Predicate Logic
(part 1)
(Chapter 2)
CSE 352 Artificial Intelligence
Professor Anita Wasilewska
Lecture Notes (3)
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View Full DocumentPredicate Logic Language
Symbols:
1.
P, Q, R…
predicates symbols
, denote
relations in “real
life”, countably infinite set
2.
x,y,z….
variables,
countably infinite set
3.
c1, c2, …
constants
, countably infinite set
4.
f, g, h
…
functional symbols
, may be empty, denote
functions in “real life”
5.
Propositional connectives
:
∨
,
∧
,
⇒
, ¬,
⇔
6
.
Symbols for quantifiers
∀
x
– universal quantifier reads: For all x…
∃
x
– existential quantifier reads: There is x…
Formulas of Predicate Logic
We use symbols
1

6
to build
formulas
of predicate logic as
follows
1. P(x), Q(x,y), R(x)… R(c1), Q(x, c3),
P(c), …
are called
atomic formulas
for any variables x, y,… and
constants c, c1, c2, …
2.
All atomic formulas are formulas ;
3.
If
A,B
are
formulas
then (like in propositional logic):
(A
∨
B) , (A
∧
B), (A
⇒
B), (A
⇔
B), ¬A
are
formulas
4.
∀
x A,
∃
y A
are
formulas,
for any variables x, y
5.
The set
F
of
all formulas
is the
smallest
set that fulfills the
conditions 1 4.
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