Home Work 3: Grade weightage twice the normal weight.
Due date: Nov 3rd

Consider a domain where we have 
fluents: p1, p2, p3, and f;
action a, b, and c.

We have the effect of action described as follows:

causes(a, f, s). in(p1, s). in(p2, s). %% meaning a causes f if p1, p2.
causes(b, p2, s2). in(p3, s2).         %% meaning b causes p2 if p3.
causes(c, p3, s3). in(neg(f), s3).     %% meaning c causes p3 if ~f.

We also have the following information about the
initial state and goal state:

initially(p1).
initially(neg(p2)).
initially(neg(p3)).
initially(neg(f)).

finally(f).
finally(p1).


(i) Write an Smodels program which will generate plans
for the above domain. I.e., each answer set of the program
will encode a plan. 
(You have the restriction that at each time point -- until
the goal is reached -- exactly one
action occurs.) Note that your programs should use the 
above as facts.

(ii) Now consider an updated domain where we have a new action d
whose effect is described by

causes(d, f, s4). in(p3, s4).  %% meaning d causes f if p3.

We also now assume that actions take time.
We have the following information about that.

duration(a,3). %% a takes 3 time units.
duration(b,5).
duration(c,4).
duration(d,6).

Now a plan is an occurrence of actions at different time
points so that no two actions overlap, and at every time
point -- until the goal is reached -- exactly one action
is under execution.

Also when you reason about the effect of actions, the effect
becomes valid only after the duration of that action
is over. Moreover, the fluent corresponding to that
effect has its truth value as ``unknown'' during the execution
of the action. For example, if p3 is true at time point 1, f
is false at time point 1,
and d occurs at time point 1, then f becomes true at time point 1+6=7,
and the value of f is unknown at time points 2..6, as we do not 
know exactly when the transition of f from false to true takes place.

Now modify your earlier planner to take into account
all this, and find a plan of minimal length. 

(iii) For this project you need to submit a report, hard copy
of your code with explanations, and if 
you only do part of the assignment then state which
part you did and which you did not.