restricted grammar can be also generate~ by a matrix grammar. Some properties of matrix grammars are shown to be ~eci~able. The problem of the explicative power of generative grammars is ~iscusse~. I. language metatheory, as indeed any metatheorT, must exactly specify the o~erations allowed in building up the theory /of language/. This may be ~one by choosing the lo~ic of the tbeorT.If language is consi~ere~ a non-finite set,a constructive logic /Kolmogorov/ must be choosen. This entails some restrictions on the notions an~ methods to be used in language theory. ~amely, we can not speak of actually infinite sets, au~ we can not use t~e quantifiers "the~ exists" an~ "all". Thus we can not include in language theory the notion Of 'language' itself in the usual way, as the set of al~ /grammatically or sentences. Similarly, we "distributional analysis" restrictinus./ , as it generally has semantically/ correct can not makeuse of /at least without any the form: