On 21 Feb 2012, at 17:53, meekerdb wrote:

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On 2/21/2012 7:38 AM, Bruno Marchal wrote:Negative amplitude of probability comes from the formula p->[]<>psatisfied by the sigma_1 arithmetical sentences (that is the UD).How does that work?

By using a theorem of Goldblatt which shows that: MQL proves A iff B proves t(A),

`MQL being a Minimal form of Quantum Logic and B being the Brouwersche`

`modal logic, with axioms`

`[ ](A->B) -> ([ ]A -> [ ]B), [ ]A -> A, A->[ ]<>A, and the Modus`

`Ponens rule + the necessitation rule.`

and the translation t(A) given by t(p) = [ ]<> p p atomic t(A & B) = t(A) & t(B) t(~A) = [ ] ~t(A)

`So B models an quantum orthologic, a bit like S4, or S4Grz, are known`

`to model Intuitionist Logic.`

`Now, the UD is modeled by the restriction of the arithmetical`

`realisation of modal logic to the Sigma_1 arithmetical sentences, for`

`which it can be shown that [ ](p->q) -> ([ ]p -> [ ]q), [ ]p -> p, p-`

`>[ ]<>p, that is the axioms of B, when [ ]p is the result of the`

`material hypostases translation, which I sum up often by Bp & Dt (but`

`which is really given by a translation like above).`

`The MP rule is sound, but we lose the necessitation rule. Nevertheless`

`we obtain still a quantum logic by using the "reverse-Goldblatt`

`translation", leading to an arithmetical interpretation of a sort of`

`quantum logic, and this where the UDA shows we need to find the`

`elementary logic of the yes/no observable in the comp physical reality.`

`That was the first step in the verification that the comp physics fit`

`empirical physics. Others have followed (orthomodularity, a violation`

`of a Bell type of inequality). Unfortunately the translation of those`

`nested modal operators (with many "[ ]<>") makes the algorith`

`intractable for more interesting "physical formula".`

`Hard to explain this without being technical, but more is said in`

`sane04 and some other papers in my url.`

Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.