An axiomatization of the modal theory of the veiled recession frame

Studia Logica 38 (1):37 - 47 (1979)
Abstract
The veiled recession frame has served several times in the literature to provide examples of modal logics failing to have certain desirable properties. Makinson [4] was the first to use it in his presentation of a modal logic without the finite model property. Thomason [5] constructed a (rather complicated) logic whose Kripke frames have an accessibility relation which is reflexive and transitive, but which is satisfied by the (non-transitive) veiled recession frame, and hence incomplete. In Van Benthem [2] the frame was an essential tool to find simple examples of incomplete logics, axiomatized by a formula in two proposition letters of degree 2, or by a formula in one proposition letter of degree 4 (the degree of a modal formula is the maximal number of nested occurrences of the necessity operator in ). In [3] we showed that the modal logic determined by the veiled recession frame is incomplete, and besides that, is an immediate predecessor of classical logic (or, more precisely, the modal logic axiomatized by the formula pp), and hence is a logic, maximal among the incomplete ones. Considering the importance of the modal logic determined by the veiled recession frame, it seems worthwhile to ask for an axiomatization, and in particular, to answer the question if it is finitely axiomatizable. In the present paper we find a finite axiomatization of the logic, and in fact, a rather simple one consisting of formulas in at most two proposition letters and of degree at most three.
Keywords No keywords specified (fix it)
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: 9,351
External links
  • Through your library Configure
    References found in this work BETA
    Citations of this work BETA

    No citations found.

    Similar books and articles
    Analytics

    Monthly downloads

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

    Added to index

    2009-01-28

    Total downloads

    1 ( #306,128 of 1,088,388 )

    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.