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Topic: Number of variables needed to axiomatize first order predicate calculus?
Replies: 4   Last Post: Mar 19, 2013 11:48 PM

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Graham Cooper

Posts: 4,319
Registered: 5/20/10
Re: Number of variables needed to axiomatize first order predicate calculus?
Posted: Mar 18, 2013 10:24 PM
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On Mar 19, 10:40 am, George Greene <gree...@email.unc.edu> wrote:
> On Mar 18, 7:39 pm, Frederick Williams <freddywilli...@btinternet.com>
> wrote:
>

> > I don't see how you will get far without modus ponens.
>
> Well, I see your point that unless everything is going to be a direct
> instance of some single axiom,
> you have to have an inference rule that produces a consequence from an
> input.
> But the question still arises, why isn't that -> ?
> You sort of need modus ponens and a deduction theorem to get from
> A / B  to A -> B, but doesn't it take more "variables" just to bridge
> that modality?
>
> It just seems to me you are operating from a textbook with a framework
> that has
> not been presented to anyone who is not also reading that textbook,
> and that
> is ITself in need of some defense.
>



If you want to forward chain or backward chain via inference rules

you're going to need another syntax symbol than ->

If not in the inference rule itself, then in a separate control module
which usually has modus ponens, cut elimination or resolution.

MP can emulate those last 2 as inference rules.

-----------

e.g. in PROLOG instead of

not(not(X)) :- thm(X).

use

if( X , not(not(X))).
and
thm(R) :- if(L,R) , thm(L) [MP]


---------------------

Both methods have a :- somewhere

You just put thm(X) around a naked theorem X in PROLOG.


Herc
--
www.BLoCKPROLOG.com





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