A study of disjunctive and conjunctive reasoning in formal logic

Abstract

When reasoning with statements containing logical connectives in everyday discourse, people sometimes employ reasoning strategies that do not comply with the dictates of logic yet are still sufficient for their purpose. Cognitive studies point to the most likely circumstances in which non-logical heuristics are likely to be employed for logical problems expressed in natural language, where they invariably lead to error. This paper describes a study aimed at determining whether trained computer scientists continue to employ non-logical heuristics when they are reasoning about logical statements expressed in a mathematical notation. The study focuses on the ways in which people reason about disjunctive and conjunctive statements. Specifically, it sought to test whether reasoning performance is affected by the polarity of logical operators or by the degree of thematic content presented in problem material. The results suggest that there was only a limited transfer of non-logical processes to the formal domain and that, although reasoning was still far from perfect, the use of a formal notation facilitated logical reasoning for the types of inference scrutinised. The implications of this finding are discussed in relation to the software engineering community where the use of formal logic based notations are gradually gaining increased acceptance.