Lecture_08_Reasoning & Problem Solving

Question 1

Formal Rules of Logic

Answer 1

1. Deductive reasoning
2. Inductive reasoning
3. Conditional reasoning

Question 1

Reasoning

Answer 1

Drawing conclusions by putting statements (premises) together using logic
1) to make sense of our present experiences and ideas, and to plan for the future
2) to establish and verify facts

Question 2

Premise

Answer 2

Statement of fact that is assumed to be true

Question 3

Deductive Reasoning

Answer 3

• Top-down reasoning”
• If the premises are true, the conclusion must also be true.
• Premise 1: All cognitive processes involve brain activities.
• Premise 2: Memory is a cognitive process.
• Conclusion: Memory involves brain activities.

Question 4

The Problem of Deductive Reasoning

Answer 4

• What’s important is the form of the argument
• The truth of the premise in the real world & your prior knowledge are irrelevant!
• Premise 1: All birds have wings.
• Premise 2: Unicorns are birds. (?)
• Conclusion: Unicorns have wings.

Question 5

Inductive Reasoning

Answer 5

Bottom-up reasoning
- If the premises are true, the conclusion is also LIKELY to be true.
- Premise 1: Restaurant A has many delicious dishes.
- Premise 2: You order an omelet.
- Conclusion: The omelet is delicious.

Question 6

The Problem of Inductive Reasoning

Answer 6

The conclusion is likely, but it’s NOT guaranteed to be true.
- Based on probability.
- 80% of brain surgeons are men.
- Lee is a brain surgeon.
- Lee is a man.

Question 7

Conditional Reasoning

Answer 7

If P-then Q
- Deductive reasoning that involves conditional statements
- Premise 1: If P, then Q
- Premise 2: A statement about whether P or Q is true or not true
- Conclusion: A statement about whether P or Q is true or not true

Question 8

2 Valid Forms of Conditional Reasoning

Answer 8

1. Affirming the antecedent (modus ponens)
2. Denying the consequence (modus tollens)

Question 9

Premise 1: If P, then Q
Premise 2: P
Conclusion: Q

Answer 9

• Valid
• Affirming the antecedent
• Modus ponens

Question 10

Premise 1: If P, then Q
Premise 2: Q
Conclusion: P

Answer 10

• Invalid
• Affirming the consequence

Question 11

Premise 1: If P, then Q
Premise 2: ~P
Conclusion: ~Q

Answer 11

• Invalid
• Denying the antecedent

Question 12

Premise 1: If P, then Q
Premise 2: ~Q
Conclusion: ~P

Answer 12

• Valid
• Denying the consequence
• Modus tollens

Question 13

Wason’s Card Selection Task

Answer 13

• 4 cards
• Each card has two sides: a letter and a digit.
• Rule: If a vowel is on one side, there is an even number on the other side
• Try to confirm this rule by turning over the fewest number of cards

Question 14

Why do participants make mistake in Wason’s Card Selection task?

Answer 14

People make mistakes by seeking verification rather than falsification

Question 15

Logical Fallacies

Answer 15

1. Begging the question
2. After this, therefore because of this
3. Ad hominem
4. Slippery slope

Question 16

Begging the question

Answer 16

Assuming the truth of the conclusion, rather than supporting it
- E.g. Humans help each other because of their kindness

Question 17

After this, therefore because of this

Answer 17

Correlation isn’t causation
- X occurred, then Y occurred
- Therefore, X caused Y
- E.g. Nearly all heroin addicts used marijuana before they tried heroin. Clearly, marijuana use leads to heroin
addiction

Question 18

Ad Hominem

Answer 18

Criticizing an individual who makes an argument
- E.g. Freud used cocaine. Therefore, we should not bother reading his books

Question 19

Slippery Slope

Answer 19

Because after stating A and B condition, there aren’t condition of C, D, E, or more
- Series of incremental inferences to arrive at undesirable conclusion
- E.g. If we allow gay marriage, the next thing we know, people will want to marry their dogs, or their cats, or what about their pigs?

