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<p></p> <p><b>New page</b></p><div>{{wiktionary|implication|implicational|implications|implies|imply}}<br /> &#039;&#039;&#039;Implication&#039;&#039;&#039; may refer to:<br /> <br /> {{TOC right}}<br /> <br /> ==Logic==<br /> * [[Logical consequence]] (also entailment or logical implication), the relationship between statements that holds true when one logically &quot;follows from&quot; one or more others<br /> * [[Material conditional]] (also material implication), a logical connective and binary truth function typically interpreted as &quot;If &#039;&#039;p&#039;&#039;, then &#039;&#039;q&#039;&#039;&quot;<br /> ** [[Material implication (rule of inference)]], a logical rule of replacement <br /> ** [[Implicational propositional calculus]], a version of classical propositional calculus that uses only the material conditional connective<br /> * [[Strict conditional]] or strict implication, a connective of modal logic that expresses necessity<br /> * &#039;&#039;[[modus ponens]]&#039;&#039;, or implication elimination, a simple argument form and rule of inference summarized as &quot;&#039;&#039;p&#039;&#039; implies &#039;&#039;q&#039;&#039;; &#039;&#039;p&#039;&#039; is asserted to be true, so therefore &#039;&#039;q&#039;&#039; must be true&quot;<br /> <br /> == Linguistics ==<br /> * [[Implicature]], what is suggested in an utterance, even though neither expressed nor strictly implied<br /> * [[Implicational universal]] or linguistic universal, a pattern that occurs systematically across natural languages<br /> ** [[Implicational hierarchy]], a chain of implicational universals; if a language has one property then it also has other properties in the chain<br /> * [[Entailment (pragmatics)]] or strict implication, the relationship between two sentences where the truth of one requires the truth of the other<br /> <br /> == Other uses ==<br /> * [[Implication table]], a tool used to facilitate the minimization of states in a state machine<br /> * [[Implication graph]], a skew-symmetric directed graph used for analyzing complex Boolean expressions<br /> * [[Implication (information science)]]<br /> <br /> == See also ==<br /> * [[Material implication (disambiguation)]]<br /> * [[Implicit (disambiguation)]]<br /> <br /> {{disambiguation}}<br /> [[Category:Conditionals]]</div>

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