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## [ontolog-forum] Fw: Approximation (was: rant on pseudoscience)

 To: "sean barker" Tue, 26 Jan 2010 20:31:30 -0000 <595360418224441FABF3C484D37E5208@SMB>
 One approach I tried is to apply fuzzy logic, so that the membership function goes from 0 when one is definiely in one region (say the town) and 1 when one is in the other (the country side).   Applying a quantization function, say Q:[0..1] ---.> {T, F} s.t. (Q(x) = T if x < t otherwise F) defines a threshold t at whch one (arbitarily) decides the transition occurs. One might then compare the effects of selecting different threshold values, for example to identify properties that do not vary with t.   A variation on this is to define a three valued quantization function R, R:[0..1] --> {in, on, out} with two thresholds t, u (and typically, u = 1-t), s.t. (Q(x) = in if x < t, Q(x)=on t =>   But people have criticized model theory because there is more to sayabout the meaning of a statement than just its truth conditions: 1. For example, the following three statements are true in    every possible model, but the fact that they talk about    different subjects indicates that they are not synonymous:     a) Every cat is a cat.     b) Every dog is a dog.     c) Every unicorn is a unicorn. 2. Not all true statements are equally important, but model    theory has nothing to say about importance or relevance.   These objections don't imply that model theory is wrong for what it does.  But they indicate that there is more to meaningthan just the truth conditions for a statement. John Just an observation on weakness #1 as identified by John above. This "weakness" also provides some concrete advantages vis-a-vis ontology alignment and mapping.  Specifically, if one accepts the premise that much of our structured thinking (say in a formal logic) reuses the same patterns or "logical building blocks," then these model structures provide a very nice way to identify agreement / conflict between ontologies in the same domain, and/or to highlight interdisciplinary borrowing of concepts, and/or to help clarify metaphors. By model structure, i mean the set of permissible models attained for a given theory, but decontextualized from the universe of discourse --- so in the trivial example above, the (logical) synonymity holds for the models allowed by "Every A is A" - i.e. if we strip the models from their referent to specific objects, then the sets of the models for the above theories are isomorphic. Of course, this captures only logically synonymous formulations, and as it has been pointed out, there's more to meaning than that. But this type of synonymity is a very useful insight that can go a long way in alleviating the problems of multiple, competing ontologies. Ali   _________________________________________________________________Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxxShared Files: http://ontolog.cim3.net/file/Community Wiki: http://ontolog.cim3.net/wiki/To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1JTo Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx-- (?`'·.¸(`'·.¸(?)¸.·'´)¸.·'´?) .,., _________________________________________________________________Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxxShared Files: http://ontolog.cim3.net/file/Community Wiki: http://ontolog.cim3.net/wiki/To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1JTo Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx -- Thanks.Ravi(Dr. Ravi Sharma)313 204 1740 Mobile_________________________________________________________________Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxxShared Files: http://ontolog.cim3.net/file/Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1JTo Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx ------------------------------------------------------------ IHMC                                     (850)434 8903 or (650)494 3973    40 South Alcaniz St.           (850)202 4416   office Pensacola                            (850)202 4440   fax FL 32502                              (850)291 0667   mobile phayesAT-SIGNihmc.us       http://www.ihmc.us/users/phayes ********************************************************************This email and any attachments are confidential to the intendedrecipient and may also be privileged. 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