Wednesday, July 18, 2012

Kinds of Categorical Fuzzy Sets

In the logic seminar in Stanford sometimes people are asked to present papers. That's how I ended up reading Takeuti and Titani on fuzzy sets, which turned to be very interesting.

Now I'm reading Gottwald on "Universes of Fuzzy Sets and Axiomatizations of Fuzzy Set Theory. Part II: Category Theoretic Approaches" and this is very interesting too, for the same reason.

I have known since around  1990 that I can construct a "fuzzy" version of dialectica categories.  I know that this construction gives us a symmetric monoidal closed category with products and coproducts, with a (admittedly complicated) linear exponential comonad, hence is a model of Linear Logic. I know that there are other fuzzy sets that are also models of Linear Logic. Presumably I can relate these models via functors.

 I have not managed, so far,   to discover what makes fuzzy logic such a "crowd-puller", such a strong favorite. so I have no idea if this attractiveness will hold for the linear logic models. Or not.

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