Pat, (01)
We have discussed these issues many times: (02)
1. All detailed reasoning or computation is done in domain-dependent
or application-dependent modules (programs or reasoning systems). (03)
2. The cross-domain words are terms like names, dates, measures,
and addresses. They use very little axiomatization other than
a specification of the formats and simple transformations, such
as 1 inch = 2.54 cm. (04)
3. Other general terms that are used across many applications have
very little detailed axiomatization. The details are *always*
in the specialized domains. (05)
We have also discussed the 2000+ primitives in Longman's list.
They are designed for vague definitions in Longman's dictionaries,
which are intended for use by human readers who have a great deal
of background knowledge to fill in the details. (06)
PC> ... in *mathematical theories* as Pat Hayes states, everything
> is a primitive and primitives have no independent meaning. But in
> an ontology that models the real world, primitives are important
> and unavoidable because the external world is part of the ontology,
> not just the symbols. (07)
Pat was explaining that in formal axioms (which are the only things
that are sufficiently precise for a computer implementation), the
total meaning of the terms is specified by their patterns of
relationships in the rules or axioms. Stating vague definitions
at the level of Longman's dictionaries is useless. (08)
In an earlier note, you pointed to the definitions in the Cosmo
ontology. But those are also vague statements that are typical
of dictionaries designed for human consumption. They may be
useful as general design guidelines, but they aren't sufficiently
precise or detailed for computer reasoning. (09)
If you look at the sources of incompatibility in computer software,
they are invariably in very subtle, very detailed, highly system
and domain specific "issues" (as MSFT calls them). Those problems
aren't the result of general or broad misunderstandings that could
be specified with the vague terms used in Longman's dictionaries. (010)
PC> ... but I am not talking about *isolated* systems of logical
> symbols, but ontologies modeling the real world. What I learned
> new from the earlier notes is that PatH seems to regard "time
> theories" that one would imagine to be models of the real-world
> to be in fact just systems of connected symbols whose meanings
> are not related to anything outside each set of symbols. (011)
Pat Hayes has done a great deal of work in connecting abstract
theories of time and space to theories about physical aspects of
the world, such as fluids in various manifestations from rain drops
to dew to mist, flowing streams, plumbing, etc. By the way, besides
his expertise in logic and mathematics, Pat also happens to be an
expert in clock repair and plumbing. He can also make very good
pencil sketches of people and places during boring talks. So he
knows how to relate logic and software to physical systems. (012)
PC> I agree with the general principle that in a mathematical theorem,
> all of the "meaning" (an undefined term in that context) resides in
> the relationships of the terms and axioms. The problem is that an
> ontology is not *just* a mathematical theorem, though a mathematical
> theorem is a *part* of it. (013)
I agree that the ontology is *intended* to be connected to the real
world. But the computer has no knowledge of those connections other
than the background knowledge encoded in the ontology or the procedures.
If you don't encode the meaning in some computer processable way,
the computer won't have access to it. (014)
You also mentioned the possibility of connecting a computer to
sensors and robotic actuators. But those connections are made
by some kinds of programs. Before you can claim those connections
as sources of background knowledge, you have to solve many thorny
issues about relating ontologies to pattern recognition software
and software for controlling the actuators. (015)
John (016)
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