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Re: [ontolog-forum] Editor COE view of a new list of categories

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Sun, 15 Jul 2007 07:39:39 -0400
Message-id: <469A077B.4060701@xxxxxxxxxxx>
Alan, Hans, Azamat, Wacek, and Jon,    (01)

I agree that I should have been more careful in my statement.
RDF uses triples to represent the data, but OWL is a full
description logic that represents axioms that can be used to
reason with and about the RDF triples.    (02)

AR> As you point out in a subsequent message, the semantics of OWL
 > can be captured by SCL. I would be interested in knowing which
 > portion of SCL - (OWL in SCL) prevents the second issue you
 > raise about "ultimately reduc[ing] to uninterpreted strings".    (03)

No language, by itself, can do anything other than relate strings
of letters or sounds to other strings.  Therefore, Common Logic,
OWL, and all other notations for logic share the same limitations.    (04)

The semantics of CL and of OWL are defined in a metalanguage that
relates the strings in the logic to a set of entities in some model.
The model may be an uninterpreted set of strings, a mathematical
structure, such as the real numbers or Euclidean geometry, or
a structure of physical entities, states, and events in the world.    (05)

Most of the models used in computer science are not grounded in
anything other than uninterpreted strings.  The axioms stated in
some version of logic may impose enough constraints on the models
that they would become fairly good structural simulacra of systems
in the real world.  Only a fully functional robot would have its
internal models connected to the world by means of perception and
action -- which are the two "gates", as Peirce called them, that
ground human languages in reality.    (06)

AA>> Moreover it [OWL] has nothing to do with a real
 >> ontology, being just a formal logical language,    (07)

vQ> Likewise FOL and any other logic.  OWL involves some more
 > ontology in that it speaks of classes and instances, while
 > (the semantics of) pure FOL includes a single sort of entities.    (08)

Formally, sorts and monadic predicates are two logically equivalent
ways of representing the ontological categories of entities.  I
prefer to use a sorted or typed notation because it has a more
direct mapping to the forms of expression in natural languages.
But the labels that represent sorts or types can always be mapped
to the labels that represent monadic predicates in an untyped
notation, while preserving logical equivalence.    (09)

vQ> You can use any language, of any expressivity, and still do
 > silly things.  Constrained expressivity does not mean that what
 > you say about the world is necessarily confused -- it is just
 > a model which is much more simple than the modeled reality.
 > (Show me a model which is as complex as what it models.)    (010)

I agree.  One reason why I like controlled NLs is that they are
just as formal as any other notation for logic, but they can be
read as easily as a natural language.  Therefore, the silliness
tends to become more obvious.    (011)

I often quote the following poem by Henry Kautz, which contains
a large kernel of truth.   A lot of nonsense has been published
in various notations for logic, which would never have been
accepted if it had been clearly written in some NL.    (012)

And by the way, I liked the paper by Jon and Susan Awbrey, which
makes some important points about the difficulty of integrating
piecemeal representations, whether stated in logic or in NLs:    (013)

    http://www.cspeirce.com/menu/library/aboutcsp/awbrey/integrat.htm    (014)

__________________________________________________________________    (015)

     If your thesis is utterly vacuous,
     Use first-order predicate calculus.
        With sufficient formality,
        The sheerest banality
     Will be hailed by all as miraculous.    (016)

     If your thesis is quite indefensible,
     Reach for semantics intensional.
        Over Montague grammar,
        Your committee will stammer,
     Not admitting it's incomprehensible!    (017)

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