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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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