The values on the cards were implicitly binary (male/female; presence/absence of red flower) in at least two of the four lexical rules used and the difficulty of double negations was observed in this study as well.
If the contrast is larger (a set of three, five or nine values), then the making of a double negation or the production of an affirmative conclusion is more difficult for Denial of the Antecedent inferences.
Most rule-based theories propose a rule for double negation. Hence, the Modus Tollens problem with a negated antecedent requires an extra-step in comparison with the Modus Tollens problem with an affirmative antecedent, which explains the difficulty of the forms.
there is a double negation in which one has to negate a negative:
If a double negation is difficult, reasoners will have more difficulty with these problems, than with problems which do not require this double negation.
What is the reason for the difficulty of a double negation and/or what influences the difficulty of a double negation?
The main prediction tested and confirmed in this study was that presenting conclusions before their premises inhibits the conclusion bias associated with inferences requiring double negations. This was based on our intuition that when conclusions are presented first, reasoners will be more likely to build models of the premises which include the conclusion.
concluded that the difficulty was associated with the difficulty of denying a negative component, or in seeing that a double negation not-not-p was equivalent to the affirmative, p.
Neither mental logicians nor mental modellers have specific proposals in their published accounts to explain this double negation effect.
Johnson-Laird (1995, personal communication) has offered the following mental models' account of the double negation effect consistent with the kind of fleshing-out mechanisms proposed above.
Our second prediction concerns the negative conclusion bias, or double negation effect.