Download Human Problem Solving

Building Control Algorithms
for
State Space Search.
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
“If we carefully factor out the influences of the task
environment from the influences of the underlying hardware
components and organization, we reveal the true simplicity of
the adaptive system. For, as we have seen, we need postulate
only a very simple information processing system in order to
account for human problem solving in such tasks as chess,
logic, and cryptarithmetic. The apparently complex behavior
of the information processing system in a given environment
is produced by the interaction of the demands of the
environment with a few basic parameters of the system,
particularly characteristics of its memories.”
Newell and Simon, Human Problem Solving (1972)
Depth-First Search via Recursion
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
A production system. Control loops until working memory
pattern no longer matches the conditions of any productions.
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
Trace of a simple production system.
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
The 8-puzzle as a production system.
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
The 8-puzzle searched by a production system with
loop detection and depth-bound , from Nilsson (1971).
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
Legal moves of a chess knight.
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
A 3 x 3 chessboard with move rules for the simplified knight tour problem.
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
Production rules for the 3 x 3 knight problem.
Production system...
(X)path(X,X)
terminating condition
(X,Y)[path(X,Y)  (Z)[move(X,Z)  path(Z,Y)]]
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
A production system solution to the 3 x 3 knight’s tour problem.
Control algorithm:
(X)path(X,X) (terminating condition)
(X,Y)[path(X,Y)  (Z)[move(X,Z)  path(Z,Y)]]
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
The recursive path algorithm
as a production system.
(X)path(X,X)
(X,Y)[path(X,Y)  (Z)[move(X,Z)  path(Z,Y)]]
Or, to prevent looping:
(X)path(X,X)
(X,Y)[path(X,Y)  (Z) [move(X,Z)  ((been(Z)  assert(been(Z))  path(Z,Y)]]
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
Data-driven search in a production system.
(match conditions…)
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
Goal-driven search in a production system.
(match actions…)
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
Bidirectional search missing in both directions, resulting in excessive search.
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
Bidirectional search meeting in the middle, eliminating
much of the space examined by unidirectional search.
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
Control of Search
Through Rule Structure
Consider the following:
abc  abc
Now let
a=the engine turns over
b=the lights come on
c=check the battery
and consider the difference (e.g., the first suggests a
particular sequence of action).
Consider alternative forms of the same expression…
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
Control of Search
Through Conflict Resolution
• Refraction
– After a rule has fired, do not let it fire again
until the working memory elements matching
its conditions have been modified. Helps
avoid looping.
• Recency
– Select rules with conditions matching patterns
most recently added to working memory.
Focuses search on a single line of reasoning.
• Specificity
– Use a more specific problem-solving strategy
than a more general one. A rule is more
specific if it has more conditions.
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
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
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
Problems with Traditional
Production Systems
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Combinatorial explosion
Deductive (only) reasoning
Domain limited/context constrained
Inflexible rule processing
Inability to use full knowledge base
Grounding in perceptual reality
Brittleness
No meta-knowledge
Knowledge acquisition
Validation
Blackboard architecture
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
Recursive algorithm to search a
space of logical inferences for
some (predicate logic) fact .
Note: a “full-blown” version of this
algorithm must:
1. Deal with retrieval order of
alternative matches.
2. Handle binary connectives
(including making the proper
substitutions during unification).
3. Solve goals involving negation.
4. Return the bindings involved in
the solution.
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
Facts and rules:
l(a)
l(j)
m(j)
n(s)
q(t)
q(s)
q(j)
s(c)
v(b)
n(X) → r(X)
k(X) → u(X)
q(X)  v(X) → u(X)
s(Y)  t(X) → u(X)
l(Z)  m(Z) → p(Z)
p(X)  q(X)  r(Y) → t(Y)
Prove u(s)
Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005
Facts and rules:
l(a)
l(j)
m(j)
n(s)
q(t)
q(s)
q(j)
s(c)
v(b)
n(X) → r(X)
k(X) → u(X)
q(X)  v(X) → u(X)
s(Y)  t(X) → u(X)
l(Z)  m(Z) → p(Z)
p(X)  q(X)  r(Y) → t(Y)