## AI: Problem Set 3

Assigned: Feb. 19

Due: March 2

### Problem 1

Let D be the domain of solid objects.
Let L be the first-order language over D with the following non-logical symbols:
inside(O1,O2) --- Object O is inside O2.

empty(O) --- Object O is empty.

accessible(O) --- Object O is accessible.

red(O) --- Object O is red.

Represent the following statements in L.
- A. An object is empty if and only if there is nothing inside it.
- B. An object is accessible if and only if it is not inside any object.s
- C. Every object is either accessible or inside some accessible object.
- D. All the accessible objects are red.
- E. If O1 is inside O2 and O2 is red, then O1 is red.
- F. If all objects are accessible, then all objects are empty.
- G. All objects are red.

### Problem 2

Convert sentences A through E above, and the negations of sentences F and G
to clausal form (CNF).
### Problem 3

Give * resolution * proofs of F and G from A-E. (No credit will
be given for a proof that is not a resolution proof.)