Shai BenDavid
1 First Order Logic / Predicate Logic
The basic idea of ﬁrst Order Logic:
There are two types of entities: objects and relations (also called properties or
predicates) among them.
Some informal examples of predicate logic:
Intended Meaning
Formula
Socrates is a Man
M
(
s
), where
M
is a property and
s
is an object
Every Man is mortal
∀
x,
(
M
(
x
)
→
T
(
x
)), where
T
is the property of being mortal
Socrates is mortal
T
(
s
)
So we get the formula:
(
M
(
s
)
∧ ∀
x
(
M
(
x
)
→
T
(
x
)))
→
T
(
s
)
Discussing Order Relations:
•
Objects:
x,y,z,.
..
•
Relation:
R
(
x,y
) denoting
x < y
Intended Meaning
Formula
R
is asymmetric
∀
x,y,R
(
x,y
)
→ ¬
R
(
y,x
)
R
is transitive
∀
x,y,z,
(
R
(
x,y
)
∧
R
(
y,z
))
→
R
(
x,z
)
Between every two points,
there exists a third
∀
x,y,R
(
x,y
)
→ ∃
z,
(
R
(
x,z
)
∧
R
(
z,y
))
Discussing Natural Numbers:
•
Objects:
x,y,z,.
..a
(denotes 0)
•
Relation:
R
(
x,y
) denoting
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 Spring '08
 A
 Predicate logic, Firstorder logic, Shai BenDavid, Formula ∀x

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