Question

# Consider the following first-order inference problem given the rules and facts: • R1: If X is...

Consider the following first-order inference problem given the rules and facts:

• R1: If X is a close relative of Y and Y is a close relative of Z then X is acquainted with Z.

• R2: If X is a parent of Y, then X is a close relative of Y.

• R3: If X is married to Y, then X is a close relative of Y.

• F1: Sam is a parent of Mike.

• F2: Mike is married to Alice.

1. (5 points) FOL representation Express the rules R1-R3 and the facts F1,F2 in first-order logic using the following constants and predicates:

• c(X,Y) — X is a close relative of Y.

• p(X,Y) — X is a parent of Y.

• m(X,Y) — X is married to Y.

• a(X,Y) — X is acquainted with Y.

• Sam, Mike, Alice : Constants.

2. (5 points) FOL reasoning Infer that Sam is acquainted with Alice using either forward or backward chaining.

Sol.

R1: c(X,Y) & c(Y,Z) ---> a(X,Z)

R2: p(X,Y) ----> c(X,Y)

R3: m(X,Y) ---> c(X,Y)

F1: p(Sam, Mike)

F2: m(Mike, Alice)

Part 2. Sam is Aquainted with Alice.

From R2: if X is parent of Y then X is a close relative of Y , so it can say that sam is parent of Mike then sam will be a close relative of Mike.

p(Sam, Mike) ---> c(Sam, Mike)...................(1)

Now From R3 it can be say that if Mike married to Alice then Mike will be a close relative of Alice.

m(Mike, Alice) ---> c(Mike, Alice).....................(2)

From Eq 1 and Eq 2 it deduce that sam is a close relative of Mike and Mike is also a close relative to Alice so From R1 it is pooved that sam is Aquainted with Alice.

c(Sam, Mike) & c(Mike, Alice) ---> a(Sam,Alice).

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