Chris,
Response to a few points: (01)
> > NO, FOL is a syntax,
>
> Not so. Really importantly not so. In fact, it is *semantics* that
> makes FOL FOL.
Oh, right. I misspoke, but what I should have said is that the semantic
component includes only a very tiny fraction of the primitive semantic
elements required to represent the intended meanings of terms used for most
objects in the real world. Without a standardized set of primitives, the
inconsistencies of independently developed ontologies will make
interoperability impractical for any but the most important cases where
communication is required. The logical representation of the semantic
primitives themselves can be built from the FOL relations, but the
distinctive characteristic of a primitive is that its meanings cannot be
fully specified by combinations of pre-existing terms. There are components
of intended meaning not represented solely by the logical specification. At
this point, we can't get into a long debate about just what the "meaning" is
in a fundamental sense, we just need to be sure that we have enough meaning
specified for the primitives to serve their function of unambiguously
representing the intended usage of those ontology elements, so that the
computer can perform its intended function, and so that accurate
communication among programs (or components or agents) that use the same
basic foundation ontology is enabled. (02)
> > and a basic vocabulary is critical.
>
> Yes, but the only critical basic vocabulary is the purely logical
> vocabulary of boolean operators and quantifiers.
>
This is an important point of disagreement. I can take two ontologies
both based on FOL, OpenCyc and SUMO, and I cannot envision any automatic
method to accurately determine whether one element in OpenCyc is the same
as, subtype, supertype, disjoint, or overlapping with a SUMO element,
because the basic vocabularies are different and need human inspection to
determine the intended meanings of the terms. Even then, it may be
impossible because the representations are not detailed and the
documentation can be inadequate to resolve ambiguities. If there is an
identifiable set of primitives (5000-10,000, say) that can be used to build
all of the more complex concepts required for applications, then separately
developed ontologies can be related to each other automatically, because the
relations between the domain terms will be deducible from comparison of the
combinations of primitive elements of which the domain ontology elements are
composed. That can't be done just using the built-in semantic elements of
FOL. (03)
[PC] > > But if all domain terms (and domain ontology elements) are
logically
> > specified using the same set of semantic primitives, the machine
> > will be able to automatically properly interpret the domain
> > representations, because it knows how to properly interpret the
> > primitives.
>
[CM] > These are stormy waters, as you well know. Strictly speaking,
> machines can't interpret anything. All they can do is process
> syntax. That's why we have to write axioms for them to process (via
> automated reasoners) that do a reasonably complete job of representing
> the information we want them to represent.
>
As engineers, the "interpretation" that is of concern is that the computer
draw the same conclusions and perform the same actions from that data as a
human would who has the same acquired information. "good enough"
representation and interpretation is all we can ask for at this stage. But
looking down the road (well beyond the needs of the current topic), I don’t
see any theoretical reason why a computer could not demonstrate the same
level of interpretation as a human, by interactive conversation or by
correctly performing requested actions (robotic) or describing the input of
a sensor. (04)
> That depends a lot on what they are supposed to be necessary and
> sufficient *for*, but think your question is simply whether it is
> reasonable to think that there could be a single, comprehensive
> foundational ontology upon which all other ontologies could be
> usefully built. While I can imagine *formally* what it would mean to
> have such an ontology -- a single theory of time/space/matter/motion/
> properties/<YourFavoriteFundamentalConceptHere> of which all other
> ontologies are extensions -- I think Ed and others have raised
> reasonable doubts about whether it is a realistic prospect.
>
OK, there are those who are not yet convinced it is feasible (I hold out
the hope for redemption). But I haven't yet heard an objection that
suggests it is so implausible as to not warrant an effort to learn whether
or not such a set of primitives can be found. The fact is that in the
dictionary field (as in LDOCE) the same principle works beautifully, and
that presents compelling evidence that combinations of primitives could also
work for logical rather than linguistic descriptions of meanings.
