Chapter 6 Building Control Algorithms For State Space Search

1. Chapter 6 Building Control Algorithms For State Space Search Contents • Recursion-Based Search • Production Systems • The Blackboard Architecture for Problem Solving Artificial Intelligence

2. Recursive Search • Recursive search • A recursive step: procedure calls itself • A terminating condition • Depth-first recursive search algorithm Artificial Intelligence

3. Recursive Search with Global Variables Global variables : open and closed Artificial Intelligence

4. Pattern-Driven Reasoning • Problem: • Given a set of assertions (predicate expressions) • Determine whether a given goal is a logical consequence of the given set of assertions • Solution • Use unification to select the implications (rules) whose conclusions match the goal • Unify the goal with the conclusion of the rule • Apply the substitutions throughout the rule • Transform the rule premise into a new subgoal • If the subgoal matches a fact, terminate • Otherwise recur on the subgoal • Recursive algorithm – next page Artificial Intelligence

5. Pattern-driven Reasoning Artificial Intelligence

6. Some Issues • The order of assertions • Logical connectives in the rule premises • Logical negation Artificial Intelligence

7. Artificial Intelligence

8. Artificial Intelligence

9. A production system. Control loops until working memory pattern no longer matches the conditions of any productions. Artificial Intelligence

10. Trace of a simple production system. Artificial Intelligence

11. The 8-puzzle as a production system Artificial Intelligence

12. The 8-puzzle searched by a production system with loop detection and depth-bound. Artificial Intelligence

13. The Knight’s Tour Problem • Problem: find a series of legal moves in which the knight lands on each square of the chessboard exactly once • Legal moves of a chess knight. Artificial Intelligence

14. A 3 x 3 chessboard with move rules for the simplified knight tour problem. Artificial Intelligence

15. Production rules for the 3 x 3 knight problem. Artificial Intelligence

16. A production system solution to the 3 x 3 knight’s tour problem. Artificial Intelligence

17. Control Algorithms • The general recursive path definition X path(X,X) X,Y[path(X,Y)  Z[move(X,Z)  path(Z,Y)]] • The revised path definition to avoid infinite loop X path(X,X) X,Y[path(X,Y)  Z[move(X,Z)  (been(Z))  assert(been(Z))  path(Z,Y)]] Artificial Intelligence

18. The recursive path algorithm as production system. Artificial Intelligence

19. A Production System in Prolog • Farmer, wolf, goat, and cabbage problem • A farmer with his wolf, goat, and cabbage come to the edge of a river they wish to cross. There is a boat at the river’s edge, but, of course, only the farmer can row. The boat also can carry only two things, including the rower, at a time. If the wolf is ever left alone with the goat, the wolf will eat the goat; similarly if the goat is left alone with the cabbage, the goat will eat the cabbage. Devise a sequence of crossings of the river so that all four characters arrives safely on the other side of the river. • Representation • state(F, W, G, C) describes the location of Farmer, Wolf, Goat, and Cabbage • Possible locations are e for east, w for west, bank • Initial state is state(w, w, w, w) • Goal state is state(e, e, e, e) • Predicates opp(X, Y) indicates that X and y are opposite sides of the river • Facts: opp(e, w). opp( w, e). Artificial Intelligence

20. Sample crossings for the farmer, wolf, goat, and cabbage problem. Artificial Intelligence

21. Portion of the state space graph of the farmer, wolf, goat, and cabbage problem, including unsafe states. Artificial Intelligence

22. Production Rules in Prolog • Unsafe states unsafe(state(X, Y, Y, C)) :- opp(X, Y). unsafe(state(X, W, Y, Y)) :- opp(X, Y). • Move rules move(state(X, X, G, C), state(Y, Y, G, C))) :- opp(X, Y), not(unsafe(state(Y, Y, G, C))), writelist([‘farms takes wolf’, Y, Y, G, C]). move(state(X, W, X, C), state(Y, W, Y, C)) :- opp(X, Y), not(unsafe(state(Y, W, Y, C))), writelist([‘farmers takes goat’, Y, W, Y,C]). move(state(X, W, G, X), state(Y, W, G, Y)) :- opp(X, Y), not(unsafe(state(Y, W, G, Y))), writelist(‘farmer takes cabbage’, Y, W, G, Y]). move(state(X, W, G, C), state(Y, W, G, C)) :-opp(X, Y), not(unsafe(state(Y, W, G, C))), writelist([‘farmer takes self’, Y, W, G, C]). move(state(F, W, G, C), state(F, W, G, C)) :- writelist([‘Backtrack from ‘, F, W, G, C]), fail. • Path rules Path(Goal, Goal, Stack) :- write(‘Solution Path Is: ‘), nl, reverse_print_stack(Stack). Path(State, Goal, Stack) :- move(State, Next), not(member_stack(Next, Stack)), stack(Next, Stack, NewStack), path(Next, Goal, NewStack), !. • Start rule Go(Start, Goal) :- empty_stack(EmptyStack), stack(Start, EmptyStack, Stack), path(Start, Goal, Stack). • Question ?- go(state(w, w, w, w), state(e, e, e, e) Artificial Intelligence

23. Data-driven search in a production system. Artificial Intelligence

24. Goal-driven search in a production system. Artificial Intelligence

25. Bidirectional search missing in both directions, resulting in excessive search. Artificial Intelligence

26. Bidirectional search meeting in the middle, eliminating much of the space examined by unidirectional search. Artificial Intelligence

27. Major advantages of production systems for artificial intelligence • Separation of Knowledge and Control • A Natural Mapping onto State Space Search • Modularity of Production Rules • Pattern-Directed Control • Opportunities for Heuristic Control of Search • Tracing and Explanation • Language Independence • A Plausible Model of Human Problem-Solving Artificial Intelligence

28. Blackboard architecture • Extend production systems • Separate productions into modules • Each module is an agent -- knowledge source • A single global structure -- blackboard Artificial Intelligence