[FRIAM] visualization of logic(s)

[Marcus Daniels]

"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. "


So you are talking about, say, swapping conjunctions and disjunctions, but you're not concerned with how terms are shared?   I think of logic languages as being strictly (search) tree structures, where a relatively fancy optimization is to do backjumps to avoid uninteresting intermediate searches.   A concurrent systems could expand opportunistically around certain predicates and work forward or backward.   One frustrating thing in a logic program is when one establishes some bad backbone that is a partial solution and then only find out much later it is involved in an impossible solution.   That is, the backtracking ends up very deep.    What is the significance of it being 2D or of some particular width/height?


Marcus

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From: Friam <friam-bounces at redfish.com> on behalf of gⅼеɳ ☣ <gepropella at gmail.com>
Sent: Friday, September 22, 2017 5:50:14 PM
To: FriAM
Subject: [FRIAM] visualization of logic(s)


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

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