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Quantifier Patterns
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De Morgan's Laws
Examples
"All Ferraris are red"
"It holds for all objects that, if the object is a Ferrari, then the object is red".
forall
x
: isFerrari(
x
) => isRed(
x
).
"Some Ferraris are black"
"There exists an object such that the object is a Ferrari and the object is black"
exists
x
: isFerrari(
x
) /\ isBlack(
x
).
"Everybody has exactly one father".
"For every person
x
, there is one person
y
such that
y
is the father of
x
and every person
z
who is father of
x
is identical to
y
".
(
forall
x
: (
exists
y
: isfather(
y
,
x
) /\ (
forall
z
: isfather(
z
,
x
) =>
z
=
y
))).
forall
x
:
exists
y
: isfather(
y
,
x
) /\
forall
z
: isfather(
z
,
x
) =>
z
=
y
.
Author:
Wolfgang Schreiner
Last Modification: October 6, 1999