Truth table task: Working memory load, latencies, and perceived relevance

Abstract

The aim of the present study is to uncover the relation between cognitive ability and the answer patterns yielded by the truth table task. According to the Classical Mental Models Theory, people with high working memory capacity answer according to two-valued or “logical” answer patterns. The Suppositional Theory and the Revised Mental Models Theory predict that the answer patterns given by the most intelligent ones are three-valued or “defective”. Correlations are examined, and in three experiments it is tested with a dual task paradigm whether a differential working memory load alters participants' answer patterns. A positive correlation is observed between cognitive ability and three-valued answer patterns, but no effect of the working memory load manipulation is revealed. With an inspection of the classification times we shed light on the processes underlying truth table judgements. We conclude that the Revised Mental Models Theory provides the best account for our results.

Keywords:

• Classification times
• Conditionals
• Mental models accounts
• Suppositional theory
• Truth table task
• Working memory load

Acknowledgments

This research was partially funded by the OT-project “A developmental study of deductive, inductive and abductive reasoning”. We thank Valérie Camos, David Over and two anonymous reviewers for their helpful comments on this manuscript.

Notes

¹De Finetti (1967, 2008) also departs from standard two-valued logic introducing a third value for the FA cases in conditional events: “null”. This truth table, with the FA cases being void, is the so-called “de Finetti table” and is comparable to the defective or three-valued truth table (see also Politzer, Over, & Baratgin, 2010). In the remainder of this paper, the terminology two-valued versus three-valued will be used.

²From the current version of the C-MMT, it is hard to predict whether participants will give either a conjunctive or a three-valued answer pattern, since both result from the initial model (depending on whether the initial model contains exhaustivity markers). Based on previous studies, in which far more three-valued than conjunctive patterns were observed, it is to be predicted that participants with a high load will produce more three-valued patterns than conjunctive patterns, but there is need for a more clear account from the C-MMT.