A Gabbay-Rule Free Axiomatization of T x W Validity

Journal of Philosophical Logic 27 (5):435 - 487 (1998)
The semantical structures called T x W frames were introduced in (Thomason, 1984) for the Ockhamist temporal-modal language, $[Unrepresented Character]_{o}$ , which consists of the usual propositional language augmented with the Priorean operators P and F and with a possibility operator ◇. However, these structures are also suitable for interpreting an extended language, $[Unrepresented Character]_{so}$ , containing a further possibility operator $\lozenge^{s}$ which expresses synchronism among possibly incompatible histories and which can thus be thought of as a cross-history 'simultaneity' operator. In the present paper we provide an infinite set of axioms in $[Unrepresented Character]_{so}$ , which is shown to be strongly complete for T x W-validity. Von Kutschera (1997) contains a finite axiomatization of T x W-validity which however makes use of the Gabbay Irreflexivity Rule (Gabbay, 1981). In order to avoid using this rule, the proof presented here develops a new technique to deal with reflexive maximal consistent sets in Henkin-style constructions
Keywords temporal logic  branching-time  synchronism  axiomatization
Categories (categorize this paper)
 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
    John P. Burgess (1979). Logic and Time. Journal of Symbolic Logic 44 (4):566-582.

    View all 10 references

    Citations of this work BETA
    Niko Strobach (2007). Fooling Around with Tenses. Studies in History and Philosophy of Science Part B 38 (3):653-672.
    Similar books and articles

    Monthly downloads

    Added to index


    Total downloads

    4 ( #198,443 of 1,088,372 )

    Recent downloads (6 months)

    1 ( #69,449 of 1,088,372 )

    How can I increase my downloads?

    My notes
    Sign in to use this feature

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