From: Wagner, G.R. (G.R.Wagner@tm.tue.nl)
Date: 12/14/04
[original qestion by MD] Can we come
up with an n-ary representation that's significant simpler or
otherwise better than the unary/binary SWRL representation?
[GW] What do you mean with "significant simpler or otherwise better"?
The issue here is simply that "objectifying" a relation may be
unnatural and create some undesirable (and unnecessary) overhead
in the language.
[PH] What kind of overhead? Why would this create any overhead?
[GW] If you don't see the overhead, this simply shows that you don't
have much experience with coding practical appplications. Or you may
be in the position of an assembler programmer who doesn't want to see
the unnatural overhead of coding a while loop with a jump/goto
statement.
[GW] In foundational ontology, one makes a distinction between formal
and material relations (both of which would be represented with the help
of predicates).
[PH] ?Does one, indeed? That seems to depend a lot of which one one
happens to be. Is there any philosophical, mathematical or practical reason
for making such a distinction?
[GW] Roughly, this distinction corresponds to the practical distinction
between predefined and user-defined properties/functions/relations in
computational formalisms. So, yes there is a practical reason for making
this conceptual distinction. A philosophical reason for it may be the
desire to explain why some relations (such as those used in mathematics)
have an extensional semantics and others have an intensional semantics.
What methodology or basic theory is used
to justify making distinctions like this? And what does this particular
distinction even mean?
[Later. I have now read some papers on the subject. The definition
appears to be purely circular: a relation is 'formal' if it is an extension which
applies directly, and is 'material' if it is an individual with a relational extension.
End of story.
[GW] It's not quite that simple, unfortunately. Most people have some intuitive
understanding of what is a formal relation because they know orderings and
other relations from mathematics. An attempt to characterize the difference between
those formal relations and other relations (between individuals that have a "history")
is to point out that (instances of) these material relations hold between their relata
because there is an individual (such as an event or a process) that affects the
history of (and that existentially depends on) these relata. This is the case for
relations such as "Person buys Product from Vendor" or "Person kisses Person",
while it is not the case for relations such as "Point1 is between Point2 and Point3"
or "Person is taller than Person" (the latter is a relation between the individual
heights of two persons, being qualities in the underlying "conceptual space"
according to the theory of Peter Gärdenfors presented in his book "Conceptual
Spaces: the Geometry of Thought", 2000).
...; and the elaborate but misguided ideas emerging from the Leipzig institute do
not stand up to even a moment's close analysis; ...
[GW] Note that there are two "Leipzig institutes" (that have arised from a schism)
and that I was referring to the work of Heinrich Herre and others on what they
call "General Formal Ontology (GFO)" and "General Ontological Language (GOL)".
Please don't confuse this with "BFO" as proposed by others and Smith, whose
work is less profound.
What would be the basis for rejecting a claim that *any* relation defines a relator universal?
[GW] A relator universal is an intensional concept, while formal/mathematical relations
are extensional.
... you have no right to prevent me treating your 'formal' relations
as 'material' relations: unless, that is, you want to claim that this is a *logical* distinction.
[GW] No, of course, the distinction between formal and material relations is not a
logical one. Most of the conceptual distinctions we make in order to understand the
real world and to construct working computational systems are not logical!
-Gerd
This archive was generated by hypermail 2.1.4 : 12/14/04 EST