# Re: modal logic KTB (a.k.a. B)

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Le 04-mars-08, à 13:20, <[EMAIL PROTECTED]> a écrit :```
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>
>> The idea is to identify an accessible world with possible results of
>> experiments. Symmetry then entails that if you do an experiment which
>> gives some result, you can repeat the experience and get those results
>> again. You can come back in the world you leave. It is an intuitive
>> and
>> informal idea which is discussed from time to time in the literature.
>
> I do not understand. What are the atomic propositions at each world?

First order Sigma_1 arithmetical sentences (with intensional nuance
driven by the modal logic itself determined by the type of points of
view (1-person, 1-person plural, etc.).

> Suppose the atomic propositions are what I currently know on a physical
> system.

This does not make sense. In the way I proceed I will use the
arithmetically derived points of view logics (the arithmetical
hypostases) to derive the logic of observability, knowability,
sensitivity ...

> Now suppose that I am in a world where I know (more or less) the
> momentum of a particle. I then measure its position and thus move in
> another world. It is now unlikely that the particle has the same
> momentum
> (due the the uncertainty principle).

Again. Just remember that I am not supposing any physics at all, nor
any "physical world".

> Thus, if I measure again its
> momentum, I might go back but I cannot be sure I will go back to the
> same
> previous world. It is true that I can measure again the position and
> get
> the same result, but it is because of reflexivity, not because of
> symmetry. Why do you say this is entailed by symmetry? This might be
> because you define the worlds of the frame in another way...

Again, I work in the oether direction.
I will try to explain you this with more details once I have more time.
Note that, relatively to the UDA and its arithmetical version, you are
quite above the current discussion. I think that if you grasp the UDA,
you will better grasp the role of the (modal) quantum logic, and how to
retrieve it from arithmetics and provability logic. Did you grasp the
UDA's  point?

>
>> I suggest you consult the Orthologic paper by Goldblatt 1974, if you
> are
>> interested.
>
> paper
> available on internet where this idea is discussed?

Unfortunately most papers bearing on this are "pre-internet". Try to
google on Dalla Chiara, Goldblatt, Quantum Logic, Quantum modal logic,
etc.
In the worst case I can send to you a copy of some papers. The text by
Maria Louisa Dalla Chiara on Quantum Logic in the handbook on
philosophical logic is quite good.
There exists also complementary works by Abramski. Some makes
interesting relations between knot theory, Temperley Lieb Algebra,
computation and combinators.
In general Abramski and linear logicians (and others) despise quantum
logic, but their reasons are not relevant in the context of deriving
the comp-physics from comp by self-reference, as UDA shows (or is
supposed to show) once we bet on the comp hypothesis.

Bruno

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

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