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Re: [ontolog-forum] Role of definitions (Remember the poor human)

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Tue, 13 Feb 2007 13:31:30 -0500
Message-id: <45D20402.5080001@xxxxxxxxxxx>
Adrian and Chris,    (01)

I agree that distinguishing those three levels is useful and
that levels #1 and #3 are rarely defined precisely:    (02)

AW> * Semantics1   Is (meta)data semantics, W3C-style
 >   * Semantics2   Specifies what an inferences should be made
 >     from any collection of rules and facts -- usually based
 >     on a model theory, e.g. as in [3].
 >   * Semantics3   Concerns the real world English meanings
 >     of logical predicates    (03)

I'm also happy that Adrian and Chris agree on the use of model
theory to put #2 on a solid foundation.    (04)

But I also believe that level #1 can be defined just as precisely
as #2.  The foundation can also be based on ideas that Tarski
presented in his famous paper on truth in formalized languages
-- namely his stratified hierarchy of metalevels.  An important
addition to Tarski's hierarchy is Dunn's semantics of laws and
facts, which I summarized in the following two papers:    (05)

    Laws, Facts, and Contexts    (06)

    Worlds, Models, and Descriptions    (07)

The major difficulty with #3 is that there is no single "real
world meaning" for most words in English or any other natural
language.  I believe that Wittgenstein's language games provide
a basis for characterizing the multiple meanings of any word:    (08)

  1. Almost all the words in any natural language can be used
     in an open-ended number of ways (which W. called "language
     games").    (09)

  2. For any particular game that is sufficiently well defined,
     the meanings of the words (word senses) may be used in a
     sufficiently narrow way that a formal definition of each
     word sense (along the same lines as #2 above) can be stated.    (010)

  3. For some words, all or most of the word senses for different
     games may have a common generalization for which a formal
     definition (as in #2) is possible.  Each word sense would
     then be a subtype of that generalization.    (011)

  4. But for some words, there is no single common generalization
     that includes all the senses.  In such a case, it is necessary
     to distinguish several generalized word senses, each of which
     could be formally defined (as in #2).    (012)

I discussed these issues in the paper I presented at FOIS'06
in November:    (013)

    A Dynamic Theory of Ontology    (014)

Following is the abstract of that paper.    (015)

___________________________________________________________________    (016)

A Dynamic Theory of Ontology    (017)

John F. Sowa    (018)

Abstract.  Natural languages are easy to learn by infants, they can 
express any thought that any adult might ever conceive, and they 
accommodate the limitations of human breathing rates and short-term 
memory.  The first property implies a finite vocabulary, the second 
implies infinite extensibility, and the third implies a small upper 
bound on the length of phrases.  Together, they imply that most words in 
a natural language will have an open-ended number of senses -- ambiguity 
is inevitable.  Peirce and Wittgenstein are two philosophers who 
understood that vagueness and ambiguity are not defects in language, but 
essential properties that enable it to accommodate anything and 
everything that people need to say.  In analyzing the ambiguities, 
Wittgenstein developed his theory of language games, which allow words 
to have different senses in different contexts, applications, or modes 
of use.  Recent developments in lexical semantics, which are remarkably 
compatible with the views of Peirce and Wittgenstein, are based on the 
recognition that words have an open-ended number of dynamically changing 
and context-dependent microsenses.  The resulting flexibility enables 
natural languages to adapt to any possible subject from any perspective 
for any humanly conceivable purpose.  To achieve a comparable level of 
flexibility with formal ontologies, this paper proposes an organization 
with a dynamically evolving collection of formal theories, systematic 
mappings to formal concept types and informal lexicons of natural 
language terms, and a modularity that allows independent distributed 
development and extension of all resources, formal and informal.    (019)

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