1. The Dual-strategy model of deductive inference
Henry Markovits
Université du Québec à Montréal

2. Logical reasoning is a critical component of advanced thinking
Logical reasoning is a critical component of advanced thinking. Conditional (if-then) reasoning is particularly important.
Ideally, logical reasoning depends on “logic” only and is independent of content.

3. Ideally, people should give the same inference to the arguments below:
If a finger is cut, the finger will bleed. A finger bleeds. Is the finger cut?
If a rock is thrown at a window, the window breaks. A window breaks. Was a rock thrown?

4. However, people make systematically different inferences for different kinds of content, even when the logical structure is identical.
One explanation for these effects is the idea that when people are making these kinds of inference, they access information in long term-memory

5. A. Feeney, V. Thompson (Eds. )
A. Feeney, V. Thompson (Eds.). Reasoning and memory, Hove, UK: Psychology Press.
Some interesting evidence for memory retrieval in reasoning is given by the following experiment (Markovits & Potvin, 2001)

6. “If Julie eats between meals, then she will gain weight”
"For each of the following three pages, suppose that the sentence at the top of the page is true and reply to the multiple choice questions.“
“If Julie eats between meals, then she will gain weight”
“Other than eating between meals, there are other reasons that could lead to Julie gaining weight. On the line below, write one of these reasons.”

7. Logical form Neutral Memory Alternatives MP 75.3 65.6 36.9 MT 51.9
Condition
Logical form
Neutral
Memory
Alternatives MP
75.3
65.6
36.9 MT
51.9
52.9
19.0 AC
72.8
56.3
85.7 DA
83.9
89.7
73.8

8. The next question is what people do with the information stored in memory

9. Probabilistic evaluation
One explanation for these strong content effects is that people are using a form of
Probabilistic evaluation
even when making what appear to be purely deductive inferences. In other words, they access some form of statistical information that generates an estimate of the likelihood of the conclusion (given the premises)
Evans, Over, & Handley, 2005; Oaksford & Chater, 2007

10. Conclusions are characterized by degree of belief (i. e
Conclusions are characterized by degree of belief (i.e. probability estimate)
Such theories assume that conclusions that have a high probability will be considered to be logically valid

11. Mental Model theory supposes that deductive inferences are made by
Constructing a representation of premises
Examining this representation for potential Counterexamples to the conclusion
Information in memory is used to generate potential counterexamples
Johnson-Laird & Byrne, 2001

12. A conclusion is considered to be logically valid if there are no counterexamples.
Content effects can be modelled by factors related to model construction

13. Both theories can potentially account for content effects in deductive reasoning, although they both require several open parameters to do so.
The dual-strategy model first proposed by Verschueren, Schaeken, & d'Ydewalle, (2005) suggests that people can use both strategies.

14. Statistical strategies are rapid, low cost forms of inference giving an immediate intuitive evaluation of conclusion likelihood based on statistical properties of premises.
Counterexample strategies make use of working memory, and are cognitively more costly. These generate judgments of certainty (or validity) and depend on the ability to construct an explicit representation of premises. Key information is presence or absence of a potential counterexample.

15. We can evaluate people’s tendency to preferentially use one of these strategies by giving them a set of identical inferences with variable statistical properties (Markovits, Lortie Forgues, & Brunet, 2012).
Presented statistical information suggests:
1. variable conclusion likelihood
2. consistent presence of counterexamples

16. Of the 1000 last times that they have observed Trolytes, the geologists made the following observations:
910 times Philoben gas has been given off, and the Trolyte was heated.
90 times Philoben gas has been given off, and the Trolyte was not heated
From this information, Jean reasoned in the following manner:
The geologists have affirmed that: If a Trolyte is heated, then it will give off Philoben gas.
Observation: A Trolyte has given off Philoben gas.
Conclusion: The Trolyte was heated.”

17. Strategy use is determined by the existence of one of two patterns.
If all inferences are responded to in a way that is consistent with presence of counterexamples
 Counterexample strategy
If inference acceptance within a given class of inference (high vs low likelihood) varies according to likelihood
 Statistical strategy

18. Using this method to identify which strategy is preferentially used, experimental results have shown:
Under strong time constraint, people will strongly tend to use a statistical strategy, with more time they will switch more to a counterexample strategy.

19. When response modality suggests a likelihood scale (i. e
When response modality suggests a likelihood scale (i.e. using degree of certainty after an initial response of logical validity), people will use a statistical strategy.

20. People’s ability to modify strategy use is under some degree of metacognitive control. When they have a high level of confidence in an initial strategy they do not change.

21. Inferential updating using explicit statistical information shows that
when making explicitly probabilistic inferences, people will use statistical information
when making inferences of logical validity, people will preferentially use counterexample information

22. Our basic paradigm is the following: Initial inference:
P implies Q, Q is true. Is P true?
New Information
Updated inference:
Inferences refer to unknown categories on a hypothetical planet.

23. We present new information, referring to results of 1000 observations in the following way.
Low probability:
50 cases where Q is true and P is true
cases where Q is true and P is false

24. N Initial inference Updated inference
Reasoning strategy N
Initial inference
Updated inference
Counterexample 53
1.51 (0.82)
0.13 (0.44)
Statistical 30
1.50 (0.78)
0.97 (0.89)

25. Conclusion
People access memory when making deductive inferences with concrete terms. But, they can use this information in different ways:
1.To generate a potential counterexample to a putative conclusion, which requires retrieval and working memory Or
2. To generate a low-cost intuitive estimate of conclusion likelihood.