ABSTRACT
In this chapter, the authors focus on contributions to their understanding of propositional reasoning in general, and conditional reasoning in particular, by proponents of formal inference-rule theories and mental model theories. The phenomena of conditional reasoning have been explained in several alternative ways. Early researchers assumed that reasoners who made only the valid Modus Ponens and Modus Tollens inferences from a conditional had interpreted it as a material implication, whereas those who made all four inferences had interpreted it as a biconditional, or material equivalence, if and only if. The conditional proof rule leads to an impasse, and so cannot account for the data. Rule theories can describe effects such as the difference found between conditionals and exclusive disjunctions, by asserting ad hoc that the rule for one inference is more accessible than the rule for another. The Model theory explains the “defective” truth table judgements for neutral conditionals.
