On 01 Apr 2011, at 01:51, Johnathan Corgan wrote:

On Thu, Mar 31, 2011 at 9:33 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:

Or something like that. Quantum logic (and also its arithmetical form) has many notion of implication. The one above is the closer to the Sazaki Hook which Hardegree used to show that orthomodularity in quantum ortholattice is related to the notion of counterfactual. You will find the reference in my

Unfortunately orthomodularity is still an open problem in the arithmetical 'quantum logic'. Eric Vandenbusche is currently trying to optimize the G*
theorem prover to get an answer.

And here I thought I was making progress in understanding Bruno's
thesis.  I clearly have a *long* way further to go in my studies :-)

AUDA certainly asks for some familiarity with logic, and logics. That means work, 'course. A good, but advanced book, helpful and important for that more advanced part is the book by Robert Goldblatt:

Goldblatt, R. I. (1993). Mathematics of Modality. CSLI Lectures Notes, Stanford California.

It contains his PhD thesis, + many papers with results that I use to relate quantum logic with arithmetical self-reference.
And there are the books by Boolos, Smullyan, etc.

Bon courage :)



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