Implication may refer to:
Logic
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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 on ...
(also entailment or logical implication), the relationship between statements that holds true when one logically "follows from" one or more others
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Material conditional (also material consequence, or implication), a logical connective and binary truth function typically interpreted as "If ''p'', then ''q''"
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material implication (rule of inference)
In propositional logic, material implication is a valid rule of replacement that allows for a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that ''P implies Q'' is logically equiv ...
, a logical rule of replacement
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Implicational propositional calculus In mathematical logic, the implicational propositional calculus is a version of classical propositional calculus which uses only one connective, called implication or conditional. In formulas, this binary operation is indicated by "implies", "if ...
, a version of classical propositional calculus which uses only the material conditional connective
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Strict conditional or strict implication, a connective of modal logic that expresses necessity
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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"
Linguistics
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Implicature, what is suggested in an utterance, even though neither expressed nor strictly implied
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Implicational universal or linguistic universal, a pattern that occurs systematically across natural languages
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Implicational hierarchy, a chain of implicational universals; if a language has one property then it also has other properties in the chain
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Entailment (pragmatics) or strict implication, the relationship between two sentences where the truth of one requires the truth of the other
Other uses
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Implication table An implication table is a tool used to facilitate the minimization of states in a state machine. The concept is to start assuming that every state may be able to combine with every other state, then eliminate combinations that are not possible. Wh ...
, a tool used to facilitate the minimization of states in a state machine
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Implication graph, a skew-symmetric directed graph used for analyzing complex Boolean expressions
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Implication (information science) In formal concept analysis (FCA) ''implications'' relate sets of properties (or, synonymously, of attributes). An implication ''A''→''B'' ''holds'' in a given domain when every object having all attributes in ''A'' also has all attrib ...
See also
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Material implication (disambiguation)
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Implicit (disambiguation)
{{disambiguation
Conditionals