1. Processing of negation in probabilistic deductive reasoning
Nicole Cruz

2. Negation paradigm If p then q If p then not-q If not-p then q
If not-p then not-q 2

3. Matching bias Which cases render the statement false?
"If the chip is triangular, then it is blue"
Which cases render the statement false?
Evans (1972); Evans, Ellis, & Newstead (1996) 3

4. Matching bias Which cases render the statement false?
"If the chip is triangular, then it is blue"
"If the chip is triangular, then it is not blue"
Which cases render the statement false?
Evans (1972); Evans, Ellis, & Newstead (1996) 3

5. Matching bias Which cases render the statement false?
"If the chip is triangular, then it is blue"
"If the chip is triangular, then it is not blue"
"If the chip is not triangular, then it is blue"
Which cases render the statement false?
Evans (1972); Evans, Ellis, & Newstead (1996) 3

6. Explanations for matching bias
Difficulty in processing implicit negation
(Evans, Clibbens, & Rood, 1996; Evans & Handley, 1999)
Further argument for matching bias as manifesttion of implicit negation effect: People endorse less all four inferences in the conditional inference task when the categorical premise is implicitly negated (Evans & Handley, 1999)
Reduction in matching bias also
- when concrete, familiar content (Evans, 1998)
- probabilistic truth table task (Oberauer, Geiger, Fischer, & Weidenfeld, 2007)
Matching bias does not seem to be smaller for people with high general cognitive ability (Evans, Handley, Neliens, & Over, 2007). 4

7. Explanations for matching bias
Difficulty in processing implicit negation
(Evans, Clibbens, & Rood, 1996; Evans & Handley, 1999)
Expected information gain + rarity assumption
→ importance of the size of the contrast class
(Oaksford & Chater, 1994; c. f. Barrouillet & Lecas, 1998)
Further argument for matching bias as manifesttion of implicit negation effect: People endorse less all four inferences in the conditional inference task when the categorical premise is implicitly negated (Evans & Handley, 1999)
Reduction in matching bias also
- when concrete, familiar content (Evans, 1998)
- probabilistic truth table task (Oberauer, Geiger, Fischer, & Weidenfeld, 2007)
Matching bias does not seem to be smaller for people with high general cognitive ability (Evans, Handley, Neliens, & Over, 2007). 4

8. Double negation effect
If the chip is not triangular, then it is blue
The chip is yellow
________________________________
Therefore, the chip is triangular 5

9. Explanations for double negation effect
Difficulty of double negation elimination
(Evans & Handley, 1999) 6

10. Explanations for double negation effect
Difficulty of double negation elimination
(Evans & Handley, 1999)
Rarity assumption -> high probability conclusion effect
(Oaksford, Chater, & Larkin, 2000)
In Oaksford, Chater, & Larkin (2000), double negation effect was observed also with familiar material 6

11. Explanations for negation effects
Matching bias
difficulty with implicit negation
rarity assumption: size of contrast class
Double negation
difficulty with double negation
rarity assumption: size of contrast class 7

12. Decomposition of the task
Negation has to be made explicit for use in reasoning (beyond detecting incongruence)
Frame context as one where possible to assert that something is the case or not
Element of the contrast class is the case
→ contrast class is the case
Contrast class is the case
→ statement itself is not the case 8

13. Operationalisation
Construct tasks that require one or more of the above steps and measure the time each step takes, and the variance it explains
Measures for Step 1.: Clear identification of reference set, composed of few disjunct elements, vs. open, ambiguous information
- Application to disjunctions:
"p or q" → "if not p then q" vs.
"if not p then q" → "p or q" 9

14. Operationalisation 2
Measures for Step 2.: Start by replicating Schroyens, Verschueren, Schaeken, & d'Ydewalle (2000)
Measures for Step 3: Implicit negation with binary categories. Test different forms of generating binarity
Study the effect of type of implicitness: pictorial, verbal, spatial, numerical inconsistencies
Search for other occurrences of negation effects 10

15. Thank you for your attention!