Hi (again) Brent,

So Brent you were right, if I understood you correctly, in quantum logic the negation can be interpreted as an orthogonality relations classifying alternative results of an experiment. The vectors of the base corresponds to the observables under scrutiny.


Le 09-déc.-05, à 18:06, Bruno Marchal a écrit :


Hi Brent,

<snip>




What is the relation of accessibility in the p,q,r world(s)? Is it negation?


Err... I guess you are talking about the reflexive and symmetric multiverse (the proximity spaces) and their antimultiverse which are the antireflexive but also symmetric (see why?) multiverse (the orthogonality spaces).

<snip>

I recall for the others that a multiverse (W,R) is said to be symmetric if for all worlds x y in W, xRy entails yRx. It is said reflexive if for all worlds x in W we have xRx, (all worlds can acces themselves) and antireflexive if for all worlds x in W we have not xRx (no worlds can access themselves)

In french: the multiverse (W,R) is symmetric if it is build in a such ways that each time you can travel from some world in W, Alpha-Centaurus say, to some world in W, Beta-Earth say, by using the travel line R (the accessibility relation), then you can go back from Beta-Earth to Alpha-Centaurus by R too.

In set theory: R is symmetrical if each time (a, b) belongs to R, then (b, a) belongs to R too. This is because in set language, binary relations are defined by their set of couples. To say "Alice loves Lewis", a set theorist would say (Alice, Lewis) belongs to love.

With drawings:   <not yet available :(  >

Hope this can help those who perhaps lack some training in math.

Bruno

http://iridia.ulb.ac.be/~marchal/


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