Definition:Logical Connective/Binary

Definition

A binary logical connective (or two-place connective) is a logical connective whose effect on its compound statement is determined by the truth value of two substatements.

In standard Aristotelian logic, there are 16 binary logical connectives, cf. Binary Truth Functions.

In the field of symbolic logic, the following four (symbols for) binary logical connectives are commonly used:

• Conjunction: the And connective $p \land q$: $p$ is true and $q$ is true.

• Disjunction: the Or connective $p \lor q$: $p$ is true or $q$ is true, or possibly both.

• The conditional connective $p \implies q$: If $p$ is true, then $q$ is true.

• The biconditional connective $p \iff q$: $p$ is true if and only if $q$ is true, or $p$ is equivalent to $q$.

Also defined as

Some sources use the term logical connective to mean binary logical connective exclusively, on the grounds that a unary logical connective does not actually "connect" anything. However, this is a trivial distinction which can serve only to confuse.

Also see

• Definition:Unary Logical Connective

Sources

• 1980: D.J. O'Connor and Betty Powell: Elementary Logic ... (previous) ... (next): $\S \text{I}: 2$: Logical Constants $(1)$