# Implication

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(Redirected from Philosophy:Definitional implication)

**Implication** may refer to:

## Logic

- Logical consequence (also entailment or logical implication), the relationship between statements that holds true when one logically "follows from" one or more others
- Material conditional (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 or strict implication, a connective of modal logic that expresses necessity
*modus ponens*, 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, 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, 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)

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