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,



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