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

 To: "[ontolog-forum]" Waclaw Kusnierczyk Tue, 17 Jul 2007 12:30:39 +0200 <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* > > 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 >    (013) -- 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) _________________________________________________________________ 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    (017) ```