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Flashcards in Problem solving Deck (42):
1

What does the Problem Space theory claim?

We analyse problems in terms of search strategies

2

What are search strategies?

Strategies that involve searching within an abstract problem space

3

A problem is made up of 3 elements. What are they?

1. A starting state (where you are)
2. A goal state (where you want to be)
3. A set of processes (operators) that transform one state into another

4

If all 3 elements of a problem can be identified, what type of problem is this?

A well-defined problem

5

What types of problems can you get?

1. Well-defined vs. ill-defined
2. Knowledge-rich vs. knowledge-lean
3. Adversary vs. non-adversary

6

What is a well-defined problem?

The start state, goal state & operators in the problem are identifiable

7

What is a knowledge-rich problem?

The problem requires specific knowledge/skills to solve it

You must access info from LTM/production memory to solve it

The start state, goal state & operators are identifiable

8

What is a knowledge-lean problem?

The problem can be solved using instructions & general problem-solving skills

9

What is an adversary problem?

It matters what others do - someone is trying to stop you reaching the goal state

You must overcome the opposition to reach the goal state

Each step towards the goal state is the largest possible move towards the goal state from the current state space

10

What is a non-adversary problem?

It doesn't matter what others do - you aren't being stopped by anyone

11

Name 3 search strategies.

1. Depth-first
2. Breadth-first
3. Best-first

12

What does the depth-first search strategy involve?

Going through all alternatives to a move before considering another move

13

What does the breadth-first search strategy involve?

Working out which move will most likely put you where you want to be
Can use cost analysis (how much it is costing you to do these things & how much you will get back)

14

What are the problems with using unguided search strategies?

X the n-tile puzzle is hard to solve by exhaustive search

X intelligence problem-solving requires SOME form of guided search
- AI researchers have suggested several forms, but some aren’t compatible with human cognition (e.g. best-first search; require too much memory/too-fast computation)

15

Why is the n-tile puzzle hard to solve by exhaustive search?

The problem space increases with the number of tiles

n=6x5x4x3x2x1 = 720 possible states for 6-tile puzzle
n=9x8x720 = 51,840 possible states for 9-tile puzzle

16

Why is the n-tile puzzle a 'limited state space'?

There is a limited number of states that the puzzle can be in

17

What is difference reduction & what does it involve?

It is a difference of local maxima

You must move away from the goal state to solve the problem

18

A chicken wants food (in another location) & they must reduce the difference between their current state & the goal state (food)

There is a barrier to the food (a fence) – the chicken pecks it

Who studied chickens in this study?
Why does this problem violate difference reduction?

Kohler (1927)

By pecking the fence, the chicken is only applying difference reduction

The chicken must move away from the goal (food) to get around the barrier --> violates difference reduction

19

What scenarios can difference reduction be applied to?

1. If you are following difference reduction, you climb up the hill & reach the peak (= the goal), & then descend

2. If you are following difference reduction, you climb up the hill & reach a peak but not the highest one --> you must go down the hill to go up again to reach the highest peak - this violates difference reduction

20

What does the Orc problem involve?

There are 3 orcs & 3 hobbits on one side of a river bank
A boat can only take 2 creatures at a time across the bank (one must steer the boat)
Goal = get all 6 creatures to the other side of the bank

Orcs must not outnumber hobbits on either side of the bank

21

How do you solve the Orc problem? Why do pps tend to make mistakes?

To solve the problem, you must move away from the other side of the bank (= the goal) to pick up more creatures --> this is a backwards step
This is where pps make a mistake - they keep wanting to do difference reduction but it doesn't solve the puzzle

22

What does the 9-dot problem involve?

You must connect 9 dots using 4 straight lines, without taking your pen off the paper

23

Why do people have difficulties with the 9-dot problem?

The dots form a square - has boundaries, so people automatically add rules...
"I have to connect dots without taking my pen off the paper AND I must do it without going outside the confines of the square"

24

Difficulty to do the 9-dot problem is called...

...maximisation - you are trying to maximise what you get our of your limited number of moves

25

What are the pps doing wrong in the 9-dot problem?

There is a problem with how they are searching the space (applying a difference reduction principle)

They have a problem with insight

26

What problem/difficulty does means-end analysis overcome?

The problem of difference reduction

27

How was means-end analysis introduced?

It was introduced as an AI procedure

Used as a description of human problem-solving alongside the formalisation of Operators as Production/Condition-Action/If-Then rules/Production System

28

Means-end analysis suggests a way of thinking about operators as...

...production rules

29

What is the process of means-end analysis?

1. Set up a goal/sub-goal
2. Look for a difference between your current state & the goal/sub-state (if there is no difference → success)
3. Look for an operator that will reduce this difference
4. Apply the operator
5. Check your new current state → apply 2-4 until the goal is reached

30

What is the difference between means-end & difference reduction?

The means can (temporarily) become the end

31

Anderson et al. (1993) found that it takes pps on average ___ seconds to make the first move in the Tower of Hanoi task (move disc A from disc B).

Anderson et al. (1993) found that it takes pps on average 8.95 seconds to make the first move in the Tower of Hanoi task (move disc A from disc B).

32

Anderson et al. (1993) found that it takes pps on average ___ seconds to make the second move in the Tower of Hanoi task (move disc B from disc C).

Anderson et al. (1993) found that it takes pps on average 2.46 seconds to make the second move in the Tower of Hanoi task (move disc B from disc C).

33

Why do patients with frontal lobe damage have difficulty on the ToH task?

Have difficulty with problems that involve planning or holding multiple sub-goals in memory

34

What type of resources does sub-goaling require?

Memory resources (to hold the goals & sub-goals)

35

Variants of ToH can be devised that require more/less sub-goals to be held in memory to solve the problem.

Who found that patients with frontal lobe damage had particular difficulty with multi-sub-goal versions?

Goel & Grafman (1995)

36

What type of effect does the water jugs problem show?
What is this effect?

The water jugs problem shows the einstellung effect - this is when you solve a problem in a certain way, even thought more appropriate methods exist

37

What does the water jugs problem involve?

Pps are told that 3 jugs contain 14, 50 & 11 litres of water - the goal is to end up with 33 litres in each jug

38

What did Luchins' (1942) water jugs problem study involve?

Experimental group: given 5 problems that were solvable using a certain method

Control group: given 5 problems that were solvable using many methods

Both groups were given 5 'impossible' problems solvable using Y=A-C

39

What did Luchins (1942) find in his water jugs problem study?

The control group solved all 5 problems using a direct method

In the experimental group, 55% of the problems were solved using a direct method, 40% were solved using a long method & 5% weren't solved at all

40

What did Luchins (1942) conclude from his water jugs problem study?

People learn a way of doing things & keep applying that method, even if it is longer & harder than other methods

41

What did Luchins (1942) name this phenomenon?

The mechanisation of thought

42

4 pps in Luchins' (1942) study had GCSE maths A* - which method did they use?

All used the long method

2 pps failed to solve the 'impossible' problems & reverted to a tedious solution
2 pps worked out a direct solution for the 'impossible' problems & thereafter used it