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## Re: [ontolog-forum] Probabilistic Ontologies

 To: "[ontolog-forum] " "Barker, Sean (UK)" Tue, 19 Jun 2007 09:33:25 +0100
 ``` Waclaw    (01) 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.    (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) Sean Barker Bristol, UK    (04) This mail is publicly posted to a distribution list as part of a process of public discussion, any automatically generated statements to the contrary non-withstanding. It is the opinion of the author, and does not represent an official company view.    (05) > -----Original Message----- > From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx > [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of > Waclaw Kusnierczyk > Sent: 19 June 2007 09:03 > To: [ontolog-forum] > Subject: Re: [ontolog-forum] Probabilistic Ontologies > > > *** WARNING *** > > This mail has originated outside your organization, either > from an external partner or the Global Internet. > Keep this in mind if you answer this message. > > Barker, Sean (UK) wrote: > > Waclaw > > > > Any interval of real numbers has cardinality Aleph-1 (not > > Aleph-0) - that is rather the point of real numbers. > > Right. Actually, card(R) = 2^aleph_0, which equals aleph^1 > according to the continuum hypothesis. > > > In the usual > > axiomatizations of Real numbers (and numbers in general) > division is > > the inverse of multiplication and 0 is not equal to 1 (the > > multiplicative identity). The use of the Alephs is not part > of the real number system. > > Is this to say that the paradox (P(X=x) = 0 and P(exists x: > X=x) = 1) is supported by this axiomatization? > > > vQ > > > > _________________________________________________________________ > 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 > > >    (06) ******************************************************************** This email and any attachments are confidential to the intended recipient and may also be privileged. If you are not the intended recipient please delete it from your system and notify the sender. You should not copy it or use it for any purpose nor disclose or distribute its contents to any other person. ********************************************************************    (07) _________________________________________________________________ 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    (08) ```
 Current Thread Re: [ontolog-forum] Probabilistic Ontologies, (continued) Re: [ontolog-forum] Probabilistic Ontologies, John F. Sowa 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