Definition:Logical Connective

Definition
A logical connective is an object which either modifies a statement, or combines existing statements into a new statement, called a compound statement.

It is almost universal to identify a logical connective with the symbol representing it.

Thus, logical connective may also, particularly in symbolic logic, be used to refer to that symbol, rather than speaking of a connective symbol separately.

In mathematics, logical connectives are considered to be truth-functional.

That is, the truth value of a compound statement formed using the connective is assumed to depend only on the truth value of the comprising statements.

Thus, as far as the connective is concerned, it does not matter what the comprising statements precisely are.

As a consequence of this truth-functionality, a connective has a corresponding truth function, which goes by the same name as the connective itself.

The arity of this truth function is the number of statements the logical connective combines into a single compound statement.

Also defined as
Some sources reserve the term logical connective for what on is defined as a binary logical connective, 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
Other terms for logical connective which may be encountered include:


 * Connective
 * Truth-functional connective
 * Propositional connective
 * Sentential connective
 * Logical constant
 * Logical operator
 * Sentence-forming operator
 * Boolean operator (in the context of mathematical logic)
 * Conjunction (as used in natural language - mathematics has a more specialised use for the term conjunction, however)

Also see

 * Definition:Truth Function


 * Definition:Connective of Propositional Logic