LAMBECK CALCULUS AND FORMAL GRAMMARS

Abstract

The work is devoted to the study of the categorical grammars based on the syntactic Lambeck calculus. It has been proved that the categorical grammars based on the Lambeck calculus generate exactly all the context-free languages, the same takes place for the Lambeck calculus with empty antecedents, for Lambeck calculus with one and for multiplicative fragment of the cyclic linear logics. It has been proved that all the elementary fragments of Lambeck calculus possess the interpolating property. The compatibility relation solubility of syntactic types in the Lambeck calculus has been proved. The results can find application in the mathematical linguistics and non-classic logics. The developed technique of studying non-commutative linear logics by means of the interpretation in the free group, modification of the Maehara and Schutte method, Craig proof of the interpolating property and also the combinatory methods have been used by an author in the investigation. The work results can be used in the Moscow State University, Novosibirsk State University, St.-Petersburg State University a.oAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio