Search vs planning Situation calculus STRIPS operators 1

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

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

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

Planning Search problem in situation solving calculus Consider the same task get milk, bananas, and a cordless drill A planning problem is represented in situation calculus by logical sentences that describe 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), …] 4

Problem Search in solving problem vs. planning 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. 5

Advantages Search inofproblem Planning solving Systems • 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. 6

The Situation Calculus Wff - well formed formula l l 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 (Mc. Carthy, Hayes, 1969, Green 1969) – A Predicate Calculus formalization of states, actions, and their effects. – So state in figure can be described by: On(B, A) On(A, C) On(A, Fl) Clear(B) l 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) l We can also have. x, y, s On(x, y, s) (y = Fl) Clear(y, s) s Clear(Fl, s) 7

Representing actions l l 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 action l state Express the effects of actions. – Example: (on, move) (expresses the effect of move on On) – positive effect axiom: 8

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

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.

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

A STRIPS planning example l l l l On(B, A) On(A, C) On(C, F 1) 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)

STRIPS Description of Operators l l l 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(F 1) A state S 1 is created applying operator O by adding A and deleting D from S 1.

Example: The move operator

Example 1: The move operator S 0 ->P x/B, y/A, z/Fl P: Clear(x) Clear(z) f(P)->G x/B, y/A, z/Fl On(x, y) G f: move(x, y, z) add: On(x, z), Clear(y) del: On(x, y), Clear(z) On(x, z) f(P) : Clear(x) Clear(y)

Example 1: The move operator A B C + Clear(F 2) S 0 ->P x/B, y/A, z/Fl P: Clear(x) Clear(z) f(P)->G x/B, y/A, z/Fl On(x, y) G f: move(x, y, z) add: On(x, z), Clear(y) del: On(x, y), Clear(z) On(x, z) f(P) : Clear(x) Clear(y)

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