Aligning Logical and Psychological Contributions to the Understanding of Human Reasoning

Modern logic is an abstract study of consequence rather than a mechanistic study of reasoning. This abstract view has much to offer psychological studies of the representations which implement human reasoning. This paper reviews recent results showing the abstract equivalence of all the main psychological competence models of syllogistic reasoning. Their apparently contrasting representations are computationally equivalent for the kind of data presented. The true empirical contrasts between theories lie in other details of implementation — in whether integrated representations are constructed and in the sequence of cases considered. These contrasts are independent of sentential, graphical or mental model representation.Logic is also a guide to representation requirements. Linear syllogism models are representable by sequences of tokens, whereas categorial syllogism models generally require attribute binding. However, one consequence of the present semantic analysis is that all categorial syllogism competence models converge on an algorithm which avoids representation of more than a single sequence.The paper goes on to consider what evidence could distinguish the representations implementing reasoning in working memory. The example of dual task paradigms is considered and some conceptual questions are raised about the identification of the modalities of working memory subsystems with linguistic and spatial representations. Carefully distinguishing memory medium from memory interpretation leads to the conclusion that it is the interpretation of the contents of memory which determines whether it holds spatial or linguistic information. It is argued that the critical dimension for understanding reasoning processes is the expressiveness of interpretation of representations.