|To:||"[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>|
|From:||"Godfrey Rust" <godfrey.rust@xxxxxxxxxxxxx>|
|Date:||Tue, 9 Sep 2008 19:50:41 +0100|
John, by "software such as FCA" do you mean the "Conexp" Concept Explorer?
Chief Data Architect
Linton House LG01
164/180 Union Street, London SE1 0LH
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
>> 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.
> Notes on Definitions by Norman Swartz
> 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]|