An Algebraic Approach to Canonical Formulas: Modal Case

Studia Logica 99 (1-3):93-125 (2011)
Abstract
We introduce relativized modal algebra homomorphisms and show that the category of modal algebras and relativized modal algebra homomorphisms is dually equivalent to the category of modal spaces and partial continuous p-morphisms, thus extending the standard duality between the category of modal algebras and modal algebra homomorphisms and the category of modal spaces and continuous p-morphisms. In the transitive case, this yields an algebraic characterization of Zakharyaschev’s subreductions, cofinal subreductions, dense subreductions, and the closed domain condition. As a consequence, we give an algebraic description of canonical, subframe, and cofinal subframe formulas, and provide a new algebraic proof of Zakharyaschev’s theorem that each logic over K4 is axiomatizable by canonical formulas
Keywords Modal logic  duality theory  relativization
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 9,360
External links
  •   Try with proxy.
  • Through your library Configure
    References found in this work BETA

    View all 6 references

    Citations of this work BETA
    Similar books and articles
    Yde Venema (1995). Cylindric Modal Logic. Journal of Symbolic Logic 60 (2):591-623.
    Holger Sturm (2000). Modal Horn Classes. Studia Logica 64 (3):301-313.
    Analytics

    Monthly downloads

    Sorry, there are not enough data points to plot this chart.

    Added to index

    2011-09-22

    Total downloads

    1 ( #306,229 of 1,088,831 )

    Recent downloads (6 months)

    0

    How can I increase my downloads?

    My notes
    Sign in to use this feature


    Discussion
    Start a new thread
    Order:
    There  are no threads in this forum
    Nothing in this forum yet.