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

3.2. A representation for planning under uncertainty 27cannot both be true at the same time. However since any state that is reachableby a sequence of actions in the domain from a valid initial state will also be valid,these invalid states are not an issue in practice. This state property ofvalidity couldbe partially derived by considering the states reachable by applying actions to anyphysically possible initial state, or it could be enforced by adding domain axioms suchas those used in [Knoblock 1991]. In what follows I will ignore this distinction.In Weaver the planning domain is generalised as follows.1. The operators in the domain include a duration which isaninteger-valued functionof the bindings of the operator (and therefore a integer for an instantiatedaction or step). This integer may represent any time unit, for example secondsor hours, although the unit must be the same for dierent operators in the samedomain.2. Operators may specify a discrete, conditional probability distribution of possibleoutcomes rather than the single possible outcome used in prodigy 4.0. Anexample of this will be described in more detail below.3. A planning domain includes a set of exogenous events E as well as the set ofoperators O. These are syntactically very similar to operators but are used tospecify the way that the world can change independently of the actions taken ina plan, as I describe below. For example, they can be used to model the actionsof other agents or natural processes.4. A total precedence order < is given over the actions and events. This is used toresolve conicts between their eects if more than one action or event produceschanges to a state. An example is given below.Weaver generalises prodigy 4.0's denition of a planning problem by specifyinga probability distribution of possible initial states rather than a single initial state.The problem also includes a threshold probability, , a minimum probability of successthat a plan must equal or exceed to be considered a solution. The objects and goalstatement in the planning problem are unchanged.In the rest of this section I make the semantics of planning domains and problemsin Weaver precise in terms of an underlying Markov decision process M dened bya planning problem. While this denition is needed to prove that Weaver correctlycomputes probabilities for plans and to discuss its coverage, on a casual reading of thethesis it can be skipped and replaced with the following summary: at each time step,several events may take place simultaneously with one action as a plan is executed.When more than one event or action complete in one time step, their results areapplied to the state in parallel. If more than one possible value is specied for someground literal in the state, the value nominated by the event or action that is highestin the pre-specied precedence order is used. Actions are usually higher than eventsin the precedence order.