Editing Logical connective (section)

==Natural language==

The standard logical connectives of classical logic have rough equivalents in the grammars of natural languages. In [[English language|English]], as in many languages, such expressions are typically [[grammatical conjunction]]s. However, they can also take the form of [[complementizer]]s, [[verb]] [[suffix]]es, and [[grammatical particle|particle]]s. The [[denotation]]s of natural language connectives is a major topic of research in [[formal semantics (natural language)|formal semantics]], a field that studies the logical structure of natural languages.

The meanings of natural language connectives are not precisely identical to their nearest equivalents in classical logic. In particular, disjunction can receive an [[exclusive disjunction|exclusive interpretation]] in many languages. Some researchers have taken this fact as evidence that natural language [[semantics (natural language)|semantics]] is [[nonclassical logic|nonclassical]]. However, others maintain classical semantics by positing [[pragmatics|pragmatic]] accounts of exclusivity which create the illusion of nonclassicality. In such accounts, exclusivity is typically treated as a [[scalar implicature]]. Related puzzles involving disjunction include [[free choice inference]]s, [[Hurford disjunction|Hurford's Constraint]], and the contribution of disjunction in [[alternative question]]s.

Other apparent discrepancies between natural language and classical logic include the [[paradoxes of material implication]], [[donkey anaphora]] and the problem of [[counterfactual conditionals]]. These phenomena have been taken as motivation for identifying the denotations of natural language conditionals with logical operators including the [[strict conditional]], the [[variably strict conditional]], as well as various [[dynamic semantics|dynamic]] operators.

The following table shows the standard classically definable approximations for the English connectives.

{| class="wikitable sortable"
|-
! English word !! Connective !! Symbol !! Logical gate
|-
| not || [[negation]] || <math>\neg</math> || [[Inverter (logic gate)|NOT]]
|-
| and || [[Logical conjunction|conjunction]] || <math>\and</math> || [[AND gate|AND]]
|-
| or || [[Logical disjunction|disjunction]] || <math>\vee</math> || [[OR gate|OR]]
|-
| if...then || [[Material conditional|material implication]]  || <math>\rightarrow</math> || [[IMPLY gate|IMPLY]]
|-
| ...if || [[converse implication]] || <math>\leftarrow</math> ||
|-
| either...or || [[Exclusive or|exclusive disjunction]] || <math>\nleftrightarrow</math> || [[XOR gate|XOR]]
|-
| if and only if || [[logical biconditional|biconditional]] || <math>\leftrightarrow</math> || [[XNOR gate|XNOR]]
|-
| not both || [[Sheffer stroke|alternative denial]] || <math>\uparrow</math> || [[NAND gate|NAND]]
|-
| neither...nor || [[Logical NOR|joint denial]] || <math>\downarrow</math> || [[NOR gate|NOR]]
|-
| but not || [[material nonimplication]] || <math>\nrightarrow</math> || [[NIMPLY gate|NIMPLY]]
|-
| not...but || [[converse nonimplication]] || <math>\nleftarrow</math>
|}