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Re: [ontolog-forum] {Disarmed} Re: OWL and lack of identifiers

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Fri, 27 Apr 2007 08:01:19 -0400
Message-id: <4631E60F.2020507@xxxxxxxxxxx>
Steve, Patrick D., and Pat H.,    (01)

On the technical issues about logic, I completely agree
with Pat, but I will admit that just learning logic is not
sufficient to quench various kinds of misconceptions about
how logic is related to language and thought.    (02)

In fact, some of what I believe are the most serious
misconceptions have been proposed by some of the most
sophisticated logicians.  Richard Montague, for example,
was a brilliant logician, who wrote the following sentence
as the opening line of one of his most famous papers:    (03)

    "I reject the contention that an important theoretical
    difference exists between formal and natural languages."    (04)

Montague's papers from the late 1960s and early '70s led
to 30+ years of attempts to develop a form of logic that is
the foundation of all NLs.   That attempt has not succeeded,
and I believe it is a dead end -- but a very interesting and
instructive dead end.    (05)

I would maintain the following points:    (06)

  1. The underlying mechanisms that enable children to learn
     language are based on powerful pattern-matching techniques
     that are very general and very efficient.    (07)

  2. The kinds of features that underlie all NLs are those that
     an infant finds easy to learn in the first 3 or 4 years
     of life.    (08)

  3. Children learn to recognize what is true or false about any
     of the language patterns in the "School of Hard Knocks" -- i.e.,
     some methods of thinking and talking produce statements that
     lead to successful actions and others lead to "hard knocks".    (09)

  4. As a result of that learning, various kinds of patterns occur
     in NLs that people repeatedly find useful for organizing and
     expressing their thoughts.  Common words that occur in those
     patterns include 'and', 'or', 'not', 'every', 'some', 'may',
     'can', 'must', etc.    (010)

  5. Logicians starting with Aristotle analyzed those patterns of
     thought and codified them as guidelines for dependable reasoning.
     Aristotle also began the analysis of "fallacies" or common ways
     of using language that are not dependable.    (011)

  6. Since the mid 1800s, Boole, De Morgan, Peirce, Frege, etc.,
     applied mathematical methods to analyze those patterns even
     further.  They codified the results of their analyses in
     many versions of logic, some of which are subsets or supersets
     of others.    (012)

  7. Among those versions, Aristotle's syllogisms are still an
     important subset of modern description logics, such as OWL.
     Another important version is FOL, which is a superset of
     syllogisms and DLs plus various rule-based languages.
     Other versions include modal logics, which handle the
     'may', 'can', 'must' words.    (013)

In short, logic is a tool for analyzing language, not the
foundation for language.  The operators of logic are abstractions
from the words and syntax of NLs, in the same way that 2+2=4 is
an abstraction from the kind of counting and arithmetic that our
stone-age ancestors expressed in the ancestors of modern languages.    (014)

John    (015)

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