Comments on: A Suite of Cool Logic Programs http://xorshammer.com/2009/05/14/a-suite-of-cool-logic-programs/ Some things in mathematical logic that I find interesting Sun, 14 Mar 2010 08:09:01 +0000 http://wordpress.com/ hourly 1 By: mkoconnor http://xorshammer.com/2009/05/14/a-suite-of-cool-logic-programs/#comment-201 mkoconnor Mon, 20 Jul 2009 23:29:47 +0000 http://xorshammer.com/?p=320#comment-201 It would prove it, probably after a very long time. There are weaker methods of geometric theorem proving available in the package (see geom.ml), but I'm not sure that any of them correspond to a "direct proof" (in fact, I'm pretty sure they don't as they are too strong). E.g., using Gröbner bases or this thing called Wu's method, both of which can be used to prove statements which can be put in the form $latex \forall{\vec{x}}(P(\vec{x})\rightarrow Q(\vec{x})$, where $latex P$ and $latex Q$ are polynomials. Embarrassingly, I can't find the book right now, and that's all I know about the situation. It would prove it, probably after a very long time. There are weaker methods of geometric theorem proving available in the package (see geom.ml), but I’m not sure that any of them correspond to a “direct proof” (in fact, I’m pretty sure they don’t as they are too strong). E.g., using Gröbner bases or this thing called Wu’s method, both of which can be used to prove statements which can be put in the form \forall{\vec{x}}(P(\vec{x})\rightarrow Q(\vec{x}), where P and Q are polynomials.

Embarrassingly, I can’t find the book right now, and that’s all I know about the situation.

]]> By: Todd Trimble http://xorshammer.com/2009/05/14/a-suite-of-cool-logic-programs/#comment-199 Todd Trimble Sun, 19 Jul 2009 23:22:56 +0000 http://xorshammer.com/?p=320#comment-199 I'm just curious about what the program would do in response to the notorious <a href="http://cs.nyu.edu/pipermail/fom/2004-August/008394.html" rel="nofollow">Steiner-Lehmus theorem</a> in Euclidean geometry. Can the program be modified so that it searches for direct proofs? I’m just curious about what the program would do in response to the notorious Steiner-Lehmus theorem in Euclidean geometry. Can the program be modified so that it searches for direct proofs?

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