Definition:Logical Connective/Binary

Definition

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

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 known as

A binary logical connective is also known as:

a two-place connective.

a dyadic connective.

Some sources just call it a binary connective.

Also see

• Binary Truth Functions In standard Aristotelian logic, there are $16$ binary logical connectives

• Definition:Unary Logical Connective

• Results about logical connectives can be found here.

Sources

• 1980: D.J. O'Connor and Betty Powell: Elementary Logic ... (previous) ... (next): $\S \text{I}: 2$: Logical Constants $(1)$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): connective
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): connective