Question 20

Mental Models of Reasoning

Answer 20

People create, combine, and evaluate specific possibilities
- Premises are stored in a concrete, meaning-based format, rather than in an abstract logical way
- Premise 1: All birds are animals
- Premise 2: Some animals are large
- Conclusion: Some birds are large
- Invalid

Question 21

Why do people make reasoning errors according to mental models?

Answer 21

People did not consider enough possibilities (mental) models
- Limited by working memory
capacity

Question 22

Bayesian (Probability) Models of Reasoning

Answer 22

• People make judgments based on probabilities, rather than engaging in pure deductive reasoning
• When people answer incorrectly on reasoning tasks, it’s because they treat them as probability tasks

Question 23

Inference Based on Probability

Answer 23

• Premise 1: There’s a high probability that a dog has fur
• Premise 2: Some don’t, but it’s a pretty good guess
• Conclusion: Therefore, Rover has fur
• When you hear “Rover is a dog”, you assume that Rover has fur.

Question 24

Dual-Process Models of Reasoning

Answer 24

1. System 1 – Fast cognition, associative process, outside consciousness
   - Pragmatic reasoning
   - Prone to errors
2. System 2 – Slow cognition, rule based and logical
   - Allows us to try to apply rules of logic!
   - But, limited by working memory

Question 25

Why do people make errors in problem solving tasks according to the dual-process model?

Answer 25

They’re relying on System 1 instead of System 2”
- Because it’s easier, faster, and requires less cognitive resources

Question 26

Problem Solving

Answer 26

Problem = any situation in which a person has a goal that is not yet achieved

Question 27

Well-Defined Problems

Answer 27

Clearly defined goal state and constraints

Question 28

Ill-Defined Problems

Answer 28

• Unclear goal state and constraints
• Difficult to create mental representations and identify a solution

Question 29

Information Processing Approach

Answer 29

Problem-solving = “searching” through a space consisting of all possible states of the problem

Question 30

Information Processing of Problem-solving

Answer 30

1. Create a PROBLEM SPACE to represent the problem. Include the initial state, goal state, instructions, constraints, and relevant info from long-term memory.
2. Select OPERATORS – actions that will transform the initial state.
3. Implement the operators – results in a new current state within the problem space.
4. Evaluate the current state – if it corresponds to the goal, a solution is reached

Question 31

General Problem Solver (GPS)

Answer 31

Computer program based on information processing framework
- Remarkable similarity between GPS algorithm & what human participants report out loud while solving a problem

Question 32

How to select operators to solve a problem?

Answer 32

Algorithmic Vs. Heuristic Strategies

Question 33

Algorithms

Answer 33

Methods that are guaranteed to lead to the solution, if followed correctly
- E.g., mathematical rules ( 998 / 21 = ? )
- But sometimes can’t use them, due to memory constraints or other processing limitations

Question 34

Heuristics

Answer 34

Methods or strategies that often lead to the solution
- But, not guaranteed to always succeed!

Question 35

Means-End Analysis

Answer 35

1. Compare the CURRENT STATE with the GOAL STATE.
   2.If there are differences, solve the LARGEST DIFFERENCE.
2. Select an OPERATOR that will solve the difference.
3. Apply the operator. If it cannot be applied, set a new goal (i.e.,
   a SUB-GOAL) to reach a state that will allow the application of
   the operator.
4. Solve this sub-goal by REPEATING 1-4

Question 36

Analogy

Answer 36

PRIOR EXPERIENCES and BACKGROUND KNOWLEDGE can be helpful
- Classify and understand the problem
- Automatize some problem-solving steps
- Draw analogy from past experiences
1) Surface similarity
2) Structural similarity

Question 37

Insight

Answer 37

the solver feels like they suddenly arrive at the solution (“Aha!”)
- Usually requires looking at the problem in a different way from the usual way

Question 38

Incubation Effect

Answer 38

Insight can occur even when you’re not consciously thinking about the problem

Question 39

What blocks insight?

Answer 39

• Self-imposed constraints
• Functional fixedness