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Re: [ontolog-forum] Next steps in using ontologies as standards

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Mon, 26 Jan 2009 00:25:51 -0500
Message-id: <497D495F.3060602@xxxxxxxxxxx>
Pat and Paola,    (01)

PH> Formal in this sense means that the syntax is exactly specified
 > in a formal grammar, which for these purposes can be defined to be
 > a context-free EBNF grammar, though other grammar notations are
 > acceptable. English, like all other natural languages, has never
 > been formalized in this sense and never will be, because it is in
 > a constant state of dynamic change.    (02)

I basically agree, but it's important to state exactly what makes
a language formal or informal.    (03)

PDM> what determines formality, and to what degree, is another
 > long discussion    (04)

No.  It can be stated very simply:    (05)

  - A language L is formal if and only if the interpretation of
    a complete expression in L is uniquely determined by its *form*
    (i.e., syntax) without any consideration of any background
    information that the interpreter might have.    (06)

  - A language L is informal if and only if a complete expression
    in L can have different interpretations by different interpreters
    or even by the same interpreter in different situations or contexts.    (07)

I use the term 'complete expression' for the basic syntactic unit
of the language L.  For a programming language, for example, it would
mean a unit of compilation such as a program from the first line to
the end.  For natural languages, there is no such thing as a completed
expression.  Even an entire book can be interpreted in different ways
by readers who have different kinds of background knowledge.    (08)

In this sense, Aristotle's syllogisms are formal, even though they
use a subset of the words and syntax of a natural language.  For
example, following is the *form* of the pattern named Barbara:    (09)

    Every A is a B.
    Every B is a C.
    Therefore, every A is a C.    (010)

When the letters A, B, and C are replaced by arbitrary common nouns,
the interpretation of the syllogism is uniquely determined --
provided that the middle term B is required to apply to exactly
the same individuals in both premises.    (011)

John Sowa    (012)

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