Exclusive Disjunctions With Three Disjuncts from First-Order Predicate Calculus

Abstract

First-order predicate logic seems to be incompatible with the way people understand embedded exclusive disjunctions with three disjuncts. In classical logic, an exclusive disjunction with three disjuncts holds when the three disjuncts hold. However, it is hard to note that for people. The theory of mental models can explain this fact. According to that theory, individuals tend to process embedded exclusive disjunctions with three disjuncts intuitively. Thus, they only consider possible situations in which just one of the disjuncts is the case. The present paper tries to explain this problem within first-order predicate logic. The main point is that, in the latter logic, in inferences having, as its first premise, an embedded exclusive disjunction with three disjuncts, and, as its second premise, the first disjunct of that very exclusive disjunction, it is possible to infer none of the other two disjuncts.