The study of reasoning and information processing in cognitive science has often used problems derived from classical propositional logic inference rules in order to see how people make decisions, often comparing the qualities of those that can and cannot successfully complete these tasks. However, the majority of research that has been done has only focused on one inference rule: the material conditional. This narrow focus does not allow for inferences to be made about the role of logical ability simpliciter in cognitive science research. In order to better understand the relationship between cognitive ability and successfully completing tasks based on four binary logical connectives (conjunction, disjunction, material implication, and biconditional), 338 participants were given the Propositional Logic Test (PLT), a N-Back task, a Belief Bias Syllogisms Task, and the Cognitive Reflection Test, that latter two of which have been used in support of a dual-process theory of reasoning. Because no previous research exists examining the dimensionality of the PLT, multiple confirmatory factory analyses (CFA) were performed on the PLT to determine its factor structure. The best fitting model was a 2-factor model with a disjunction factor and conditionals factor, indicating that the PLT is multi-dimensional and there are limitations on its use as a summed score. Multiple regression analyses were then performed on the PLT and the two factors present to reveal what differences between participants may be masked by using the PLT as a summed score. The results indicate that ability to properly make the deductive inferences on the PLT is strongly associated with measures of Type 2 thinking and moderately associated with general intelligence. Furthermore, the disjunction factor was moderately related to both traditional measures of cognitive ability and Type 2 processing, and the conditionals factor was strongly related to the ability to engage in Type 2 processing and only weakly related to traditional measures of cognitive ability. Thus, the ability to engage in specific types of deductive inferences requires different cognitive abilities, and the ability to engage in basic logical reasoning is significantly predicted by measures of general intelligence, but this alone is not sufficient
