About: S5 (modal logic)

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In logic and philosophy, S5 is one of five systems of modal logic proposed by Clarence Irving Lewis and Cooper Harold Langford in their 1932 book Symbolic Logic. It is a normal modal logic, and one of the oldest systems of modal logic of any kind. It is formed with propositional calculus formulas and tautologies, and inference apparatus with substitution and modus ponens, but extending the syntax with the modal operator necessarily and its dual possibly .

Attributes	Values
rdf:type	place
rdfs:label	S5 (logica modale) (it) S5 (modal logic) (en) S5 (lógica modal) (pt) S5 (модальная логика) (ru) S5 (模态逻辑) (zh)
rdfs:comment	In logic and philosophy, S5 is one of five systems of modal logic proposed by Clarence Irving Lewis and Cooper Harold Langford in their 1932 book Symbolic Logic. It is a normal modal logic, and one of the oldest systems of modal logic of any kind. It is formed with propositional calculus formulas and tautologies, and inference apparatus with substitution and modus ponens, but extending the syntax with the modal operator necessarily and its dual possibly . (en) Em lógica e filosofia, S5 é um dos cinco sistemas de lógica modal propostos por Clarence Irving Lewis e Cooper Harold Langford no livro Symbolic Logic, de 1932. É uma lógica modal normal, e um dos mais velhos sistemas de lógica modal. (pt) S5 — одна из пяти систем модальной логики, предложенных и в книге «Символическая логика» (англ. Symbolic Logic, 1932). Является и одной из старейших систем модальной логики. Будучи простейшей модельной логикой, образуется формулами логики высказываний, тавтологиями, аппаратом вывода с и modus ponens. Синтаксис при этом дополнен модальным оператором необходимости и двойственным ему оператором возможности . С точки зрения семантики Крипке S5 относится к моделям, где отношение достижимости является отношением эквивалентности: оно рефлексивно, симметрично и транзитивно. (ru) 在逻辑和哲学中，S5 是和在他们1932年的书《Symbolic Logic》中提议的五个模态逻辑之一。它是正规模态逻辑和最古老的模态逻辑系统之一。 (zh)
dcterms:subject	Modal logic
Wikipage page ID	12708106 (xsd:integer)
Wikipage revision ID	1119297403 (xsd:integer)
Link from a Wikipage to another Wikipage	Propositional calculus Modal logic Ontological argument Possible world Modal operator Kripke frame Gottfried Wilhelm Leibniz NP-complete Cooper Harold Langford Thomas Aquinas Logic Kripke semantics Propositional logic Substitution (logic) Adjoint functors Transitive relation Clarence Irving Lewis Alvin Plantinga Equivalence relation Tautology (logic) Accessibility relation Modal logic Symmetric relation Modus ponens Philosophy Reflexive relation Euclidean relation Five Ways (Aquinas) Normal modal logic
Link from a Wikipage to an external page	http://plato.stanford.edu/entries/logic-modal/ http://home.utah.edu/~nahaj/logic/structures/systems/s5.html
sameAs	S5 (modal logic) S5 (modal logic) S5 (modal logic) S5 (modal logic) S5 (modal logic) S5 (modal logic) S5 (modal logic)
dbp:wikiPageUsesTemplate	dbt:Reflist dbt:Short_description
has abstract	In logic and philosophy, S5 is one of five systems of modal logic proposed by Clarence Irving Lewis and Cooper Harold Langford in their 1932 book Symbolic Logic. It is a normal modal logic, and one of the oldest systems of modal logic of any kind. It is formed with propositional calculus formulas and tautologies, and inference apparatus with substitution and modus ponens, but extending the syntax with the modal operator necessarily and its dual possibly . (en) Em lógica e filosofia, S5 é um dos cinco sistemas de lógica modal propostos por Clarence Irving Lewis e Cooper Harold Langford no livro Symbolic Logic, de 1932. É uma lógica modal normal, e um dos mais velhos sistemas de lógica modal. (pt) S5 — одна из пяти систем модальной логики, предложенных и в книге «Символическая логика» (англ. Symbolic Logic, 1932). Является и одной из старейших систем модальной логики. Будучи простейшей модельной логикой, образуется формулами логики высказываний, тавтологиями, аппаратом вывода с и modus ponens. Синтаксис при этом дополнен модальным оператором необходимости и двойственным ему оператором возможности . С точки зрения семантики Крипке S5 относится к моделям, где отношение достижимости является отношением эквивалентности: оно рефлексивно, симметрично и транзитивно. (ru) 在逻辑和哲学中，S5 是和在他们1932年的书《Symbolic Logic》中提议的五个模态逻辑之一。它是正规模态逻辑和最古老的模态逻辑系统之一。 (zh)
gold:hypernym	Systems
prov:wasDerivedFrom	wikipedia-en:S5_(modal_logic)?oldid=1119297403&ns=0
page length (characters) of wiki page	4947 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:S5_(modal_logic)
is Link from a Wikipage to another Wikipage of	Epistemic modal logic Index of philosophy articles (R–Z) Structural proof theory Cooper Harold Langford Axiom S5 C. I. Lewis Algebraic logic List of NP-complete problems Natural deduction Predicate functor logic Hypersequent Modal collapse Autoepistemic logic Method of analytic tableaux Philosophical logic Existential graph Normal modal logic S5 Logic S5
is Wikipage redirect of	Axiom S5 Logic S5
is foaf:primaryTopic of	wikipedia-en:S5_(modal_logic)

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