Logical disjunction

Classical disjunction is a truth functional operation which returns the truth value "true" unless both of its arguments are "false". Its semantic entry is standardly given as follows:[4]

In systems where logical disjunction is not a primitive, it may be defined as[5]

Operators corresponding to logical disjunction exist in most programming languages.

The or operator can be used to set bits in a bit field to 1, by or-ing the field with a constant field with the relevant bits set to 1. For example, x = x | 0b00000001 will force the final bit to 1, while leaving other bits unchanged.[citation needed]

Many languages distinguish between bitwise and logical disjunction by providing two distinct operators; in languages following C, bitwise disjunction is performed with the single pipe operator (|), and logical disjunction with the double pipe (||) operator.

Logical disjunction is usually short-circuited; that is, if the first (left) operand evaluates to true, then the second (right) operand is not evaluated. The logical disjunction operator thus usually constitutes a sequence point.

In a parallel (concurrent) language, it is possible to short-circuit both sides: they are evaluated in parallel, and if one terminates with value true, the other is interrupted. This operator is thus called the parallel or.

Although the type of a logical disjunction expression is boolean in most languages (and thus can only have the value true or false), in some languages (such as Python and JavaScript), the logical disjunction operator returns one of its operands: the first operand if it evaluates to a true value, and the second operand otherwise.[citation needed]

The Curry–Howard correspondence relates a constructivist form of disjunction to tagged union types.[citation needed]

This inference has sometimes been understood as an entailment, for instance by Alfred Tarski, who suggested that natural language disjunction is ambiguous between a classical and a nonclassical interpretation. More recent work in pragmatics has shown that this inference can be derived as a conversational implicature on the basis of a semantic denotation which behaves classically. However, disjunctive constructions including Hungarian vagy... vagy and French soit... soit have been argued to be inherently exclusive, rendering ungrammaticality in contexts where an inclusive reading would otherwise be forced.[1]

Similar deviations from classical logic have been noted in cases such as free choice disjunction and simplification of disjunctive antecedents, where certain modal operators trigger a conjunction-like interpretation of disjunction. As with exclusivity, these inferences have been analyzed both as implicatures and as entailments arising from a nonclassical interpretation of disjunction.[1]

In many languages, disjunctive expressions play a role in question formation. For instance, while the following English example can be interpreted as a polar question asking whether it's true that Mary is either a philosopher or a linguist, it can also be interpreted as an alternative question asking which of the two professions is hers. The role of disjunction in these cases has be analyzed using nonclassical logics such as alternative semantics and inquisitive semantics, which have also been adopted to explain the free choice and simplification inferences.[1]

In English, as in many other languages, disjunction is expressed by a coordinating conjunction. Other languages express disjunctive meanings in a variety of ways, though it is unknown whether disjunction itself is a linguistic universal. In many languages such as Dyirbal and Maricopa, disjunction is marked using a verb suffix. For instance, in the Maricopa example below, disjunction is marked by the suffix šaa.[1]