1. Chapter 4 Predicate Logics

2. Representing simple facts in logic
The End
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
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3. Representing Instance and Isa
Figure 5.3 page 138. : representing class membership
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4. Computable functions and predicate
The End
Figure 5.4 page 142. :a set of facts about Marcus
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5. Computable functions and predicate
Figure 5.5 page 143. : Prove Marcus is dead
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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
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7. EX05EX05 can_swim can_swim(What) , 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).
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8. predecessor Z X Y parent parent sister For any X and Y,
X is a sister of Y if
Both X and Y have the same parent, and
X is a female.
Sister(X,Y) :- parent(Z,X), parent(Z,Y), female(X).
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9. predecessor A B C D E parent parent parent parent 344-471 AI & ES
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10. predecessor A B C D E predecessor(X,Z) :- parent(X,Y), parent(Y,Z).
parent(Y1,Y2),
parent(Y2,Z).
parent B
parent C
predecessor(X,Z) :-
parent(X,Y1),
parent(Y1,Y2),
parent(Y2,Y3),
parent(Y3,Z).
parent D
parent E
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11. Parent1.Pro parent(jim,joe). 344-471 AI & ES Chapter 4 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).
pam
bob
ann
jim
joe
john
jack
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).
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12. predecessor A B C D E 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. A
parent B
parent C
parent D
parent E
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13. Parent2.Pro parent(jim,joe). predecessor(X,Z) :- parent(X,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).
predecessor(X,Z) :- parent(X,Z).
predecessor(X,Z) :- parent(X,Y), predecessor(Y,Z).
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14. ISA Relationship isa isa isa isa isa isa isa isa isa isa isa
Animal kingdom
Plant kingdom
isa
isa
isa
Animal
Human
plant
isa
isa
isa
isa
Dog
Cat
Suwit
Sunee
Flower
isa
isa
isa
isa
Toop
Mew
Rose
Carnation
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15. isa1.Pro 344-471 AI & ES Chapter 4 is(X,Z) :- isa(X,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).
is(X,Z) :- isa(X,Z).
is(X,Z) :- isa(X,Y), is(Y,Z).
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16. bear.Pro ?black(X),big(X) ?brown(X),big(X) ?big(X),black(X)
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)
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17. One that would have the fruit
must climb the tree