Re: logical/set theoretic programming

• To: mathgroup at smc.vnet.net
• Subject: [mg74207] Re: [mg74024] logical/set theoretic programming
• From: "Richard Palmer" <rhpalmer at gmail.com>
• Date: Wed, 14 Mar 2007 03:52:12 -0500 (EST)
• References: <200703061032.FAA02208@smc.vnet.net>

```One of the "Programming in Mathematica" series books implements a
versiion of Prolog.  This version just might do the trick.

On 3/6/07, Christopher Arthur <caa0012 at unt.edu> wrote:
> Hello, any suggestions on how to program set theory?
> Suppose that I have a notation set up well, and I have a set of rules
> of implication.  The next step is to teach mathemania how to compute...
> For example, I define a notation for AbstractComplement[X,A], and I
> want to associate it with it the rule
> Implies[Subset[A,X]&&Element[x,A],!Element[x,AbstractComplement[X,A]].
> In other words, a point can't be in a subset and its complement.  My
> feeling is that alone this rule should be enough to decide the
> falsehood of a statement such as
> Subset[B,W]&&Exists[y,Element[y,B]&&Element[y,AbstractComplement[W,B]]
>
> where in this case i've purposefully changed the variables because i
> don't want to tie the rule to any particular symbols.  How can we set
> up Simplify,Reduce,Refine or something similar to decide on this rule?
> Especially, without having to make the rule explicit in the expression
> to simplify. Christopher Arthur
> Student, Mathematics
> University of North Texas
>
>

--
Richard Palmer
Cell 508 982-7266

```

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