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