Implication may refer to:


  • 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 implication, material consequence, or implication), a logical connective and binary truth function typically interpreted as "If p, then q"
  • Strict conditional or strict implication, a connective of modal logic that expresses necessity
  • Implication elimination or modus ponens, 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, 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

See also

  • Material implication (disambiguation)
  • Implicit (disambiguation)
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