Implication may refer to:

Logic

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 *

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 is ...

(also material consequence, or implication), a logical connective and binary truth function typically interpreted as "If ''p'', then ''q''" **

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 **

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 *

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 necessity ...

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"

Linguistics

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 A linguistic universal is a pattern that occurs systematically across natural languages, potentially true for all of them. For example, ''All languages have nouns and verbs'', or ''If a language is spoken, it has consonants and vowels.'' Research i ...

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 al ...

, a chain of implicational universals; if a language has one property then it also has other properties in the chain *

Entailment (pragmatics) Linguistic entailments are entailments which arise in natural language. If a sentence ''A'' entails a sentence ''B'', sentence ''A'' cannot be true without ''B'' being true as well. For instance, the English sentence "Pat is a fluffy cat" entails ...

or strict implication, the relationship between two sentences where the truth of one requires the truth of the other

Other uses

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 *

Implication graph In mathematical logic and graph theory, an implication graph is a skew-symmetric, directed graph composed of vertex set and directed edge set . Each vertex in represents the truth status of a Boolean literal, and each directed edge from verte ...

, a skew-symmetric directed graph used for analyzing complex Boolean expressions *

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 ...

Logic

Linguistics

Other uses

See also