Re: Set Theorists use EXTENSIONALITY ..... Logic Programmers UNIFY!

Article View: sci.logic

Article #716

#716

From: Jan Burse
Date: Thu, 13 Jun 2013 08:30

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Graham Cooper schrieb:
> [1]
>
> ~tail <- ~head
>
> directly follows from
>
> head <- tail

There is actually a variant of contraposition
which has found its way into logic programming.
One might observe the following:

A Horn clause, in Prolog notation:

     p(s) :- q(t), B2, .., Bn

Can be written as:

     p(s) v ~q(t) v ~B2 v .. v Bn

Which is logically equivalent to the following,
again using double negation elimination:

     ~q(t) v ~~p(s) v ~B2 v .. v Bn

Now we can use new predicate names so that:

     q*(t) <-> ~q(t)

     p*(t) <-> ~p(t)

And arrive at the following:

     q*(t) v ~p*(s) v ~B2 v .. v Bn

Or written in Prolog notation again:

     q*(t) :- p*(s), B2, .., Bn

The above doesn't yield negative information per
se. It can be used for abductive reasoning, we
apply the following trick on the toplevel. Instead
of asking for X as follows:

     P, X |- G

We ask for X as follows:

     P, ~G |- ~X

The modified clauses will be executed backward chaining,
but they will simulate a form of forward chaining.

Didn't try it myself, but one can read about it for
example here:

Y Yamamoto, 2010
Research on Logic and Computation in Hypothesis Finding
http://www.nii.jp/graduate/thesis/pdf/201009/yamamoto_Dr_thesis.pdf

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From: Jan Burse <janburse@fastmail.fm>
Newsgroups: sci.logic,comp.lang.prolog,aus.computers
Subject: Re: Set Theorists use EXTENSIONALITY ..... Logic Programmers UNIFY!
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