have you had a look at Universal logic?
Maybe there are points of interest in there for you (the wikipedia
article is only a stub, but contains some names to google).
Brian Tenneson wrote:
> I was skimming though a book by Roberto Cignoli, Itala D'Ottaviano, and
> Daniele Mundici called Algebraic Foundations of Many-Valued Reasoning.
> Recall that I conjectured that the Physicist's universe has an
> MV-algebra structure. I probably should have said that the Physicist's
> universe is the category of all MV-algebras, or some such.
> In this book I'm studying, I have lifted some facts which might prove
> interesting when settling my conjecture (which obviously might be as
> insignificant as the conjecture 0+1=1).
> From book:
> Let A be the category of l-groups (lattice-ordered Abelean groups) with
> a strong distinguished unit.
> Let M be the category of MV-algebras. (I think a briefer way to say that
> would be "let M be MV-algebra".)
> OK, now... Chapter 7 of the aforementioned book has as its goal proving
> the following statement:
> There is a natural equivalence between A and M, meaning that there is a
> functor, call it F, between A and M. In other words, between A and M,
> there is a full, faithful, and dense functor F.
> Thus another way to state my conjecture is this:
> The universe is an (or at least has the structure of an) l-group with a
> strong distinguished unit. Does this ring any bells with physicists?
> What, "physically" or observably, is this strong distinguished unit, if so?
Department of Philosophy of Science
University of Vienna
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