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## Re: [ontolog-forum] Probabilistic Ontologies

 To: "[ontolog-forum] " "Barker, Sean (UK)" Tue, 19 Jun 2007 10:08:56 +0100
 ``` See below    (01) Sean Barker Bristol, UK    (02) 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.    (03) > -----Original Message----- > From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx > [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of > Waclaw Kusnierczyk > Sent: 19 June 2007 09:44 > 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 > > > > 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. > > 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.    (04) Reduce to 0: for any sequence of intervals In = [xn, yn], xn, yn in Reals, xn < yn, for arbitrary epsilon > 0, there exists N such that for all n > N (yn - xn) < epsilon.    (05) ******************************************************************** 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. ********************************************************************    (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, 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 Re: [ontolog-forum] Two ontologies that are inconsistent but both needed, Smith, Barry