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## Re: [ontolog-forum] Universal and categories in BFO & DOLCE

 To: "'[ontolog-forum] '" "Rich Cooper" Fri, 9 Sep 2011 11:31:09 -0700 <244E9D80D213479681F072C32D6FC659@Gateway>
 ```Dear John,    (01) Comments below, -Rich    (02) Sincerely, Rich Cooper EnglishLogicKernel.com Rich AT EnglishLogicKernel DOT com 9 4 9 \ 5 2 5 - 5 7 1 2    (03) -----Original Message----- From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F. Sowa Sent: Friday, September 09, 2011 4:29 AM To: ontolog-forum@xxxxxxxxxxxxxxxx Subject: Re: [ontolog-forum] Universal and categories in BFO & DOLCE    (04) Dear Matthew,    (05) I agree with your point:    (06) > 1. Stop thinking of inheritance and specialisation as being synonymous. > Inheritance of properties can happen through other relationships as well.    (07) > 2. Think in set theoretic terms. So each member of a subset is a member of > the superset. If a method belongs to the superset, it is not "inherited" by > the subset, but it applies to each member of the subset because it is also a > member of the superset.    (08) But please note that inheritance is not applicable to an arbitrary set, but only to a set S that satisfies two conditions:    (09) 1. There is some predicate P(x) that is true of every element x of S.    (010) In this case, S is the set of all sentence signatures. So if signature x is a transitive and y is intransitive, then x and y do not share the transitive-intransitive property, but they do share the signature property.    (011) 2. Any method, property, or whatever that can be inherited by every element of S must be characterized by some predicate m(x) that is implied by P(x):    (012) For all x, if P(x), then m(x).    (013) This predicate P(x) is not necessarily the defining predicate for S because there might be some larger set {x | P(x)}, which includes S as a proper subset.    (014) So for all x, if Transitive(x) then method    (015) (PTrans(x) or MTrans(x))    (016) is applicable, and those x can be directed along a different specialization arc than YTrans(x) which share the Intransitive(x) property?    (017) I have to think about that one for a while to understand its sentential signature implications, but it sounds like a fruitful thing to think about.    (018) The critical point is that there must exist some such predicate P(x) that meets the two conditions above.    (019) I would call that predicate P *intensional* information about the set S, but you don't have to use the word 'intensional' if you don't like it.    (020) John    (021) I don't have to like it; if it works it works and that is truth enough for functional purposes. So Transitive(x) and Intransitive(x) are "intensional" informations about x.    (022) How can I apply that to sentential signature descriptions, i.e., how would one distinguish "intensional" characteristics of signatures from a linguistic categorization viewpoint?    (023) Thanks; that seems worth spending some thought on.    (024) -Rich    (025) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Config Subscr: 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 join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J    (026) ```
 Current Thread Re: [ontolog-forum] Universal and categories in BFO & DOLCE, (continued) Re: [ontolog-forum] Universal and categories in BFO & DOLCE, John F. Sowa Re: [ontolog-forum] Universal and categories in BFO & DOLCE, John F. Sowa Re: [ontolog-forum] Universal and categories in BFO & DOLCE, Rich Cooper Re: [ontolog-forum] Universal and categories in BFO & DOLCE, John F. Sowa Re: [ontolog-forum] Universal and categories in BFO & DOLCE, Rich Cooper Re: [ontolog-forum] Universal and categories in BFO & DOLCE, John F. Sowa Re: [ontolog-forum] Self Interest Ontology; was Universal and categories in BFO & DOLCE, Rich Cooper Re: [ontolog-forum] Universal and categories in BFO & DOLCE, John F. Sowa Re: [ontolog-forum] Universal and categories in BFO & DOLCE, Ron Wheeler Re: [ontolog-forum] Universal and categories in BFO & DOLCE, John F. Sowa Re: [ontolog-forum] Universal and categories in BFO & DOLCE, Rich Cooper <= Re: [ontolog-forum] Universal and categories in BFO & DOLCE, doug foxvog Re: [ontolog-forum] Self Interest Ontology, Rich Cooper Re: [ontolog-forum] Universal and categories in BFO & DOLCE, Matthew West Re: [ontolog-forum] Universal and categories in BFO & DOLCE, Rich Cooper Re: [ontolog-forum] Universal and categories in BFO & DOLCE, Matthew West Re: [ontolog-forum] Universal and categories in BFO & DOLCE, AzamatAbdoullaev