[FRIAM] visualization of logic(s)

[gⅼеɳ ☣]

Given the discussion of logic(s), I imagine a visualization where we take a language, maybe ZFC, come up with a set of sentences, maybe 100 or so, and place them on a 2D grid, where each grid point shows their truth value.  So, you'd have a 10x10 grid of T's and F's based on how those sentences evaluated in ZFC.  You also include a button or something that allows you to modify the language in some way.  E.g. click on the button and it removes the axiom of regularity and you see the grid points change from T to F.  I suppose you could do this with a smattering of sentences from first- and (first- plus) second-order logic as well.  I suppose it would be critical which sentences you included in the grid and their relationship with the underlying language.  In addition to T and F, you might also have something like ∞ for undefined, undecidable, or nonsense.

What do you think?  Is this a silly idea?  Does something like it exist already?  Would it be interesting?  Useless?

-- 
☣ gⅼеɳ