Re: [ontolog-forum] Thing and Class

["Godfrey Rust" <godfrey.rust@xxxxxxxxxxxxx>]

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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