1. Deductive Reasoning: Why People Are Not Always Logical
Pavle Valerjev
Department of psychology
University of Zadar

2. Thinking Psychology of thinking
Reasoning
Problem solving
Judgment and decision making
Undirected thinking (Gilhooly, 1996)
Cognitive approach: Thinking as a process of mental representation manipulation

3. Deductive reasoning - examples
Conditional reasoning
Modus ponens (MP)
If it rains, the streets are wet.
It rains.
Therefore, the streets are wet.
Logical form of MP:
P <implicates> Q P
Therefore, Q.
Syllogistic reasoning
Barbara (AAA) conclusion
All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.
Logical form:
Major premise: MaP
Minor premise: SaM
Conclusion: SaP

4. Deductive reasoning – more examples
Conditional reasoning
If it rains, the streets are wet.
The streets are wet.
Therefore, it rains.
WRONG
There is no valid conclusion.
Proof? Truth table.
Syllogistic reasoning
All males are animals.
Some animals are aggressive.
Therefore, some males are aggressive.
WRONG CONCLUSION AGAIN
There is no valid conclusion.
Proof? Euler circles. P Q
If P, then Q. 1

5. Non-deductive types of reasoning
Inductive reasoning
making generalizations
The proportion Q of the sample has attribute A.
Therefore, the proportion Q of the population has attribute A.
statistical reasoning
The proportion Q of the population has attribute A.
Therefore, there is a Q probability that member x of population has attribute A.
analogical reasoning
P and Q are similar in respect to properties a, b. Object P has been observed to have further property x.
Therefore, Q probably has property x also.

6. Reasoning process Task presentation
Mental representations of the situation expressed in task
Mental manipulation which generates the answer
Answer
Evaluation of the answer

7. Cognitive biases and perceptive illusions
Cognitive biases can be as useful for research on thinking as perceptual illusions are useful for understanding perception.
For example:
Representativeness heuristics
→ conjunction fallacy; gambler’s fallacy
Availability and simulation heuristics
→ hindsight bias

9. Wason selection task
Example: Rule: If there is a vowel on one side of the card, then there is an even number on the opposite side. Which cards would you turn over in order to test the rule?
P not-P Q not-Q

10. Wason selection task Original research:
Wason (1966) – 4% of valid answers (P and not-Q)
Some other evidence of the classic effect:
Valerjev & Pedisić (2001) – 4-8% valid (depending on condition); 47-49% typical error (P and Q)
Valerjev (2000) – 14% valid; 74% typical error (participants were instructed to choose TWO cards)
Valerjev & Dujmović (2016) – 4% valid; 58% typical error; and on average 85% confidence rating that they choose the right answer.

11. Confirmation bias and other biases
Evans (1989) – Biases in human reasoning
Confirmation bias – tendency to search, interpret and remember information that confirms someone’s preconceptions
Klayman & Ha (1987) – „positive test strategy”
Nickerson (1998) – looking for supportive evidence
Quick intuitive heuristic that is useful in realistic conditions

12. Other biases in reasoning
Matching bias and belief bias (Evans, 1989; 1998, 2007)
Belief bias:
Valerjev, Bajšanski & Gulan (2011)
Testing of belief bias and Type 1 vs Type 2 reasoning
Modus ponens tasks with (or without) content conflict
Content conflict conditional: If the child cries, then the child is happy.
Non-conflict conditional: If the child cries, then the child is sad.
2 different instructions:
To make conclusions according to one’s BELIEF
To make conclusions according to LOGICAL RULES

13. Bias in base-rate task Dujmović & Valerjev (2016)
Stereotypical base-rate task (De Neys, 2014; Pennycook, Fugelsand & Koehler, 2015)
Examples:
(Congruent stereotype and base rate)
Person A is organized. Person A is a member of this group.
The group consists of 874 accountants and 126 artists.
What is more probable? Person A is an accountant or an artist?
(Incongruent stereotype and base-rase)
Person B is physically strong. Person B is a member of this group.
The group consists of 860 teachers, and 140 boxers.
What is more probable? Person B is a teacher or a boxer?

14. Bias in base-rate task - results
High proportion of stereotypical answers even in incongruent situations.
Participants neglected the base-rate and answered according to the content.
Participants also made high metacognitive judgments (80-90% confident) These judgments were negatively correlated with response times.
Faster = more confident.

