CPSC 420 - AI
Homework #5
due: Monday, April 30, 2007

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1. Describe the following scene using Event Calculus:

It rained on Saturday.  The rain started before lunch and ended during
lunch, at which point the sun came out and lasted the rest of the day.

Prove (e.g. via natural deduction in first-order logic) that it was
sunny during dinner (all throughout) using axioms of Interval Logic
(p. 339).  Be sure to include statements encoding your assumptions
about the relationship between the intervals of lunch, dinner, and
night (as part of Saturday).  (for simplicity, assume we eat before
nightfall)

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2. Do problem 13.8 in the textbook.

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3. Do problem 14.1 in the textbook.

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4. Write a complete set of axioms in Situation Calculus for describing
actions in the Wumpus World.  Don't forget to include Frame Axioms
(for all things that don't change).

Then, write STRIPS operators for each action.

Here are details:

Use a (x,y) coordinate system to represent where location of agent and objects.
Assume cave is 4x4, e.g. coordinate of rooms are (1,1)..(4,4).

  action: forward
    moves 1 step forward, depending on the direction the agent is facing
    also affects the location of any object the agent is holding
    if agent is facing a wall, moving forward has no effect

  action: turn 
    parameters: left or right (90 degrees)
    agent can be facing north, south, east, or west
    
  action: pickup
    parameter: object name, must be "movable" (like gold and gun)
    agent can only hold one thing at a time

  action: putdown
    effect: no longer holding anything

  action: shoot
    must be holding gun
    if facing room with wumpus, then wumpus dies