On the Products of Linear Modal Logics

Mark Reynolds, M. Zakharyaschev

    Research output: Contribution to journalArticle

    31 Citations (Scopus)

    Abstract

    We study two-dimensional Cartesian products of modal logics determined by infinite or arbitrarily long finite linear orders and prove a general theorem showing that in many cases these products are undecidable, in particular, such are the squares of standard linear logics like K4.3, S4.3, GL.3, Grz.3, or the logic determined by the Cartesian square of any infinite linear order. This theorem solves a number of open problems posed by Gabbay and Shehtman. We also prove a sufficient condition for such products to be not recursively enumerable and give a simple axiomatization for the square K4.3 x K4.3 of the minimal liner logic using non-structural Gabbay-type inference rules.
    Original languageEnglish
    Pages (from-to)909-931
    JournalJournal of Logic and Computation
    Volume11
    Issue number6
    DOIs
    Publication statusPublished - 2001

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