4 found
Order:
  1.  83
    Multimo Dal Logics of Products of Topologies.Johan van Benthem, Guram Bezhanishvili, Balder ten Cate & Darko Sarenac - 2006 - Studia Logica 84 (3):369-392.
    We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion ${\bf S4}\oplus {\bf S4}$ . We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies. We prove that both of these logics are complete for the product of rational numbers ${\Bbb Q}\times {\Bbb Q}$ (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   19 citations  
  2.  65
    The Geometry of Knowledge.Johan van Benthem & Darko Sarenac - unknown
    The most widely used attractive logical account of knowledge uses standard epistemic models, i.e., graphs whose edges are indistinguishability relations for agents. In this paper, we discuss more general topological models for a multi-agent epistemic language, whose main uses so far have been in reasoning about space. We show that this more geometrical perspective affords greater powers of distinction in the study of common knowledge, defining new collective agents, and merging information for groups of agents.
    Direct download  
    Translate
     
     
    Export citation  
     
    Bookmark   9 citations  
  3.  8
    Cardinal Spaces and Topological Representations of Bimodal Logics.Benedikt Löwe & Darko Sarenac - 2005 - Logic Journal of the IGPL 13 (3):301-306.
    We look at bimodal logics interpreted by cartesian products of topological spaces and discuss the validity of certain bimodal formulae in products of so-called cardinal spaces. This solves an open problem of van Benthem et al.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  4. Modal Logics for Product Topologies.Johan van Benthem, Guram Bezhanishvili, Balder Ten Cate & Darko Sarenac - 2006 - Studia Logica 84 (3):375-99.