Transcript Document

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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Recursive Search
Recursive search
– A recursive step: procedure calls itself
– A terminating condition
Depth-first recursive search algorithm
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Recursive Search with Global Variables
Global variables : open and closed
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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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Patterndriven
Reasoning
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Some Issues
The order of assertions
Logical connectives in the rule
premises
Logical negation
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A production system. Control loops until working
memory pattern no longer matches the conditions of any
productions.
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Trace of a simple production system.
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The 8-puzzle as a production system
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The 8-puzzle searched by a production system with loop
detection and depth-bound.
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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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A 3 x 3 chessboard with move rules for the simplified
knight tour problem.
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Production rules for the 3 x 3 knight problem.
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A production system solution to the 3 x 3 knight’s tour
problem.
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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)]]
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The recursive path algorithm as production system.
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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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Sample crossings for the farmer, wolf, goat, and cabbage
problem.
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Portion of the state space graph of the farmer, wolf,
goat, and cabbage problem, including unsafe states.
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Unsafe states
Production Rules in Prolog
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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Data-driven search in a production system.
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Goal-driven search in a production system.
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Bidirectional search missing in both directions, resulting in
excessive search.
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Bidirectional search meeting in the middle, eliminating
much of the space examined by unidirectional search.
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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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Blackboard architecture
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•
•
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Extend production systems
Separate productions into modules
Each module is an agent -- knowledge source
A single global structure -- blackboard
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