To: | "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx> |
---|---|
From: | "Godfrey Rust" <godfrey.rust@xxxxxxxxxxxxx> |
Date: | Tue, 9 Sep 2008 19:50:41 +0100 |
Message-id: | <1AA31B28C76B436EA581E76E6CF3371A@GodfreyPC> |
John, by "software such as FCA" do you mean the
"Conexp" Concept Explorer?
Godfrey Rust
Chief Data Architect Rightscom/Ontologyx Linton House LG01 164/180 Union Street, London SE1 0LH www.rightscom.com Direct +20 8579 8655 Rightscom Office +20 7620 4433 Mobile 07967 963674 ----- Original Message -----
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
Sent: Tuesday, September 09, 2008 7:26
PM
Subject: Re: [ontolog-forum] Thing and
Class > > Aristotle's syllogisms are basically that subset of FOL > that uses just monadic predicates. > > > I am surprised that all of Aristotle's syllogisms > > are still valid under multiple inheritance. > > There is nothing magic about multiple inheritance. It is > just a use of implication applied to monadic predicates. > >> Multiple inheritance may not have contradictions, >> but it does introduce ambiguity. For example, >> A is genus-1 with differentia-1 >> and >> A is genus-2 with differentia-2 >> >> In other words, A has two different definitions. > > If the two definitions are equivalent, there is no ambiguity > whatever. For example, you might define the type Dog as > Mammal with differentia A, and I might define Dog as Animal > with differentiae A & B. > > But if (Mammal & A) is logically equivalent to (Animal & A & B), > then our definitions are identical. With software such as FCA, > all such implications are automatically generated. > > > In today's jargon, A has two different word senses, > > which apply in two different contexts. > > If two word senses are provably identical, they are the > *same* word sense. In mathematics, it is very common for > different authors to state different definitions that are > provably equivalent. For some good analysis and examples, > I recommend the article cited below, from which I extracted > an example that illustrates the above point. > > That article should be required reading for anyone who is > defining, using, or talking about ontologies. > > John > ________________________________________________________________ > > http://www.sfu.ca/philosophy/swartz/definitions.htm > > Notes on Definitions by Norman Swartz > > Excerpt: > > Consider the case of "square". What is 'the' intensional definition > of "square"? Here are five competing candidates, i.e. sets of logically > necessary and jointly sufficient conditions. > > 1. "square" =df "a plane closed figure that has exactly four sides > all of which are straight and equal to one another and whose interior > angles each measure 90 degrees" > > 2. "square" =df "a plane closed figure having four straight sides > and whose diagonals are both equal in length to one another and bisect > one another at right angles" > > 3. "square" =df "a straight-sided, plane, closed figure, every > diagonal of which cuts the figure into two right isosceles triangles" > > 4. "square" =df "an equilateral parallelogram containing no > (interior) acute angles" > > 5. "square" =df "an equilateral parallelogram containing four axes > of symmetry" > > The first of these may be the closest (fairest) representative of what > most persons 'have in mind' when they use the term "square", but the > other four 'definitions' also 'pick out' the identical extension. If the > former is to be privileged as being the one to earn the accolade "'the' > intensional definition", it cannot be on its logical features alone: it > can be regarded as 'the' intensional definition only by invoking > empirical data about language-users' tacit rules. > > > _________________________________________________________________ > 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 > > > ______________________________________________________________________ > This email has been scanned by the MessageLabs Email Security System. > For more information please visit http://www.messagelabs.com/email > ______________________________________________________________________ > > _________________________________________________________________ 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 (01) |
<Prev in Thread] | Current Thread | [Next in Thread> |
---|---|---|
|
Previous by Date: | Re: [ontolog-forum] Thing and Class, Michael F Uschold |
---|---|
Next by Date: | Re: [ontolog-forum] Thing and Class, Pat Hayes |
Previous by Thread: | Re: [ontolog-forum] Thing and Class, John F. Sowa |
Next by Thread: | Re: [ontolog-forum] Thing and Class, John F. Sowa |
Indexes: | [Date] [Thread] [Top] [All Lists] |