Artificial Intelligence

Homework #2

Exploring Prolog

Due: March 21

Please turn in a printed listing of your Prolog clauses and a sample run of the execution testing your program.  No email is necessary.

1. Write the Prolog clauses for Ackerman's function. 

A(m, n)	n + 1	m == 0,
	A(m-1, 1)	m > 0, n == 0
	A(m-1, A(m, n-1))	otherwise

2. Design a Prolog database to represent the structure of the United States Government. It should use a vocabulary including the following:
    

   Constants:
   executive_arm	legislative_arm	judicial_arm
   president	congress	supreme_court
   vice_president	senate	house_of_representatives
   courts_of_appeal	dept_of_treasury	dept_of_state
   budget	bills	laws
   veto	suits	override
   sec_of_state	sec_of_treasury
   Relations:
   head_of	has_veto_power_over	has_review_power_over
   can_override_veto_by	must_initiate	can_impeach
   can_invalidate	is_apart_of	reports_to

   
   Construct Prolog queries interpreting the following questions
                            

   1. Who has review power over laws?
   2. What can the House of Representatives invalidate?
   3. Who is the head of the Department of Treasury?
   4. Who reports to the President?

3. Design a Prolog system for basic computational geometry. Develop the following relations.  Demonstrate Points, Segments (both vertical and horizontal), Rectangles, Triangles, and Regular Rectangles.

   Point(X, Y)
   Seg( P1, P2 )
   Vertical( Seg( P1, P2 ))
   Horizontal( Seg( P1, P2 ))
   Rectangle( P1, P2, P3, P4 )
   Triangle( P1, P2, P3 )
   Regular( R )