Solutions to Exercises of Week 4a

1). Which of the following are legal terms or predicates. Justify your answer.

a). (IF APPLE RED)

This could be legal if APPLE and RED are shorthand for predicates. But it would be illegal if they are relations.

b). (IF (APPLE x) (RED x))

This would be legal if APPLE and RED are relations.

c). (IF (TALL JOHN) (HEAVY JOHN))

This would be legal if TALL and HEAVY are relations and JOHN is an object constant.

d). (IF (TALL JOHN) (> (WEIGHT JOHN) 200))

This would be legal if TALL is a relation and WEIGHT is a function.

e). (AND (Connected Bolt Plate) (Connected Bolt Plate Washer))

This would be legal if Connected is a relation that has varying arity as it has two arguments in the first expression and two in the second.

2). Represent each of the following sentences as prefix predicates:

a). Coyote is an Animal.

(ANIMAL Coyote)

b). All classes are long and boring.

(ALL x (IF (CLASS x) (AND (LONG x) (BORING x))))

c). Some classes are long and boring.

(EXIST x (AND (CLASS x) (LONG x) (BORING x)))

d). This class is long but not boring.

(AND (CLASS ME290M) (LONG ME290M) (NOT(BORING ME290M) ))

f). This class is neither dull nor boring.

(AND (CLASS ME290M) ((NOT(LONG ME290M))(NOT(BORING ME290M) ))

3). Represent the following "influence diagram" in the drawing below as prefix predicates. In influence diagrams, nodes represent states and arrows represent influences. Use the following relation: (INFLUENCE x y) states that x influences y.

x influences y: (INFLUENCE x y)
x influences z: (INFLUENCE x z)
y influences z: (INFLUENCE y z)

ME290MExpert Systems in Mechanical Engineering

Solutions to Exercises of Week 4a

ME290M
Expert Systems in Mechanical Engineering