While the logical word or is grammatically similar to and, its logical role is to weaken claims by hedging them with a second alternative rather than to strengthen them by adding with a second assertion. This difference from conjunction is expressed by the truth table of the connective disjunction, according to which a disjunction is true when at least one true sentence among its components, which are called disjuncts. The symbol ∨ (logical or) is our notation for the operator disjunction, and its scope is marked by parentheses. Alternatively, we can write a disjunction φ ∨ ψ as either φ or ψ, where either serves (like both with conjunction) to indicate scope.

The truth of a disjunction when both its components are true distinguishes inclusive disjunction from another logical form, exclusive disjunction, whose compounds are true only when exactly one component is true. While English sentences stated with or often convey the idea that two alternatives are not both true, it can be argued that this information is conveyed as an implicature rather than an implication and that, as far as its truth conditions are concerned, the English word or may be taken as a sign of inclusive disjunction.

As is true of conjunction, there are cases where a word like or marking disjunction appears in a sentence but the sentence cannot be analyzed as a disjunction due to our inability to replace pronouns by their antecedents. Also, English has serial disjunctions just as it has serial conjunctions; and serial disjunction in English can be mimicked to some degree by run-on disjunctions, which suppress parentheses. Disjunction can be expressed in English by the phrase at least one, one of the group of related phrases indicating numerical compounding operations. In some cases, sentences containing these phrases can be analyzed by employing disjunction along with conjunction and negation.

Finally, disjunction provides an alternative, and more natural, way of analyzing neither-nor claims.