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What does the Problem Space theory claim?

We analyse problems in terms of search strategies


What are search strategies?

Strategies that involve searching within an abstract problem space


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


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

A well-defined problem


What types of problems can you get?

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


What is a well-defined problem?

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


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


What is a knowledge-lean problem?

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


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


What is a non-adversary problem?

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


Name 3 search strategies.

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


What does the depth-first search strategy involve?

Going through all alternatives to a move before considering another move


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)


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)


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


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

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


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


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


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


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


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


What does the 9-dot problem involve?

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


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"


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


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


What problem/difficulty does means-end analysis overcome?

The problem of difference reduction


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


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

...production rules


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


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

The means can (temporarily) become the end