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## Re: [ontolog-forum] Probabilistic Ontologies

 To: "[ontolog-forum] " "Barker, Sean (UK)" Tue, 19 Jun 2007 08:55:17 +0100
 ``` Waclaw    (01) Any interval of real numbers has cardinality Aleph-1 (not Aleph-0) - that is rather the point of real numbers. 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.    (02) Sean Barker 0117 302 8184    (03) > -----Original Message----- > From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx > [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of > Waclaw Kusnierczyk > Sent: 19 June 2007 07:43 > 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. > > Kathryn Blackmond Laskey wrote: > > To do probability right, you need real numbers, and you need to be > > able to do continuous distributions. For example, > consider a number > > picked at random between zero and one. (Imagine a spinner that can > > land anywhere on the disk with equal likelihood; measure > the distance > > around the edge to where it landed and divide by the > circumference -- > > the number you get is uniformly distributed between zero > and one.) The > > probability of getting a number in any sub-interval of the unit > > interval is equal to the length of the sub-interval. But the > > probability of getting any specific number is zero. > > > > 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. > > Isn't the issue due to approximation? In P(X = x) = 0 for > any x in the selected interval of real numbers, what is the > zero? The probability that a random variable will take on a > specific value from a particular set of values is per > definitionem equal to the inverse of the cardinality of the > set -- right? An interval -- a dense set of real numbers, > e.g., the unit interval (0.0, 1.0) -- has the cardinality > aleph_0 (I guess). The zero in P(X = x) = 0 is in fact the > inverse of aleph_0; it is not exactly the usual 0, it is an > approximation. For every x in the interval, P(X = x) is > infinitesimal, but is not exactly 0. If infinitesimals were > equal to 0, would integration make sense? > It may be practically zero, but when discussing paradoxes of > probability, it may be worth mentioning. > > (Ignore if I am getting this wrong.) > > 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 > > >    (04) ******************************************************************** 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. ********************************************************************    (05) _________________________________________________________________ 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) ```
 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, 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