CSIS1118
Foundations of Computer Science
Predicate Logic
Hubert Chan
([O1,O2]; chapters 1.3, 1.4)
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Subjects and Predicates
Do you still remember the definition of propositions?
Is “x > 3” a proposition?
N
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f
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No, unless the value of x is fixed.
Let P(x) denote the statement “x > 3” where P(x) is called a
propositional function
.
P(x) has a truth value once the value of x is fixed.
E.g. P(5) is true; P(1) is false.
P actually refers to the property “is greater than 3” and is called the
predicate
. Note that x is a variable (the subject).
A propositional function can have more than one variable (multi-
value predicates).
E.g. Let Q(x, y) denote “x + y > 10”.
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Then, Q(4, 5) is false; Q(5, 6) is true.