Le 29-févr.-08, à 04:55, Zone a écrit :
>
> Does anyone know of an intuitive interpretation of the modality in the
> modal logic KTB (a.k.a .B)?
Do you know Kripke models and frames? A class of Kripke frames where T
( Bp -> p) and B, i.e. p -> BDp ) are valid (with B = the box, D =
diamond = not box not) are the reflexive frames (each world is
accessible from itself, (this is for T) and symmetrical (for B). This
means B is valid in the frames where "result of experience" can be
verified or repeated, and B is natural for the physical context. The
logic B (KTB) can be used to capture a notion of vagueness, and, by a
theorem of Goldblatt, it can be used to formalise classicaly a minimal
form of von Neuman quantum logic in a manner similar to the way the
modal logic S4, or S4Grz, capture intuitionistic logic.
In a nutshell, a frame respects B (= makes B true in all worlds for any
valuation of the propositional letters) if the accessibility relation
is symmetrical (and vice versa). You can always come back to a world
you have just leave.
Hope this helps,
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Mon Mar 03 2008 - 06:06:28 PST