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- Relevance_logic abstract "Relevance logic, also called relevant logic, is a kind of non-classical logic requiring the antecedent and consequent of implications to be relevantly related. They may be viewed as a family of substructural or modal logics. (It is generally, but not universally, called relevant logic by Australian logicians, and relevance logic by other English-speaking logicians.)Relevance logic aims to capture aspects of implication that are ignored by the "material implication" operator in classical truth-functional logic, namely the notion of relevance between antecedent and conditional of a true implication. This idea is not new: C. I. Lewis was led to invent modal logic, and specifically strict implication, on the grounds that classical logic grants paradoxes of material implication such as the principle that a falsehood implies any proposition. Hence "if I'm a donkey, then two and two is four" is true when translated as a material implication, yet it seems intuitively false since a true implication must tie the antecedent and consequent together by some notion of relevance. And whether or not I'm a donkey seems in no way relevant to whether two and two is four.How does relevance logic formally capture a notion of relevance? In terms of a syntactical constraint for a propositional calculus, it is necessary, but not sufficient, that premises and conclusion share atomic formulae (formulae that do not contain any logical connectives). In a predicate calculus, relevance requires sharing of variables and constants between premises and conclusion. This can be ensured (along with stronger conditions) by, e.g., placing certain restrictions on the rules of a natural deduction system. In particular, a Fitch-style natural deduction can be adapted to accommodate relevance by introducing tags at the end of each line of an application of an inference indicating the premises relevant to the conclusion of the inference. Gentzen-style sequent calculi can be modified by removing the weakening rules that allow for the introduction of arbitrary formulae on the right or left side of the sequents.A notable feature of relevance logics is that they are paraconsistent logics: the existence of a contradiction will not cause "explosion". This follows from the fact that a conditional with a contradictory antecedent that does not share any propositional or predicate letters with the consequent cannot be true (or derivable).".
- Relevance_logic wikiPageExternalLink logic-relevance.
- Relevance_logic wikiPageID "185076".
- Relevance_logic wikiPageLength "6734".
- Relevance_logic wikiPageOutDegree "39".
- Relevance_logic wikiPageRevisionID "630169335".
- Relevance_logic wikiPageWikiLink Alan_Ross_Anderson.
- Relevance_logic wikiPageWikiLink Alonzo_Church.
- Relevance_logic wikiPageWikiLink Antecedent_(logic).
- Relevance_logic wikiPageWikiLink Atomic_formula.
- Relevance_logic wikiPageWikiLink C._I._Lewis.
- Relevance_logic wikiPageWikiLink Category:Non-classical_logic.
- Relevance_logic wikiPageWikiLink Category:Paraconsistent_logic.
- Relevance_logic wikiPageWikiLink Category:Substructural_logic.
- Relevance_logic wikiPageWikiLink Clarence_Irving_Lewis.
- Relevance_logic wikiPageWikiLink Classical_logic.
- Relevance_logic wikiPageWikiLink Consequent.
- Relevance_logic wikiPageWikiLink Entailment.
- Relevance_logic wikiPageWikiLink First-order_logic.
- Relevance_logic wikiPageWikiLink Gentzen.
- Relevance_logic wikiPageWikiLink Gerhard_Gentzen.
- Relevance_logic wikiPageWikiLink Ivan_E._Orlov.
- Relevance_logic wikiPageWikiLink Ivan_Orlov_(philosopher).
- Relevance_logic wikiPageWikiLink Kripke_semantics.
- Relevance_logic wikiPageWikiLink Logic.
- Relevance_logic wikiPageWikiLink Logical_connective.
- Relevance_logic wikiPageWikiLink Logical_consequence.
- Relevance_logic wikiPageWikiLink Logician.
- Relevance_logic wikiPageWikiLink Material_conditional.
- Relevance_logic wikiPageWikiLink Modal_logic.
- Relevance_logic wikiPageWikiLink Moh_Shaw-Kwei.
- Relevance_logic wikiPageWikiLink Natural_deduction.
- Relevance_logic wikiPageWikiLink Nuel_Belnap.
- Relevance_logic wikiPageWikiLink Paraconsistent_logic.
- Relevance_logic wikiPageWikiLink Paradoxes_of_material_implication.
- Relevance_logic wikiPageWikiLink Predicate_calculus.
- Relevance_logic wikiPageWikiLink Principle_of_explosion.
- Relevance_logic wikiPageWikiLink Propositional_calculus.
- Relevance_logic wikiPageWikiLink Relevant_type_system.
- Relevance_logic wikiPageWikiLink Sequent.
- Relevance_logic wikiPageWikiLink Sequent_calculus.
- Relevance_logic wikiPageWikiLink Stanford_Encyclopaedia_of_Philosophy.
- Relevance_logic wikiPageWikiLink Stanford_Encyclopedia_of_Philosophy.
- Relevance_logic wikiPageWikiLink Strict_conditional.
- Relevance_logic wikiPageWikiLink Strict_implication.
- Relevance_logic wikiPageWikiLink Substructural_logic.
- Relevance_logic wikiPageWikiLink Substructural_type_system.
- Relevance_logic wikiPageWikiLink Truth-functional_logic.
- Relevance_logic wikiPageWikiLink Truth_function.
- Relevance_logic wikiPageWikiLink Vacuous_truth.
- Relevance_logic wikiPageWikiLink Wilhelm_Ackermann.
- Relevance_logic wikiPageWikiLinkText "Relevance logic".
- Relevance_logic wikiPageWikiLinkText "relevance logic".
- Relevance_logic wikiPageWikiLinkText "relevant logic".
- Relevance_logic hasPhotoCollection Relevance_logic.
- Relevance_logic wikiPageUsesTemplate Template:Non-classical_logic.
- Relevance_logic wikiPageUsesTemplate Template:Portal.
- Relevance_logic subject Category:Non-classical_logic.
- Relevance_logic subject Category:Paraconsistent_logic.
- Relevance_logic subject Category:Substructural_logic.
- Relevance_logic hypernym Kind.
- Relevance_logic comment "Relevance logic, also called relevant logic, is a kind of non-classical logic requiring the antecedent and consequent of implications to be relevantly related. They may be viewed as a family of substructural or modal logics.".
- Relevance_logic label "Relevance logic".
- Relevance_logic sameAs Lògica_rellevant.
- Relevance_logic sameAs Relevanzlogik.
- Relevance_logic sameAs Lógica_relevante.
- Relevance_logic sameAs 適切さの論理.
- Relevance_logic sameAs Lógica_de_relevância.
- Relevance_logic sameAs m.0198ph.
- Relevance_logic sameAs Relevanslogik.
- Relevance_logic sameAs Q176630.
- Relevance_logic sameAs Q176630.
- Relevance_logic sameAs 相干逻辑.
- Relevance_logic wasDerivedFrom Relevance_logic?oldid=630169335.
- Relevance_logic isPrimaryTopicOf Relevance_logic.