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

 To: "[ontolog-forum]" paola.dimaio@xxxxxxxxx Tue, 17 Jul 2007 17:36:42 +0700
 Waclawthanks for this I was hoping to get the mathematical representation of this reasoning so that I can learn somthing from my 'to do' listwhile I reason about nature -the problem is that y (fred, the bat) is not a bird y is a mammal -therefore, if y is not a bird, and it flies, not only birds fly(tell me what I am missing)POn 7/17/07, Waclaw Kusnierczyk wrote: Re induction.The pattern John shows as induction is (correct me if I am wrong):From:P(x1), P(x2), ..., P(xn)Q(x1), Q(x2), ..., Q(xn)induce:forall x, P(x) => Q(x)e.g., x1, x2, ..., xn are birds and they fly, therefore if y is a bird, it flies.(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.)The pattern above is a case of generalization:  from a number of examples, you infer (here induce) a general rule.John, would you agree that the following is also a case of induction (aninductive specialization)?exists x, P(x) and Q(x)P(y)induce (?):  Q(y) e.g., some birds fly, y is a bird, therefore y flies.vQpaola.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* >> 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>>>     _________________________________________________________________>     Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/>     Subscribe/Config:>     http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ >     >     Unsubscribe: mailto: ontolog-forum-leave@xxxxxxxxxxxxxxxx>     >     Shared Files: http://ontolog.cim3.net/file/>     Community Wiki: http://ontolog.cim3.net/wiki/>     To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx >     >>>>> --> Paola Di Maio> School of IT> www.mfu.ac.th > *********************************************>>> ------------------------------------------------------------------------ >>> _________________________________________________________________> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ > Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/> Unsubscribe: mailto: ontolog-forum-leave@xxxxxxxxxxxxxxxx> Shared Files: http://ontolog.cim3.net/file/> Community Wiki: http://ontolog.cim3.net/wiki/ > To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx>--Wacek Kusnierczyk------------------------------------------------------Department of Information and Computer Science (IDI) Norwegian University of Science and Technology (NTNU)Sem Saelandsv. 7-97027 TrondheimNorwaytel.   0047 73591875fax    0047 73594466------------------------------------------------------ _________________________________________________________________Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxxShared Files: http://ontolog.cim3.net/file/Community Wiki: http://ontolog.cim3.net/wiki/To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx -- Paola Di Maio School of ITwww.mfu.ac.th********************************************* ``` _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (01) ```