LAMBECK CALCULUS AND FORMAL GRAMMARS

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

Владимир Андреевич Успенский (27.11.1930-27.06.2018)

International audienceThe genre of the journal Uspekhi Matematicheskikh Nauk1 suggests that we should mainly review the mathematical results of Vladimir Uspensky. However, the whole of his personality and the scope of his activities oblige us to take a broader view. He was an outstanding mathematician, but this also manifested itself in diverse areas where he was active and in his results even outside mathematics. We will also discuss these areas in our survey. During Uspensky’s lifetime no tribute paper dedicated to him appeared in this journal, and this makes it particularly important to (finally) publish a biography of him as a scholar in Uspekhi Matematicheskikh NaukСам жанр журнала "Успехи математических наук" предполагает обзор прежде все-го математических результатов Владимира Андреевича Успенского. Однако вся его личность и деятельность обязывают к более широкому взгляду на вещи. Владимир Андреевич был выдающимся математиком, и это проявлялось в различных сферах его деятельности и её результатах и вне математики. Об этих сферах также будет идти речь в нашем обзоре. При жизни В. А. Успенский обходился без юбилейных статей в "Успехах". Это делает особенно важным опубликовать, хотя и с опозданием, его биографию как учёного в УМН