Disjunction

In logic, disjunction is a binary connective (∨) classically interpreted as a truth function the output of which is true if at least one of the input sentences (disjuncts) is true, and false otherwise. Its supposed connection with disjunctive words of natural language like or has long intrigued philosophers, logicians and linguists. In this entry we give an overview of logical and linguistic analyses of disjunction with focus on developments at the interface between logic and language. Sections 1 and 2 present disjunction as a binary connective in classical logic and in a number of non-classical interpretations. Section 3 discusses some basic facts concerning disjunctive words in natural language, and introduces a generalized, cross-categorial notion of disjunction as the join operator in a (Boolean) algebra. Section 4 and 5 present Grice’s account of the use of or in conversation and recent developments in the discussion on inclusive and exclusive uses of linguistic disjunctive words. Finally, sections 6 and 7 introduce two recent non-classical accounts of linguistic disjunction and discuss applications to phenomena of free choice, disjunctive questions and counterfactuals with disjunctive antecedents.