Two-Valued Logic is Not Sufficient to Model Human Reasoning, but Three-Valued Logic is: A Formal Analysis

There is an ongoing debate in the psychology of reasoning whether and how logic can be used to describe the human inference process. Many psychological findings indicate that humans deviate from classical logic inferences. Some researchers have proposed to use ternary logics instead to model human reasoning processes. In this article we re-analyze the famous Wason Selection Task that has been researched in more than 100 publications and can be regarded as one of the most important reasoning experiment in the psychology of reasoning. It investigates how participants check if a given conditional statement holds. Most cognitive modeling approaches have focused on explaining the general response pattern. Instead, we focus on the pattern generated by each participant. In particular, we conduct a meta-analysis to identify these patterns. Thereafter, we analyze these patterns. If there is a two-valued model of human reasoning processes, then there must be two-valued truth-tables that can generate the patterns. Finally, we show by a search through the space of all two-valued truth tables that there are patterns that cannot be explained by two-valued logics. However, these patterns can be explained, when extending the representation to three-valued logics.