Barwise's information frames and modal logics : научное издание

Описание

Тип публикации: статья из журнала

Год издания: 2003

Аннотация: The paper studies Barwise's information frames and answers the John Barwise question: to find axiomatizations for the modal logics generated by information frames. We find axiomatic systems for (i) the modal logic of all complete information frames, (ii) the logic of all sound and complete information frames, (iii) the logic of allПоказать полностьюhereditary and complete information frames, (iv) the logic of all complete, sound and hereditary information frames, and (v) the logic of all consistent and complete information frames. The notion of weak modal logics is also proposed, and it is shown that the weak modal logics generated by all information frames and by all hereditary information frames are K and K4 respectively. To develop general theory, we prove that (i) any Kripke complete modal logic is the modal logic of a certain class of information frames and that (ii) the modal logic generated by any given class of complete, rarefied and fully classified information frames is Kripke complete. This paper is dedicated to the memory of talented mathematician John Barwise.

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Издание

Журнал: Archive for Mathematical Logic

Выпуск журнала: Т. 42, 3

Номера страниц: 261-277

ISSN журнала: 09335846

Издатель: Springer-Verlag GmbH

Авторы

  • Rybakov V.V. (Department of Computing and Mathematics, Manchester Metropolitan University, All Saints, Manchester M15 6BH, U.K. e-mail: V.Rybakov@mmu.ac.uk)