Applications of Planning

- Sceduling actions with Resources (metric-temporal planning)
- Autonomous Agents
- Software Integration (modules are operators)
- Decision Support 
- Interfaces (e.g. NLIA - Natural Language Interface to Appliances)
- Web Services

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Classical Planning
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Scaling up from explicit state models:
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1. Search Space: 
   - Forward, Regression -- Disjunctive Refinement 
     # In general, we handle sets of states
       * sets contain single states in deterministic planning
       * sets contain multiple states in non-deterministic planning
     # Need to look inside the black-box of a state
       * States can be expressed by propositional formulae 
       * The number of propositions in a problem is equal to D^M, 
         where D = arity of varible values and M = number of variables
     # The goal state is a set of states because it is incompletely
       specified in both non and deterministic planning.
     # The initial state is a set of states only in non-deterministic 
       planning.
   - Plan -- Conjunctive Refinement

2. Search Control
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3. Customization
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Domain Independent vs. Domain Specific
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Independent:
  - Input: 
    1. Initial State
    2. Goal State
    3. Action Set
  - Ouput: Plan
  - Includes planners that learn domain knowledge while planning on 
    single problems and across sets of problems

Specific:
  - Input:
    1-3 of Independent
    4. Domain knowledge (that is "taught" to the planner by a human)
  - Output: Plan
  
Customizable:
  - Hybrid of Independent and Specific
  - Can take domain knowledge, but doesn't require it


Modeling 
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 - Actions are cross-product relations between states
 - A planning agent knows it is in a subset of the state space
   * If the subset is more than one state then
     a. a policy in a deterministic domain is being found,
      or
     b. the domain is not fully observable 
        # e.g. 15 states in a deterministic domain could result in
	  2^15 belief states if there is no knowlege of the current state