Implication Explained

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 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 that 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)