Chris, (01)
JS> Are you claiming that anybody who hears or sees
> the word 'class' is expected to look up the axioms
> associated with the word every time they run into it? (02)
CM> Well, no, I think the concept in question could be
> described informally just fine. Though a quick look
> at the axioms would alway do one good. (03)
The point I was making is that it's better if the common
English sense is sufficient and there is no need to check
either a formal or an informal definition. I agree that
it's good to RTFM (Read the fine manual), but it helps to
remember axioms if they're consistent with informal usage. (04)
JS>> Why not just use the word 'type', whose common meaning
>> implies the axioms we want to use? (05)
CM> I found your arguments that type is somehow more natural
> than class entirely unpersuasive. I think it is fraught
> with very similar ambiguities. (06)
There is a very big difference between ambiguity and
inconsistency. The general definition I suggested for
'type' in my previous note (copy below) is ambiguous
in the sense that it allows many different special cases,
but it does not create any inconsistency with any of them. (07)
The problem with 'class' is that many, if not most of
the special cases are defined extensionally, and they
would be inconsistent with an intensional definition
along the lines we require for ontology. (08)
Inconsistency is far more serious than ambiguity.
You can resolve an ambiguity just by adding another
qualification, but getting out of an inconsistency
is much harder. (09)
CM> What tilts the scales toward "class" in my view is
> a pragmatic matter, viz., its adoption and use by the
> W3C languages. (010)
Four points: (011)
1. The number of programmers who use the word 'class'
in a conflicting sense in O-O languages is probably
larger than the number of people who have learned
RDF and OWL. (012)
2. The number of programmers who use the word 'type'
for datatypes in a way that is consistent with the
definition given below is even larger. (013)
3. The set of all educated English speakers is a much
larger group, and they would all be familiar with
a sense of the word 'type' consistent with the
definition below. (014)
4. Anybody who learns RDF and OWL would probably
belong at least to group #3 and maybe also to
groups #1 or #2. Therefore, they would already
be familiar with the word 'type' in the sense
below and/or with definitions of 'class' that
are incompatible with #3. (015)
The size of group #3 is the most compelling reason for
'type', and it would be a mistake to go with a choice
that is familiar to just a very much smaller group. (016)
John
______________________________________________________ (017)
The notion of type that I am advocating, which I claim
is very close to the common English meaning of the word,
has the following minimal structure: (018)
1. For each type t, a set of axioms that define the
conditions for any x to be an instance of t. (019)
2. A partial ordering called subtype, which is determined
by the axioms for the types, not by their instances
in any particular model. (020)
This definition implies that types are intensional because
two types can have the same instances in a particular model,
yet their axioms might not be not provably equivalent. That
makes them intensional according to Church's criterion. (021)
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