1. Building Control Algorithms For State Space Search
Chapter 6
Building Control Algorithms For State Space Search
Contents
Recursion-Based Search
Production Systems
The Blackboard Architecture for Problem Solving
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2. Artificial Intelligence
Recursive Search
Recursive search
A recursive step: procedure calls itself
A terminating condition
Depth-first recursive search algorithm
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3. Recursive Search with Global Variables
Global variables : open and closed
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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
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5. Artificial Intelligence
Pattern-driven Reasoning
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6. Artificial Intelligence
Some Issues
The order of assertions
Logical connectives in the rule premises
Logical negation
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7. Artificial Intelligence
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8. Artificial Intelligence
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9. Artificial Intelligence
A production system. Control loops until working memory pattern no longer matches the conditions of any productions.
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10. Artificial Intelligence
Trace of a simple production system.
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11. The 8-puzzle as a production system
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12. Artificial Intelligence
The 8-puzzle searched by a production system with loop detection and depth-bound.
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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.
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14. Artificial Intelligence
A 3 x 3 chessboard with move rules for the simplified knight tour problem.
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15. Artificial Intelligence
Production rules for the 3 x 3 knight problem.
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16. Artificial Intelligence
A production system solution to the 3 x 3 knight’s tour problem.
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17. Artificial Intelligence
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,Y[path(X,Y)  Z[move(X,Z)  (been(Z))  assert(been(Z))  path(Z,Y)]]
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18. Artificial Intelligence
The recursive path algorithm as production system.
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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).
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20. Artificial Intelligence
Sample crossings for the farmer, wolf, goat, and cabbage problem.
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21. Artificial Intelligence
Portion of the state space graph of the farmer, wolf, goat, and cabbage problem, including unsafe states.
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22. Artificial Intelligence
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)
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23. Artificial Intelligence
Data-driven search in a production system.
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24. Artificial Intelligence
Goal-driven search in a production system.
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25. Artificial Intelligence
Bidirectional search missing in both directions, resulting in excessive search.
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26. Artificial Intelligence
Bidirectional search meeting in the middle, eliminating much of the space examined by unidirectional search.
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27. Artificial Intelligence
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
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28. Extend production systems Separate productions into modules
Blackboard architecture
Extend production systems
Separate productions into modules
Each module is an agent -- knowledge source
A single global structure -- blackboard
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