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Re: [ontolog-forum] Proceedings: "Database & Ontology" mini-series Sessi

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Waclaw Kusnierczyk <Waclaw.Marcin.Kusnierczyk@xxxxxxxxxxx>
Date: Tue, 17 Jul 2007 12:30:39 +0200
Message-id: <469C9A4F.3070908@xxxxxxxxxxx>
Re induction.    (01)

The pattern John shows as induction is (correct me if I am wrong):    (02)

From:
P(x1), P(x2), ..., P(xn)
Q(x1), Q(x2), ..., Q(xn)    (03)

induce:
forall x, P(x) => Q(x)    (04)

e.g., x1, x2, ..., xn are birds and they fly, therefore if y is a bird, 
it flies.    (05)

(Note that this is symmetrical wrt. P and Q;  but if you add Q(y) and 
~P(y), you can still induce the above but not the inverse.)    (06)


The pattern above is a case of generalization:  from a number of 
examples, you infer (here induce) a general rule.    (07)

John, would you agree that the following is also a case of induction (an 
inductive specialization)?    (08)

exists x, P(x) and Q(x)
P(y)    (09)

induce (?):  Q(y)    (010)

e.g., some birds fly, y is a bird, therefore y flies.    (011)

vQ    (012)



paola.dimaio@xxxxxxxxx wrote:
> Thanks John
> 
> 
> I do not mean to insist on this lilliputian quibble but...
> 
> 
>  >   Given: Tweety, Polly, and Hooty are birds. Fred is bat.
>  >          Tweety, Polly, and Hooty fly. Fred flies.
>  >   Assume: Every bird flies.
> 
> 
> 
> could you explain how does the bat part of your statement end up in the 
> assumption that every bird flies? or does the assumption completely 
> ignores the fact that Fred is a bat. yet it flies?
> if the assumption is based on taking into account both parts of the 
> statement, then the assumption as stated above seems incomplete -
> 
> this logic right?
> 
> not everything that flies is a bird, and not every bird flies
> 
> I ll make something up for the class
> 
> (feel free to ignore )
> 
> P
> 
> On 7/14/07, * John F. Sowa* <sowa@xxxxxxxxxxx <mailto:sowa@xxxxxxxxxxx>> 
> wrote:
> 
>     Paola,
> 
>     In my previous note, I forgot to answer the following question:
> 
>     PDM> My assumption, following your example 2 would be:
>      > not only birds fly -  would I be right?
> 
>     JFS> 2. Induction. Assume a general principle that subsumes many facts.
>      >
>      >   Given: Tweety, Polly, and Hooty are birds. Fred is bat.
>      >          Tweety, Polly, and Hooty fly. Fred flies.
>      >   Assume: Every bird flies.
> 
>     PDM> NOT ONLY BIRDS FLY.
> 
>     Yes, that is true.  But that is a separate observation.
> 
>     The assumption made by induction is "Every bird flies."
> 
>     The additional statement "Not only birds fly" follows
>     from two facts plus some background knowledge plus an
>     inference.  Following are the facts as given:
> 
>          Fred is a bat.  Fred flies.
> 
>     The additional background knowledge, which was not stated
>     in the slide, is
> 
>          No bat is a bird.
> 
>      From that statement and the preceding facts, one can infer
>     by deduction:
> 
>          Some things fly that are not birds.
> 
>     Then it is possible to rephrase that conclusion as a qualifier
>     to the preceding:
> 
>          Every bird flies, but not only birds fly.
> 
>     In short, you could add that statement, but it is derived
>     by a more complex series of steps.  For teaching purposes,
>     it might be better to show that in a separate slide.
> 
>     (And, of course, the statement "Every bird flies" has to be
>     qualified when you consider penguins and kiwis.  You also have
>     to exclude injured birds, baby birds, sleeping birds, and
>     dead birds -- remember the dead parrot from Monty Python.)
> 
>     John
> 
> 
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> 
> -- 
> Paola Di Maio
> School of IT
> www.mfu.ac.th <http://www.mfu.ac.th>
> *********************************************
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-- 
Wacek Kusnierczyk    (014)

------------------------------------------------------
Department of Information and Computer Science (IDI)
Norwegian University of Science and Technology (NTNU)
Sem Saelandsv. 7-9
7027 Trondheim
Norway    (015)

tel.   0047 73591875
fax    0047 73594466
------------------------------------------------------    (016)

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