15. Dual process theory Mental skills Cognitive biases Analytical
Properties of the two thinking systems:
Mental skills
Analytical
Non-intuitive
Conscious
Slow and serial
High effort
Low capacity
Deliberate, access to working memory
Type 2 process
System 2 thinking
Cognitive biases
Heuristics
Intuitive
Unconscious
Rapid
Low effort
High capacity
Automatic
Type 1 processes
System 1 thinking
Evans (1989, 2007, 2013), Evans & Stanovich (2013), Sloman (1996), ect.

16. Some misconceptions about dual process theory
Distinction between two systems is not always so simple
There are many dual-process theories but they are not all the same
Type 2 is not always slow
There is not only one „System 1” that performs all Type 1 processing; TASS „the set of automated subsystems” (Stanovich, 2004)

17. Theories of deductive reasoning
Formal rules theories
Domain-specific reasoning theories
Probability theories
Mental model theory

18. Mental model theory
Johnson-Laird (1983, 2001, 2013); Johnson-Laird & Byrne (1991)
Mental model –representations of the states of affairs; possible valid conclusions
Mental models in conditional
Example:
If P, then Q If it rains, then the streets are wet.
[p] [q] [it rains] [streets are wet]
[¬ p] [q] [it does not rain] [streets are wet]
[¬ p] [¬ q] [it does not rain] [streets are not wet]

19. Computational constraints and limitations described by mental model theory
Initial model representation
Number of models
Content of models
Arrangement of models

20. Initial model Premise can be represented with more than one model
Conditional has three possible models
Initially, only the first model is constructed to represent the conditional
[it rains] [streets are wet] …
[it does not rain] [streets are wet]
[it does not rain] [streets are not wet]
Implication: Modus ponens (MP) is easier then Modus tollens (MT)
Evidence:
Valerjev (2006); Valerjev, Bajšanski & Gulan (2013a, 2013b)
Mental chronometry studies
MPs are significantly faster and more accurate than MTs

21. How models are generated?
Valerjev (2009)
Likelihood judgment experiment
Conditional form: If P, then Q.
Biconditional form: If and only if P, then Q.
Possible cases: P Q; P not-Q; not-P Q; not-P not-Q

22. Number of mental models
Greater number of models = greater working memory load = less efficiency
MT (3) is harder than MP (1)
Valerjev (2006) – mental chronometry experiment
Conditional and disjunctive tasks with different number of required models.
Accuracy as function of number of m.m Response time as function of number of m.m.

23. Content effects Models content: Knauff & Johnson-Laird (2002)
Abstract content, spatial relations, events, processes etc.
Knauff & Johnson-Laird (2002)
Bajšanski, Valerjev, & Gulan (2011) – conditionals with up-down relations and with content that was expected to be placed up or down (congruent and incongruent)
Example:
If the roof is up, then the cellar is down. (congruent)
If the road is down then the car is up. (congruent)
Orientation effect:
F(1, 23)=17.44, p<.001
Content congruence effect
F(1, 23)=5.16, p<.05

24. Arrangement of the models
Girrotto, Mazzocco, & Tasso (1997) – different order of premises made MT more accurate
Valerjev, Bajšanski, & Gulan (2010)
Manipulation of the conditional order
Standard: If P, then Q.
Reverse: Q, if P.
Congruent and incongruent spatial content. If A is left, then B is right.
MPs processed more efficient in standard order
MTs processed more efficient in reverse order
MPs and MTs have an opposite reasoning direction

25. Spatial priming of mental models
Valerjev, Bajšanski, & Gulan (2013) – visual priming experiment where visual prime was antecedent and consequent in congruent or incongruent spatial order that interfered with mental model
Congruent priming: If A is left, then B is right.
[prime stimulus] A B
Incongruent priming: If A is left, then B is right.
[prime stimulus] B A
Congruent prime: faster MPs
Incongruent prime: faster MTs
Both effects, directionality and visual-spatial priming were significant and opposite for MPs and MTs
Spatial order of mental representation significantly affects reasoning

26. Conclusion Many biases and computational constraints affect reasoning
Two important properties of mind:
Bounded rationality which is fast
System 1
Flexibility – opportunity to switch from system 1 to system 2 if needed

27. References
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28. Thank you for your attention