Definition and Classification Of Problem Solving. well defined vs. ill defined- Routine vs. Non Routine -Adversary vs. Non adversary - Knowledge Rich vs. Knowledge Lean Problems.

1. Done by
Haseena Thasneem kk

2. “ A Problem exists when a
living organism has a goal
but does not know how
this goal is to be reached”
Karl Duncker,1945

3. ‘ Problem solving is an
active process where
the person accesses
stored knowledge and
manipulates
information in order to
achieve a solution ’

4.  Current approaches to
understanding problem solving
behavior use a common frame
work for describing problems.
 This framework is based on
Newell and Simon’s
(1972) View of problem
solving.
 Here problems are described in
terms of their problem space,
initial state, goal state, and
operators.

5.  The problem space is the problem
solver’s internal or mental representation of
the problem. it can include the initial,
current, and goal states as well as operators
that change the problem from one state to
another.
 The initial state described the problem as
it is presented to the problem solver at the
beginning.
For example: the initial state of a
cryptarithmetic problem would include a
series of letters arranged in a particular
sequence such as,
DONALD+
GERALD
ROBERT
And, perhaps some starting information (D=5)

6.  The goal state describes the solution or
final state of the problem.
in the case of this problem, goal is to
substitute a different single digit (from 0 to
9) for each of the ten distinct letters in the
problem so that the digits add up properly.
At the end the solution will show two rows of
five digit numbers that add together to form
another five digit number.
 the problem solver uses operators to move
from the initial state to the goal state.
Operators that modify Problem states.
in the case of the cryptarithmetic problem,
one class of operators involve substitution .
for instance, 5 would be substituted for D
and 0(zero) would be substituted for T. other
operators would be based on the problem
solvers knowledge of addition and
arithmetic.
As operators are applied , the problem state
changes.

7.  The Current state of a refers to the
intermediate state of a problem that is
currently being used by the problem
solver.
based on the operations discussed so
far, the current state of the
cryptarithmetic problem would be,
5ONALD
GERAL5
ROBER0
the application of operators will changes
the current state of the problem and this
procedure should eventually result in the
goal state being achieved.

9.  A Well-defined problem is one for
which the initial and goal states as well
as the operators and actions needed to
move from one state to another can be
specified.
 A correct answer exist for a well defined
problem.
An anagram is a good example of a
well –defined problem. the anagram
“CLEPOMX” Is the initial state. By
applying operators that rearrange the
letters, the goal state, a
word(COMPLEX), is achieved.
it is of three types:
 Problem of inducing Structure
 Problem of transformation
 Problem of arrangement.

10.  Problem of inducing
structure.
the classic example of it involves
the use of analogies. For example ,
Up is to Down as Black is to…….?
In problem solving notation,
this problem is represented as
up: down::black: ? The relationship
for the first pair is one of opposites.
Therefore, the correct response
to maintain that structure (and
relationship)is white, the opposite of
black.

11. Problem of transformation
it requires the problem solver to apply a
sequence of operations or moves that
will transform an initial state into the
goal.
Puzzles such as the Cryptarithmetic
problem described earlier are a good
example of problems of transformation.
 Problem of arrangement
such as the anagram problem involves
taking the elements of the problem and
rearranging them until some criterion is
achieved. the elements are not
transformed into another form but are
rearranged.

12.  An Ill- defined problem has
components of the problem space that
are not specified(either initial or goal
states or operators or some
combinations).
 There may also be no one “correct”
answer.
(Buying an automobile or renting an
apartment are two good examples of
ill- defined problem.
in both cases, the goal state, the car
purchased or apartment that is rented,
is not always known at the beginning
of the problem. while the person have
a ideal car or apartment in mind. often
the one purchased or rented is not the
ideal, but rather a compromise based
on a number of factors.)
Many of problems studied in laboratory
are Well- defined, many of problems
faced in life are ill defined.

13.  Routine problems
it involves application of operators in a
predictable, systematic manner known
to the problemsolver.Multi plying two
four-digit number is a routine problem.
the solver need only follow the rules for
multiplying the digits to arrive at the
solution.
• Non- routine problems
it requires the problem solver to apply
operators in a novel fashion or use a
procedure that is not well known to the
user. Most of the psychological research in
problem solving is based on no routine
problems. Our insight into the problem
solving process devoleps from studies
involving nonroutine applications to
problems.

14.  In an Adversary Problem ,
the problem involves competition
between two or more players. Chess is
one example of an Adversary problem
that has been studied extensively in
problem- solving research.
the opportunity for a competitor to
change the problem space and to counter
or alter changes made by the problem
solver can make the problem space much
more complex than in a nonadversary
problem.
 The problem solver does not face a
competitor in solving a nonadversary
problem. There has been considerable
research in some domains of adversary
problems, example: chess playing;
however the majority of problem solving
research has focused on nonadversary
problems.
The amount of control a researcher
can exert over the problem space is much
greater for nonadversary problems than
for adversary problems.

15.  There is a further important
distinction between knowledge-
rich and knowledge-lean
problems. Knowledge-rich
problems can only be solved by
individuals possessing a
considerable amount of specific
knowledge, whereas knowledge-
lean problems do not require the
possession of such knowledge. In
approximate terms, most
traditional research on problem
solving has involved the use of
knowledge-lean problems,
whereas research on expertise
(e.g., chess grandmasters) has
involved knowledge-rich
problems