SUO: *Date 07 Apr 2002 -- Common Logic & Common Sense
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Bill,
I am going to limit myself to trying to get one single point across
before I even think about going any further. All of this talk about
the expressive capacity or the representational power of FOL, in any
given syntax for it, is simply not being contested, nor is it of any
relevance to the questions of efficiency and the integrity of inquiry
that I have been trying to address here. All that is computable is
turing-computable, and there are times when we actually do write out
turing programs for all sorts of theoretical investigations, and yet
no one in their right might would try to write a turing program to
do their taxes, not unless they want to finish up the job in jail.
So, all of this stuff about "Show me something of clear and present
practical import that I cannot represent in FOL" is just beside the
point. The question is "How well can it be done within the limits
of this or that concretely specific syntax for FOL?" And the answer
is almost always "Not well". It's the same way with roman numerals:
How do you multiply roman numerals? You convert them to decimals,
multiply them out in that medium, and then convert the answer back
to roman numerals. Which is exactly how almost all of the apparent
progress & success in Principian Mold systems is actually achieved.
Jon Awbrey
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BA = Bill Andersen wrote:
JA = Jon Awbrey
JS = John Sowa
JS: There is much more to knowledge representation than just FOL.
FOL is a prerequisite to any and every full-bodied knowledge
representation. It is necessary, but not sufficient.
But nonetheless, it is necessary.
JS: Bottom line: If we don't provide FOL plus contexts plus metalevels
(as the CL standard is designed to do), we are going to be stuck
with kludges built on top of RDF and XML for another 50 years.
BA: John has made my points much more effectively than my
lame attempts to do so. Point 1 was that FOL *must*
be one tool in your toolbox -- there will undoubtedly
be others. Point 2 was that FOL has enough expressive
power to do the vast majority of what we need. Neither
of which is to be read as an endorsement of KIF or any
other concrete syntax.
BA: As for Jon Awbrey's accomplishments in theorem proving, I say great!
But I think he and I are using the term "ontology" to describe very
different things. All I want is for a computer system, for example,
to be capable of detecting that a model that has a person being
older than one of their ancestors is a bad thing, and to be
able to communicate that information to other computer
systems that claim to represent information about
people, parents, ancestors and so on.
BA: I am NOT talking about the ability to prove novel theorems in mathematics.
BA: As a builder of systems to represent information in such a way
that sense can be made of it, that it can be kept consistent
with the agreed upon meanings of terms in a community of use,
and that it can be exchanged freely within such communities,
I am interested first and foremost in doing the mundane things
right. Once that is done, then maybe we can worry about doing
novel things. But we don't even do the mundane things right
at this point.
BA: I challenge Jon (or anyone else) to give one example -- just one --
of some *practical* representation task, having a bearing on the
ontology task as stated above, that cannot be done with FOL in
whatever syntactic guise. Actually, I can think of one --
defining a relation to be finite -- which I understand is
not expressible in FOL, and may be useful on a practical
level (not sure of this) for communicating the meaning
of a term to a peer with whom one (or some system)
may want to communicate. So, I admit that there
is room for more tools and principles.
BA: But, saying things like:
JA: | Logic today is in a horrible mess -- it is dissociated from all of
| the real action in mathematics, programming, and science generally,
| and it is not fair to blame Peirce for the state that has resulted.
BA: doesn't help. What is it exactly that Jon (or, not to pick on Jon, anyone else)
wants to do that requires that this "mess" be supplanted by other principles.
Why is it that we should be concerned with "the real action" in mathematics,
for example, if we can't even at this point, as I've stated before, exchange
my address book between a Palm Pilot and an email program without screwing
it up? If someone could demonstrate that, rather than just talking in
vague generalities, folks (including myself) may become more inclined
to listen.
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