Dear Bruno,

Thank you for your reply.

You wrote that 'B is valid in the frames where "result
of experience" can be verified or repeated'. Can you
be more explicit because I cannot see the relation
with the fact that the accessibility relation is
reflexive and symmetric (a proximity relation).

I know that in the Provability Logic GL, []A is to be
read as "A is provable". (I write [] for Box). "A is
provable" does not mean that I have an explicit proof
of A. Indeed, in the context of the first-order
arithmetic, "A is provable" only means that "there
exists a number which is a code of a proof of A".

I also know that in S4, []A is to be read as "A is
constructively provable": S4, which was shown by
Sergei Artemov to be a forgetful projection of the
Logic of Proofs LP. 

Could we also interpret B also in terms of some kind
of provability?

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