BITS
Pilani
Pilani Campus
MODULE:
PREDICATE LOGIC
Semantics
 Satisfiability and Validity
 Validity is undecidable
Sundar B.
CS&IS,
BITS Pilani
0
29092016
CS/IS F214
Logic in Computer Science
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Predicate Logic: Satisfiability
•
Recall:
•
=
l
M
denotes that
evaluates to TRUE given the set of
premises
•
under model M and lookup table
l
•
We say a predicate logic formula
is
satisfiable
•
if it evaluates to TRUE (without any premises) under
some model
M
and
some lookup table
l
:
•
i.e.
=
l
M
for some
M
and some
l
29092016
1
Sundar B.
CS&IS,
BITS Pilani
Predicate Logic: Validity
•
Recall:
•
=
denotes that
evaluates to TRUE given the set of
premises
under all models (and all lookup
tables).
•
We say a predicate logic formula
is
valid
•
if it evaluates to TRUE (without any premises)
under
all models
:
i.e.
=
29092016
2
Sundar B.
CS&IS,
BITS Pilani
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Predicate Logic: Validity: Example 1
•
X (p(X) > q(X)) = (
X p(X)) > (
X q(X))
•
Justification:
•
Let
M
be any model such that
•
X (p(X) > q(X)) =
M
(
X p(X)) > (
X q(X))
•
Suppose that
for not every element
of (the universe in)
M,
p(X)
is true
:
•
then we are done. (Why?)
•
Otherwise suppose
X p(X)
. Therefore,
for every
element
a
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 Summer '17

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