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Re: [ontolog-forum] Thing and Class

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
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----- 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

> Dick,
>
> 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.
>

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