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
papers.
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 :)
Bruno
http://iridia.ulb.ac.be/~marchal/
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