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Re: [ontolog-forum] Existentials (WAS: Re: brainwaves (WAS: to concept o

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Fri, 14 Dec 2007 09:17:15 -0500
Message-id: <4762906B.2070005@xxxxxxxxxxx>
Pat and Pat,    (01)

PH> If its functional it must be existential (in your sense).
 > If you are seriously worried about terminology, a good term
 > for these might be Skolem assertions.    (02)

I agree that would be useful for those people who have heard
of Skolem and Skolemizing.  But the term 'functional dependency'
which has been used in the database field for over 30 years,
depends only on some acquaintance with functions.    (03)

I also agree that not every A-E quantifier pattern implies
a unique existential.  However, it does imply that there
exists something.    (04)

Therefore, it would be reasonable to call it an 'implicit
existential'.  A functional dependency would make a stronger
point that the implicit existential term happens to imply
a unique individual.    (05)

And by the way, in the CGIF notation for Common Logic, I used
a vertical bar to mark functional dependencies, since CG notation
is basically relational rather than functional.  That also makes
it possible to mark more than one functional dependency in the
same relation.    (06)

For example, the divide relation takes four arguments --
a dividend x, a divisor y, a quotient q, and a remainder r:    (07)

    (divide x y q r)    (08)

In CGIF notation, a vertical bar could be used to indicate that
the last two arguments are functionally dependent on the first two:    (09)

    (divide x y | q r)    (010)

This would be equivalent to a conjunction of two functions:    (011)

    (quotient x y | q)  (remainder x y | r)    (012)

An employee relation in a database might have many functional
dependencies:    (013)

    (employee emp_id | name department manager salary)    (014)

A relation with many arguments might have criss-crossing or
transitive functional dependencies.  In CGIF notation, those
could be written as a conjunction of several relations with bars
to indicate the dependencies.    (015)

John    (016)

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