So is the following understanding correct?
If you have two statements
Fred is a human
Fred is an animal
And assuming you know nothing more about any of the three
terms in both these statements, then each of the following would be an
appropriate induction
A human is an animal
An animal is a human
A human and an animal are similar
It would only then be from further information that you
would find the first of these two inductions has a larger truth value than
the second and that the third probably has a larger truth value than the
second..
Edward W. Porter
Porter & Associates
24 String Bridge S12
Exeter, NH 03833
(617) 494-1722
Fax (617) 494-1822
[EMAIL PROTECTED]
-----Original Message-----
From: Pei Wang [mailto:[EMAIL PROTECTED]
Sent: Saturday, October 06, 2007 7:03 AM
To: [email protected]
Subject: Re: [agi] Do the inference rules of categorical logic make sense?
Right. See concrete examples in
http://nars.wang.googlepages.com/NARS-Examples-SingleStep.txt
In induction and abduction, S-->P and P-->S are usually (though not
always) produced in pair, though usually (though not always) with
different truth values, unless the two premises have the same truth-value
--- as Edward said, it would be illogical to produce difference from
sameness. ;-)
Especially, positive evidence equally support both conclusions, while
negative evidence only deny one of the two --- see the "Induction and
Revision" example in
http://nars.wang.googlepages.com/NARS-Examples-MultiSteps.txt
For a more focused discussion on induction in NARS, see
http://www.cogsci.indiana.edu/pub/wang.induction.ps
The situation for S<->P is similar --- see "comparison" in
http://nars.wang.googlepages.com/NARS-Examples-SingleStep.txt
Pei
On 10/6/07, Lukasz Stafiniak <[EMAIL PROTECTED]> wrote:
> Major premise and minor premise in a syllogism are not
> interchangeable. Read the derivation of truth tables for abduction and
> induction from the semantics of NAL to learn that different ordering
> of premises results in different truth values. Thus while both
> orderings are applicable, one will usually give more confident result
> which will dominate the other.
>
> On 10/6/07, Edward W. Porter <[EMAIL PROTECTED]> wrote:
> >
> >
> > But I don't understand the rules for induction and abduction which
> > are as
> > following:
> >
> > ABDUCTION INFERENCE RULE:
> > Given S --> M and P --> M, this implies S --> P to some degree
> >
> > INDUCTION INFERENCE RULE:
> > Given M --> S and M --> P, this implies S --> P to some degree
> >
> > The problem I have is that in both the abduction and induction rule
> > -- unlike in the deduction rule -- the roles of S and P appear to be
> > semantically identical, i.e., they could be switched in the two
> > premises with no apparent change in meaning, and yet in the
> > conclusion switching S and P would change in meaning. Thus, it
> > appears that from premises which appear to make no distinctions
> > between S and P a conclusion is drawn that does make such a
> > distinction. At least to me, with my current limited knowledge of
> > the subject, this seems illogical.
>
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