Planning under Uncertainty in Dynamic Domains - Carnegie Mellon ...

3.1. Overview of prodigy 4.0 21associated with each variable in the operator's preconditions. The object's type mustmatch the variable's type and the set of objects must agree with all the functionsused in the variable specications. The instantiated operator is applicable in a stateif the literal made from its preconditions statement is true in that state.If an instantiated operator is applied to a state, a new state is produced correspondingto the result of applying the operator in the original state. The new stateis specied as follows. First, the test corresponding to each conditional eect set isevaluated in the state. If it is true, the corresponding conditional eects are treatedas regular eects, otherwise they are discarded. Next the literals mentioned in eachadd or del statement are examined for variables, and any variables mentioned in thepreconditions slot are replaced with their object values from the instantiation of theoperator. If there are variables that are not mentioned in the preconditions slot, theyare treated as universally quantied. For each such variable, a variable specicationmust be given in the eects slot, mentioning a type and optionally some bindingsfunctions in the same way as in the preconditions slot. Each literal in the eects thatmentions one of these variables is replaced with a set of literals, corresponding toevery object in the planning problem that matches the variable specication. Afterthe literals in the eects are all translated into one or more literals that mentionno variables, the state transformation is made. First the literals mentioned in delstatements are made false in the state. Next the literals mentioned in add statementsare made true in the state. Any literal that is not mentioned in the eects of theinstantiated operator has the same truth value in the new state as in the old state.For example, suppose a planning problem uses a domain that includes the Move-Bargeoperator as shown, and includes the objects barge1 of type Barge and Richmond andOakland of type Place. If the initial state has the true literal (at barge1 Richmond),then the instantiated operator(Move-Barge =barge1 =Richmond =Oakland)will be applicable in the initial state. Applying it would lead to a new state, in which(at barge1 Richmond) would be false and (at barge1 Oakland) would be true,with all other literals unchanged.A plan in prodigy 4.0 is a totally-ordered sequence of instantiated operators(O 1 ;O 2 ;...O n ). The plan can be re-formulated in a partial order after creation ifdesired [Veloso 1992]. I will refer to an instantiated operator in a plan as a step inthe plan. A plan is a solution to the planning problem if:1. O 1 is applicable in the initial state and applying it leads to the state S 1 ,2. each step O i for 2 i n is applicable in the state S i,1 and applying it leadsto the state S i and3. the goal description is satised in state S n .For example, given the initial state above and the goal (at barge1 Oakland), theplan consisting of the single step (Move-Barge =barge1 =Richmond=Oakland) is a solution for this planning problem.