Problem Solving: Understanding Procedural Knowledge and Elements of Problem Solving, Slides of Brain and Cognitive Science

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Problem Solving

Procedural Knowledge

 Declarative knowledge – knowledge about facts and things

 Procedural knowledge – knowledge about how to perform various cognitive activities.

 To a cognitive psychologist all cognitive activities are fundamentally problem- solving in nature.  Sultan and the bananas

Elements of Problem Solving

 Goal directedness – behavior is

organized toward a goal.

 Subgoal decomposition – the original

goal can be broken into subtasks or subgoals.

 Operator application – the solution to the

overall problem is a sequence of known operators (actions to change the situation).

A Sample Problem

Steps in Solution (States)

Search

 Operator – an action that will transform the current problem state into another problem state.

 The problem space is a maze of states.

 Operators provide paths through the maze – ways of moving through states.

 Problem solving is a search for the appropriate path through the maze.  Search trees – describe possible paths.

Acquisition of Operators

 How do we learn ways of transforming

problem states (operators)?  Discovery – trial and error, exploration.  Instruction – depends on language.  Observation and imitation – monkey see, monkey do.

 Examples are chances for observation:

 13% solved with instruction, 28% with an example, 40% with both.

Analogy and Imitation

 Analogy – the solution for one problem is

mapped into a solution for another.  The elements from one situation correspond to the elements of the other.

 Tumor radiation example.

Imaging Studies of Analogy

Stimuli used by Cristoff. Only (c) involves analogical reasoning. Children under age 5, primates and patients with frontal lobe damage cannot do (c).

Production Systems

 Production rules – rules for solving a problem.

 A production rule consists of:

 Goal  Application tests  An action

 Typically written as if-then statements.

 Condition – the “if” part, goal and tests.  Action – the “then” part, actions to do.

Sample Production Rules

Operator Selection

 How do we know what action to take to

solve a problem?

 Three criteria for operator selection:

 Backup avoidance – don’t do anything that would undo the existing state.  Difference reduction – do whatever helps most to reduce the distance to the goal.  Means-end analysis – figure out what is needed to reach goal and make that a goal

Difference Reduction

 Select the operator that will produce a state that is closer to the goal state.  Or the one that produces a state that looks more similar to the goal state.

 Also called “hill climbing”.

 Only considers whether next step is an improvement, not overall plan.

 Sometimes the solution requires going against similarity – hobbits & orcs.

Means-End Analysis

 Newell & Simon – General Problem Solver (GPS).  A more sophisticated version of difference reduction.  What do you need, what have you got, how can you get what you need?  Focus is on enabling blocked operators, not abandoning them.  Larger goals broken into subgoals.

 GPS solution to Tower of Hanoi problem.