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Chapter 4
Predicate Logics
344-471 AI & ES Chapter 4 2
Representing simple facts in logic
It is raining.
RAINING If it is raining then it is not sunny.
RAINING ~ SUNNY All men are motal.
MORTALMAN
man(mortal)
X : man(X) mortal(X)
1. Change sentences 1–8 on page 134 to predicate logic.
2. prove ~loyalto(Marcus,Caesar) on page 136 Fig. 5.2
344-471 AI & ES Chapter 4 3
Representing Instance and Isa
Figure 5.3 page 138. : representing class membership
344-471 AI & ES Chapter 4 4
Computable functions and predicate
Figure 5.4 page 142. :a set of facts about Marcus
344-471 AI & ES Chapter 4 5
Computable functions and predicate
Figure 5.5 page 143. : Prove Marcus is dead
344-471 AI & ES Chapter 4 6
Propositional Logic
Given Axioms Converted to Clause Form
P P
(P Q) R ~P v ~Q v R
(S v T) Q ~S v Q
~T v Q
T T
344-471 AI & ES Chapter 4 7
predicates
type(symbol, symbol)
is_a(symbol, symbol)
lives(symbol, symbol)
can_swim(symbol)
goal
can_swim(What) ,
write("A ", What, " can swim.").
clauses type(ungulate, animal). type(fish, animal).
is_a(zebra, ungulate). is_a(herring, fish). is_a(shark, fish).
lives(zebra, on_land). lives(frog, on_land). lives(frog, in_water). lives(shark, in_water).
can_swim(Y) :- type(X,
animal) , is_a(Y, X) , lives(Y,
in_water).
EX05EX05 can_swim
344-471 AI & ES Chapter 4 8
Z
X Y
parent parent
sister
For any X and Y,
X is a sister of Y if
1. Both X and Y have the same parent, and
2. X is a female.
Sister(X,Y) :- parent(Z,X), parent(Z,Y), female(X).
predecessor
344-471 AI & ES Chapter 4 9
A
B
C
E
D
parent
parent
parent
parent
predecessor
344-471 AI & ES Chapter 4 10
A
B
C
E
D
predecessor(X,Z) :-
parent(X,Y),
parent(Y,Z).
parent
parent
parent
parent
predecessor(X,Z) :-
parent(X,Y1),
parent(Y1,Y2),
parent(Y2,Z).
predecessor(X,Z) :-
parent(X,Y1),
parent(Y1,Y2),
parent(Y2,Y3),
parent(Y3,Z).
predecessor
344-471 AI & ES Chapter 4 11
predicates
parent(symbol,symbol)
predecessor(symbol,symbol)
clauses
parent(pam,bob).
parent(tom,bob).
parent(bob,ann).
parent(ann,jim).
parent(jim,joe).
parent(joe,john).
parent(john,jack).
parent(tom,liz).
predecessor(X,Z) :- parent(X,Z).
predecessor(X,Z) :- parent(X,Y), parent(Y,Z). predecessor(X,Z) :- parent(X,Y1),parent(Y1,Y2),parent(Y2,Z).
predecessor(X,Z) :- parent(X,Y1),parent(Y1,Y2),parent(Y2,Y3)
parent(Y3,Z).
ann
bob
pam
jim
john
joe
jack
Parent1.Pro
344-471 AI & ES Chapter 4 12
A
B
C
E
D
parent
parent
parent
parent
For all X and Z,
X is a predecessor of Z if there is a Y such that
1. X is a parent of Y and
2. Y is a predecessor of Z.
predecessor
344-471 AI & ES Chapter 4 13
predecessor(X,Z) :- parent(X,Z).
predecessor(X,Z) :- parent(X,Y), predecessor(Y,Z).
predicates
parent(symbol,symbol)
predecessor(symbol,symbol)
clauses
parent(pam,bob).
parent(tom,bob).
parent(bob,ann).
parent(ann,jim).
parent(jim,joe). parent(joe,john).
parent(john,jack).
parent(tom,liz).
Parent2.Pro
344-471 AI & ES Chapter 4 14
Animal kingdom Plant kingdom
Animal Human
Dog Cat
Toop
Suwit
Mew
Sunee
plant
Flower
Rose Carnation
isa
isa
isa
isa isa
isaisa
isa
isa
isaisa
ISA Relationship
344-471 AI & ES Chapter 4 15
is(X,Z) :- isa(X,Z).
is(X,Z) :- isa(X,Y), is(Y,Z).
predicates
isa(symbol,symbol)
is(symbol,symbol)
clauses
isa(human,animal_kingdom).
isa(plant,plant_kingdon).
isa(flower,plant).
isa(rose,flower).
isa(carnation,flower).
isa(suwit,human).
isa(sunee,human).
isa(dog,animal).
isa(animal,animal_kingdom).
isa(cat,animal).
isa(toop,dog).
isa(mew,cat).
isa(white,cat).
isa1.Pro
344-471 AI & ES Chapter 4 16
predicates
big(symbol)
small(symbol)
brown(symbol)
black(symbol)
gray(symbol)
dark(symbol)
clauses
big(bear).
big(elephant).
small(cat).
brown(bear).
black(cat).
gray(elephant).
dark(Z) :- black(Z).
dark(Z) :- brown(Z).
?black(X),big(X)
?brown(X),big(X)
?big(X),black(X)
?black(X), big(X)
No solution
?brown(X),big(X)
X=bear
?big(X),black(X)
No solution
bear.Pro
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