BONUS QUESTION

This is the exercise done in class today. I do not think anyone 
finished it, so here is an opportunity to get a bonus.  

To get a bonus (in addition to the score you'll get for the in
class exercise) please email me your answers by Monday morning.
                       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
You'll get the bonus if your answers are correct.  The bonus
is 1% of the final grade.


Here are a few points to consider when answering;

* when you use the successor-state formulation you need to write 
  one (or more) axiom per predicate (not one per action).
* variables are universally quantified, so if you want an 
  existentially quantified variable you need to use the quantifier.
* the idea of successor state axioms is that you specify that the
  value of the predicate in the situation reached after executing 
  action a is true if and only if the action made it true (there might
  be some other conditions that have to be true for the action to be
  doable) or it was already true and no action made it not to be true.

  For example, in this case, 
  Aa,s,x,y At(Shakey,y,Result(a,s)) <=> a=Go(x,y) ^ At(Shakey,x,s)
				    V
				    At(Shakey,y,s) ^ (a/=Go(x,y))

  Note that Result(a,s) is the situation obtained when doing action a 
  in situation s, so the first part of the expression says that
  (Shakey is at y in the situation obtained by doing action a) if and 
  only if (the action is to go from x to y and Shakey was in x) or 
  (Shakey was already in y and the action was different than go).

  This axiom is not sufficient for the predicate At, because At is
  used to specify the location of an entity, and in addition to 
  Shakey there are boxes that can be pushed around by Shakey.  
  For Shakey to push a box, both Shakey and the box have to be At 
  the same location.  After pushing, both Shakey and the are At the 
  new location.  When writing the axioms, do not assume that there
  is only one box.

  You'll have to write axioms for the other predicates.
  When you write the axioms for ClimbUp and for ClimDown, you can 
  assume that Shakey is on the Floor when it is not on a box.
  Similarly, when you write the axioms to TurnOn and TurnOff a switch
  do not assume there is only one switch.


Here is the description of the problem you were given in class.

Write in situation calculus using the successor-state formulation
the actions of Shakey the robot (see question 11.13 in textbook):


ACTIONS

Go(x,y): Shakey is at x, y is in the same room.

Push(b,x,y): push box b from location x to location y in the same room

ClimUp(b): climb onto a box. Shakey must be on the floor at the box
location.

ClimDown(b): climb down from a box. Shakey must be on the box, after
climbing down it will be on the floor at the box location

TurnOn(s): turn a light switch on.  Shakey must be ontop of a box at the
light switch location

TurnOff(s): turn a light switch off.  Shakey must be ontop of a box at the
light switch location


Use the following PREDICATES

At(object,location,situation)
On(Shakey,object,situation)
TurnedOn(switch,situation)
Box(b)
Switch(s)