lecture12

# lecture12 - Articial Intelligence Planning as Satisability...

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Planning as Satisfiability; page 1 of 20 Artificial Intelligence Planning as Satisfiability Pushing the Envelope: Kautz and Selman Planning, Propositional Logic, and Stochastic Search Russell and Norvig: Chapters 5, 11 we follow the following paper http://www.cs.cornell.edu/home/selman/papers-ftp/plan.ps

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Planning as Satisfiability; page 2 of 20 AIPS-98 Planning Competition Round Round 1 Round 2 Planner BLACKBOX HSP IPP STAN BLACKBOX HSP IPP STAN Av. Time 1.49 35.48 7.40 55.41 2.46 25.87 17.37 1.33 Solved 63 82 63 64 8 9 11 7 Shortest 55 61 49 47 6 5 8 4
Planning as Satisfiability; page 3 of 20 first-order logic (= situation calculus) initial state At(Home, s0) goal state (= query) EXISTS s AND Have(Drill, s) operators FORALL a, s a = Buy(Milk) AND At(Supermarket, s) Have(Milk, s) AND NOT a = Drop(Milk) AND NOT Have(Drill, s0) AND NOT Have(Milk, s0) AND NOT Have(Bananas, s0) At(Home, s) AND Have(Milk, s) AND Have(Bananas, s) Have(Milk, Result(a,s)) EQUIV OR

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Planning as Satisfiability; page 4 of 20 problems with first-order logic - inefficient - does not necessarily generate a GOOD plan
Planning as Satisfiability; page 5 of 20 initial state goal state propositional logic - initial and final situation At(Home,s0) NOT At(SM,s0) NOT At(HWS,s0) NOT Have(Drill,s0) NOT Have(Milk,s0) NOT Have(Bananas,s0) At(Home,s9) Have(Drill,s9) Have(Milk,s9) Have(Bananas,s9) notice: these are not really predicates they are variables (for example, At(home,s0) could be replaced with x) we use knowledge to eliminate variables such as Sells(SM, Milk) from the encoding

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Planning as Satisfiability; page 6 of 20 propositional logic - operators (1) different encodings are possible - graphplan-based encodings - linear encodings - state-based encodings here:
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