implies A = B



Implication may refer to:


Logical consequence Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid logical argument is one ...
(also entailment or logical implication), the relationship between statements that holds true when one logically "follows from" one or more others *
Material conditional The material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol \rightarrow is interpreted as material implication, a formula P \rightarrow Q is true unless P is true and Q i ...
(also material consequence, or implication), a logical connective and binary truth function typically interpreted as "If ''p'', then ''q''" ** material implication (rule of inference), a logical rule of replacement ** Implicational propositional calculus, a version of classical propositional calculus which uses only the material conditional connective *
Strict conditional In logic, a strict conditional (symbol: \Box, or ⥽) is a conditional governed by a modal operator, that is, a logical connective of modal logic. It is logically equivalent to the material conditional of classical logic, combined with the necessi ...
or strict implication, a connective of modal logic that expresses necessity * ''
modus ponens In propositional logic, ''modus ponens'' (; MP), also known as ''modus ponendo ponens'' (Latin for "method of putting by placing") or implication elimination or affirming the antecedent, is a deductive argument form and rule of inference. ...
'', or Implication elimination, a simple argument form and rule of inference summarized as "''p'' implies ''q''; ''p'' is asserted to be true, so therefore ''q'' must be true"


Implicature In pragmatics, a subdiscipline of linguistics, an implicature is something the speaker suggests or implies with an utterance, even though it is not literally expressed. Implicatures can aid in communicating more efficiently than by explicitly sayi ...
, what is suggested in an utterance, even though neither expressed nor strictly implied * Implicational universal or linguistic universal, a pattern that occurs systematically across natural languages **
Implicational hierarchy Implicational hierarchy, in linguistics, is a chain of implicational universals. A set of chained universals is schematically shown as in (1): (1) A < B < C < D It can be reformulated in the following way: If a language has property D, then it a ...
, a chain of implicational universals; if a language has one property then it also has other properties in the chain * Entailment (pragmatics) or strict implication, the relationship between two sentences where the truth of one requires the truth of the other

Other uses

* Implication table, a tool used to facilitate the minimization of states in a state machine * Implication graph, a skew-symmetric directed graph used for analyzing complex Boolean expressions * Implication (information science)

See also

* Material implication (disambiguation) * Implicit (disambiguation) {{disambiguation Conditionals