## 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.)