Action: Play(g,l,t) "Play game g at location l at time t" Preconditions: RightNow(t), Scheduled(g,l,t), At(l), TimeAfter(t,n) Add: HadFunAt(g), RightNow(n) Delete: RightNow(t) Action: Go(h,t) "Go from h to t" Preconditions: At(h) Add: At(t) Delete: At(h)
Where the state predicates are interpreted as follows:
RightNow(t) "The current time is t" TimeAfter(t,n) "The next time after t is n" At(l) "Jack is at l" Scheduled(g,l,t) "Game g is scheduled to be played at location l at time t" HadFunAt(g) "Game g has been played and it was fun"Jack doesn't like to waste any time not doing any sports so he has a sports car which is very fast and can get from one facility to another immediately. Also notice that when playing a game Jack gets so into it that he forgets about the gradual progress of time. For him time just "jumps" from the starting time to the ending time of the game.
Consider the initial state:
At(IF) RightNow(9:30am) TimeAfter(9:30am, 10:30am) TimeAfter(10:30am, 11:30am) Scheduled(Ping-pong, Gregory, 9:30am) Scheduled(Soccer, IF, 9:30am) Scheduled(Soccer, IF, 10:30am)
Jack's goals are (given in this order):
HadFunAt(Ping-pong) & HadFunAt(Soccer)
a) Show a detailed, nested trace of subgoals and actions (like that given on pages 19-22 of the lecture notes on planning) resulting when STRIPS is used to solve this problem. Assume that different instantiations of an action (i.e. different ways of binding its variables) that are capable of achieving a goal (such as different times of playing a game) are considered as alternative actions for achieving the goal. Assume that when there are multiple action instantiations for achieving a goal, that STRIPS first considers the action instantiation with the least number of currently unsatisfied preconditions. Finally, clearly show the final plan constructed and all the facts that are true in each state of the world after each action is executed.
b) Would STRIPS be able to solve this problem if the order of the goals
were reversed? Would it get an optimal solution, a suboptimal solution, or no
solution at all? Briefly explain exactly what would happen in this case.
|P(`atom' | m)||0.1||0.01||0.2|
|P(`carbon' | m)||0.005||0.03||0.05|
|P(`proton' | m)||0.05||0.001||0.05|
|P(`life' | m)||0.001||0.1||0.008|
|P(`earth' | m)||0.005||0.006||0.003|
|P(`force' | m)||0.05||0.005||0.008|
Assuming the probability of each evidence word is independent given the
category of the text, compute the posterior probability for each
of the possible categories for each of the following short texts. Assume
the categories are disjoint and complete for this application. Assume
that words are first stemmed to reduce them to their base form (atoms ->
atom; forces -> force, protons -> proton). Simply ignore any word stems
that are not in the table above.
a) The carbon atom is the foundation of life on earth.
b) The carbon atom contains 12 protons.
c) String theory attempts to unify all of the forces on earth.