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## Re: [ontolog-forum] Probabilistic Ontologies

 To: "[ontolog-forum]" Waclaw Kusnierczyk Tue, 19 Jun 2007 10:43:47 +0200 <46779743.8050105@xxxxxxxxxxx>
 ```Barker, Sean (UK) wrote: > Waclaw > > From the point of view of practical mathematics, probability > over continuous distributions is defined through probability density > functions, with the probability for any interval being the integral of > the pdf over that interval. If you reduce the interval to zero, then the > probability goes to zero. No problem there.    (01) Depends on what you mean by 'reduce to zero'. There is the empty interval, and infinitely many singleton intervals [x,x]. For the empty interval, obviously P(X = x | x in the empty interval) = 0. For any singleton interval, it is not that obvious to me that P(X = x) = 0 for some x for which the 'reduced to zero' interval [x,x] is considered.    (02) > > I'm not sure what you want to say with "P(exists x: > X=x) = 1" > since the domain of X is fixed by definition, and therefore "the > probability that X takes a value in its domain" doesn't seem to mean > very much - probability is about random events, not things that are true > by definition.    (03) This part comes from Kathy's post, and she should be asked:    (04) [KL] This raises some tricky mathematical issues. In finite domains, we can equate probability zero with unsatisfiability and probability 1 with validity. But in the example I gave above, UniformRand = X is satisfiable for any X between zero and one, yet (Prob (UniformRand = X)) is zero for all X, and moreover, Prob(Exists X UniformRand=X)) is equal to 1.    (05) vQ    (06) _________________________________________________________________ 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    (07) ```
 Current Thread Re: [ontolog-forum] Probabilistic Ontologies, (continued) Re: [ontolog-forum] Probabilistic Ontologies, Kathryn Blackmond Laskey Re: [ontolog-forum] Probabilistic Ontologies, Pat Hayes Re: [ontolog-forum] Probabilistic Ontologies, Kathryn Blackmond Laskey Re: [ontolog-forum] Probabilistic Ontologies, Pat Hayes Re: [ontolog-forum] Probabilistic Ontologies, John F. Sowa Re: [ontolog-forum] Probabilistic Ontologies, Waclaw Kusnierczyk Re: [ontolog-forum] Probabilistic Ontologies, Waclaw Kusnierczyk Re: [ontolog-forum] Probabilistic Ontologies, Barker, Sean (UK) Re: [ontolog-forum] Probabilistic Ontologies, Waclaw Kusnierczyk Re: [ontolog-forum] Probabilistic Ontologies, Barker, Sean (UK) Re: [ontolog-forum] Probabilistic Ontologies, Waclaw Kusnierczyk <= Re: [ontolog-forum] Probabilistic Ontologies, Barker, Sean (UK) Re: [ontolog-forum] Probabilistic Ontologies, John F. Sowa Re: [ontolog-forum] Probabilistic Ontologies, John F. Sowa Re: [ontolog-forum] Two ontologies that are inconsistent but both needed, Pat Hayes Re: [ontolog-forum] Two ontologies that are inconsistent but both needed, Kathryn Blackmond Laskey Re: [ontolog-forum] Two ontologies that are inconsistent but both needed, Christopher Menzel Re: [ontolog-forum] Two ontologies that are inconsistent but both needed, Kathryn Blackmond Laskey Re: [ontolog-forum] Two ontologies that are inconsistent but both needed, Christopher Menzel Re: [ontolog-forum] Two ontologies that are inconsistent but both needed, Smith, Barry Re: [ontolog-forum] Two ontologies that are inconsistent but both needed, clynch