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Jon Heggland wrote:
> Yes, but the relation predicate is not. Given relations A(x,y) and B
> (y,z) with predicates PA(x,y) "employee x works in department y" and PB
> (y,z) "department y is led by manager z".
Although you made an excellent point later, here I'm confused by the lack of quantifiers in the above sentences. Wouldn't it be more precisely to say
"there exists employee x and department y such that x works in y" "there exists department y and manager z such that y is led by z"
Predicate logic sentences without quantifiers are assumed to have implicit universal quantifier, right? Let's manipulate closed sentences only, from now on.
> The predicate PJAB(x,y,z) of A join B is "employee x works in department
> y, and department y is led by manager z" (or more simply, "employee x
> works in department y which is led by manager z").
"there exists employee x and department y such that x works in y
AND
there exists department y and manager z such that y is led by z"
which can be reduced to
"there exists employee x, department y, and manager z such that x works in y and y is led by z"
> The predicate PUAB(y) of A generalized union B is "there exists an
> employee x such that employee x works in department y, or there exists a
> manager z such that department y is led by manager z"
"there exists department y such that
...there exists employee x such that x works in y
OR
...there exists manager z such that y is led by z"
Isn't this logically equivalent to
> Whereas the predicate POAB(x,y,z) of A <OR> B is "employee x works in
> department y, or department y is led by manager z".
"there exists employee x and department y such that x works in y
OR
there exists department y and manager z such that y is led by z"
It looks like the way we choose free variable is an interpretation made outside of logic, and both sentences are logically equivalent. Received on Fri Jul 01 2005 - 13:08:22 CDT