Two different definitions ...
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. (01)
I am talking about truly different definitions, as in
** the different word senses of synsets in WordNet
** the different definitions of the same word in a dictionary (02)
For example, Aristotle defined man as
man is animal with rational
but the more common definition of man is
man is human with gender = male
Clearly, in Aristotle's context
man is human with gender = male or female
man is human
In the RDF/OWL world without context, we can
combine these statements and derive further
statements such as
woman is human with gender = female
woman is man with gender = female (03)
Ayn Rand do speak od mKR done;
mKE do enhance od Real Intelligence done;
knowledge := man do identify od existent done;
knowledge haspart proposition list;
----- Original Message -----
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
Sent: Tuesday, September 09, 2008 11:26 AM
Subject: Re: [ontolog-forum] Thing and Class (05)
> 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.
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