1. 1 Search vs. planning Situation calculus STRIPS operators Search vs. planning Situation calculus STRIPS operators

2. 2 Search in problem solving Problem solution: A path through the state space tree State space search: Search is a traversal of the tree until the goals is reached. State transitions is performed by operators a b c abcabc

3. 3 Search in problem solving Standard search algorithms seems to fail since the goal test is inadequate. Difficulty using standard search algorithms What is “finish”?

4. 4 Search in problem solving Consider the same task get milk, bananas, and a cordless drill A planning problem is represented in situation calculus by logical sentences that describe the three main parts of a problem. Initial state: At(home, S 0 )   Have(Milk, S 0 )   Have(Banana, S 0 )   Have(Drill, S 0 ) Goal state:  s At(home, s)  Have(Milk, s)  Have(Bananas, s)  Have(Drill, s) Operators:  a, s Have(Milk, Result (a,s))  [ (a=Buy(Milk))  At(Supermarket, s)  (Have(Milk, s)  a  Drop(Milk) )] Plan : p = [Go(Supermarket), Buy(Milk), Buy(Bananas), Go(HWS), …] Planning problem in situation calculus

5. 5 Search in problem solving Representation of states PS: Direct assignment of a symbol to each state PL: Logic sentences Representation of goals PS: A goal state symbol PL: Sentences that describe objective Representation of actions PS: Operators that transform one state symbol into another PL: Addition/deletion of logic sentences describing world state Representation of plans PS: Path through state space PL: Ordered or partially-ordered sequence of actions. Problem solving vs. planning

6. 6 Search in problem solving Uniform language for describing states, goals, actions, and their effects. Ability to add actions to a plan whenever they are needed, not just in an incremental sequence from some initial state. Ability to capture the fact that most parts of the world are independent of most other parts. It performs better for complex worlds over standard search algorithm since searching space becomes huge when there are many initial states and operators in standard search algorithms. Advantages of Planning Systems

7. 7 The Situation Calculus A goal can be described by a wff:  x On(x, B) if we want to have a block on B Planning: finding a set of actions to achieve a goal wff. Situation Calculus (McCarthy, Hayes, 1969, Green 1969) – A Predicate Calculus formalization of states, actions, and their effects. – S o state in figure can be described by: On(B, A)  On(A, C)  On(A, Fl)  Clear(B) we reify the state and include them as arguments The atoms denotes relations over states. On(B, A, S 0 )  On(A, C, S 0 )  On(C, Fl, S 0 )  Clear(B, S 0 ) We can also have.  x, y, s On(x, y, s)   (y = Fl)   Clear(y, s)  s Clear(Fl, s) Wff - well formed formula

8. 8 Reify the actions: denote an action by a symbol –actions are functions move(B,A,Fl): move block B from block A to Fl move (x,y,z) - action schema do: A function constant, do denotes a function that maps actions and states into states Express the effects of actions. –Example: (on, move) (expresses the effect of move on On) –positive effect axiom: action state Representing actions

9. 9 Effect axioms for (clear, move) figure 21 precondition are satisfied with B/x, A/y, S 0 /s, F 1 /z what was true in S 0 remains true move(x, y, z) matching?

10. STRIPS: describing goals and state STRIPS: STanford Research Institute Planning System Basic approach in GPS (general Problem Solver): Find a “difference” (Something in G that is not provable in S 0 ) Find a relevant operator f for reducing the difference Achieve precondition of f; apply f; from resultant state, achieve G.

11. STRIPS planning STRIPS uses logical formulas to represent the states S 0, G, P, etc: Description of operator f:

12. On(B,A) On(A,C) On(C,F1) Clear(B) Clear(Fl) The formula describes a set of world states Planning search for a formula satisfying a goal description On(A, C) On(C, Fl) On(B, Fl) Clear(A) Clear(B) A STRIPS planning example

13. A STRIPS operator has 3 parts: –A set, PC - preconditions –A set D - the delete list –A set A - the add list Usually described by Schema: Move(x,y,z) –PC: On(x,y) and On(Clear(x) and Clear(z) –D: Clear(z), On(x,y) –A: On(x,z), Clear(y), Clear(F1) A state S 1 is created applying operator O by adding A and deleting D from S 1. STRIPS Description of Operators

14. Example: The move operator

15. Example1: The move operator S0S0 G P: On(x,y) Clear(x) Clear(z) f: move(x,y, z) add: On(x,z), Clear(y) del: On(x,y), Clear(z)    x/B, y/A, z/Fl f(P) : On(x,z) Clear(x) Clear(y) S 0 ->P x/B, y/A, z/Fl f(P)->G   

16. Example1: The move operator S0S0 G P: On(x,y) Clear(x) Clear(z) f: move(x,y, z) add: On(x,z), Clear(y) del: On(x,y), Clear(z)    x/B, y/A, z/Fl f(P) : On(x,z) Clear(x) Clear(y) S 0 ->P x/B, y/A, z/Fl f(P)->G    Clear(F2) + ABCABC

17. S 0 ->G 0 S 0 ->G 1 pre: On(B, A) Clear(B) Clear(Fl) G 1 ->S 1 Move(B, A Fl) S 1 ->G 0 S 0 : On(B,A) On(A,C) On(C,F1) Clear(B) Clear(Fl) G 0 : On(A, C) On(C, Fl) On(B, Fl) Clear(A) Clear(B) Tree representation