Considering that AI is over 50 years old, the KIF was proposed back in 1992
(or so), and every year the country loses over 100 billion dollars in
information transfer inefficiency, it seems to me that at this point *every*
plausible proposal to solve the semantic interoperability problem should be
tried. I haven't heard anything better, just some wishful thinking that
somehow something will evolve from everyone building his/her own ontology
unrelated to others, or using some off-the shelf components in a locally
idiosyncratic way. If you think my suggestion is implausible, what
alternative do you think is more likely to achieve agreement on a foundation
ontology or some other means of semantic interoperability within a few
years? Remember, the clock is ticking - delay is very very costly. IF
there are plausible alternatives that don't cost any more than 30 million
over 3 years, I would vote to fund them too. (05)
Pat (06)
Patrick Cassidy
MICRA, Inc.
908-561-3416
cell: 908-565-4053
cassidy@xxxxxxxxx (07)
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of Christopher Menzel
> Sent: Tuesday, January 06, 2009 3:11 PM
> To: [ontolog-forum]
> Subject: Re: [ontolog-forum] Next steps in using ontologies as
> standards
>
> On Jan 6, 2009, at 1:34 PM, Patrick Cassidy wrote:
It is of course required that a first-order language
> have a certain type of syntax that includes a minimal set of
> connectives, the apparatus of quantification, and a certain
> recursively defined class atomic and molecular sentences (though even
> here there is great variability -- see the grammar of Common Logic,
> where this variability is explicitly built in). But what makes a
> logical framework -- i.e., a language plus a semantics -- first-order
> is the fact that it has certain semantic properties (specifically --
> not that it matters much here -- by what is known as Lindström's
> Theorem, compactness and the downward Löwenheim-Skolem properties).
>
> > and a basic vocabulary is critical.
>
> Yes, but the only critical basic vocabulary is the purely logical
> vocabulary of boolean operators and quantifiers.
>
> > I think that optimally the FO needs to include the semantic
> > primitives,
>
> Again, assuming by a semantic primitive you mean a syntactic item
> that, relative to the semantics, cannot be defined in terms of any
> other syntactic items, the semantic primitives of FOL consist of (some
> subset of) the purely logical vocabulary. If you are talking about
> NON-logical primitives, then I think what you have in mind are the
> basic constants and predicates of a first-order *theory* that are
> intended to represent concepts from some intended domain. The only
> way to establish that they are indeed primitive is to look at the
> axioms of the theory and determine whether or not they are definable
> (in the formal sense) in terms of other constants and predicates in
> the theory.
>
> > otherwise people will create relations that have the same terms and
> > different meanings, and different terms for the same meaning, and
> > there will be no automatic way to recognize the similarities or
> > differences.
>
> That's just what we have axioms for, no?
>
> > But if all domain terms (and domain ontology elements) are logically
> > specified using the same set of semantic primitives, the machine
> > will be able to automatically properly interpret the domain
> > representations, because it knows how to properly interpret the
> > primitives.
>
> These are stormy waters, as you well know. Strictly speaking,
> machines can't interpret anything. All they can do is process
> syntax. That's why we have to write axioms for them to process (via
> automated reasoners) that do a reasonably complete job of representing
> the information we want them to represent.
>
> > This is not a trivial issue that can be dismissed with offhand
> > comments. It is at the core of what it means to represent meanings,
> > and it should be seriously investigated by a project involves most
> > of the most knowledgeable ontologists, and some representation of
> > potential users -- especially natural language researchers.
>
> Well, it seems to me that this is what logical AI since the early days
> has been all about (though I think the bulk of NL research has had
> other fish to fry.)
>
> > I ask the question again: is it not at least interesting, if not (as
> > I believe) of central importance to the practice of ontological
> > engineering to learn whether a necessary and sufficient inventory of
> > semantic primitives can in fact be identified?
>
> That depends a lot on what they are supposed to be necessary and
> sufficient *for*, but think your question is simply whether it is
> reasonable to think that there could be a single, comprehensive
> foundational ontology upon which all other ontologies could be
> usefully built. While I can imagine *formally* what it would mean to
> have such an ontology -- a single theory of time/space/matter/motion/
> properties/<YourFavoriteFundamentalConceptHere> of which all other
> ontologies are extensions -- I think Ed and others have raised
> reasonable doubts about whether it is a realistic prospect.
>
> -chris
>
>
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