[Solved]: How to solve this Planning Domain Definition Language (PDDL) question?

Problem Detail: 

These are 5 action descriptions with conditional effects:

Action(A, Precond:{X}, Effect:{when P : ~X), Z})

Action(B, Precond:{Y}, Effect:{when Z : ~P), ~Y,~Z,X})

Action(C, Precond:{~Z}, Effect:{when P : ~X), Y})

Action(D, Precond:{~X}, Effect:{when Q : X)})

Action(E, Precond:{Z}, Effect:{when Q : ~Z)})

What state would result from executing the action sequence [E,D,A,B,C] in the state {P,Q,Y,Z}?

I know the answer but I really don't know how to achieve it. Anyone please shed some light? (Please include workings)

Asked By : compski

Answered By : Pål GD

I will turn my comment into an answer. Recall that if your state is $\{P,Q,Y,Z\}$, and an effect of an action is $\sim\!Z$ (from now on written $\neg Z$), then the new state will not contain $Z$, i.e., the state will be, if nothing else is an effect, $\{P,Q,Y\}$.

Since the question asks what the result of a sequence of actions will be, we need to solve this in the order of that sequence. The sequence asked was $[E,D,A,B,C]$, and the state was $\{P,Q,Y,Z\}$? Observe that we by square brackets denote a sequence (i.e., an ordered list) and by curly brackets, an unordered set (the usual kind).

Action $E$ in state $\{P,Q,Y,Z\}$: Precondition $Z$ is good since $Z$ is in the state. Effect is "when $Q$, $\neg Z$". The new state will thus be $\{P,Q,Y\}$. We omit writing $\neg Z$ since every element not occurring in the state will be assumed to be not held.

Action $D$ in state $\{P,Q,Y\}$: Precondition $\neg X$ is good. Effect: "when $Q$, $X$". Hence new state will be $\{P,Q,X,Y\}$.

Action $A$ in state $\{P,Q,X,Y\}$: Precondition is good, $X$ is in the state. Effect: "when $P$, $\neg X$, and $Z$". $P$ is in the state, hence we remove $X$ and we also add $Z$. New state is $\{P,Q,Y,Z\}$.

Action $B$ in state $\{P,Q,Y,Z\}$: Precondition $Y$ is good. Effect "when $Z$, $\neg P$, also $\neg Y$, $\neg Z$ and $X$". $Z$ is true, hence we lose $P$. We also lose $Y$ and $Z$ and gain $X$. New state is $\{Q,X\}$.

Action $C$ in state $\{Q,X\}$: Precondition is $\neg Z$, so good. Effect: "when $P$, $\neg X$, and $Y$". This is the first time we encounter an implication in which the antecedent $P$ is false, so we don't remove $X$. We still add $Y$, though. Hence the new, and final state is $$ \{Q,X,Y\}. $$

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Question Source : http://cs.stackexchange.com/questions/13257