Logical Connectives

In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant used to connect two or more formulas. For instance in the syntax of propositional logic, the binary connective {\displaystyle \lor }\lor can be used to join the two atomic formulas {\displaystyle P} P and {\displaystyle Q} Q, rendering the complex formula {\displaystyle P\lor Q}P\lor Q.

Common connectives include negation, disjunction, conjunction, and implication. In standard systems of classical logic, these connectives are interpreted as truth functions, though they receive a variety of alternative interpretations in nonclassical logics. Their classical interpretations are similar to the meanings of natural language expressions such as English not, or, and, and if, but not identical. Discrepancies between natural language connectives and those of classical logic have motivated nonclassical approaches to natural language meaning as well as approaches which pair a classical compositional semantics with a robust pragmatics.

English word	mantrakshar	Connective	Venn Diagram	Symbol	Logical gate
not		Negation		¬	NOT
and		Conjunction		∧	AND
not both		Alternative denial		↑	NAND
or		Disjunction		∨	OR
neither…nor		Joint denial		↓	NOR
if…then		Material implication		→	IMPLY
one or the other but not both		Exclusive or			XOR
if and only if		Biconditional		↔	XNOR
…if		Converse implication		←
but not		material nonimplication		↛	NIMPLY

left is less than right		left < right
left is more than right		left > right
right is less than left		right < left
right is more than left		right > left