Editing Logical connective (section)

{{Short description|Symbol connecting sentential formulas in logic}}
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{{For|other logical symbols|List of logic symbols}}
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[[File:Logical connectives Hasse diagram.svg|300px|right|thumb|[[Hasse diagram]] of logical connectives.]]

In [[Mathematical logic|logic]], a '''logical connective''' (also called a '''logical operator''', '''sentential connective''', or '''sentential operator''') is a [[logical constant]]. Connectives can be used to connect logical formulas. For instance in the [[syntax (logic)|syntax]] of [[propositional logic]], the [[Binary relation|binary]] connective <math> \lor </math> can be used to join the two [[atomic formula]]s <math> P</math> and <math> Q</math>, rendering the complex formula <math> P \lor Q </math>.

Common connectives include [[negation]], [[disjunction]], [[Logical conjunction|conjunction]], [[material conditional|implication]], and [[Logical biconditional|equivalence]]. In standard systems of [[classical logic]], these connectives are [[semantics of logic|interpreted]] as [[truth function]]s, though they receive a variety of alternative interpretations in [[nonclassical logic]]s. Their classical interpretations are similar to the meanings of natural language expressions such as [[English language|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 [[formal semantics (natural language)|compositional semantics]] with a robust [[pragmatics]].