Algebraic semantics (mathematical logic) (original) (raw)
In mathematical logic, algebraic semantics is a formal semantics based on algebras studied as part of algebraic logic. For example, the modal logic S4 is characterized by the class of topological boolean algebras—that is, boolean algebras with an interior operator. Other modal logics are characterized by various other algebras with operators. The class of boolean algebras characterizes classical propositional logic, and the class of Heyting algebras propositional intuitionistic logic. MV-algebras are the algebraic semantics of Łukasiewicz logic.
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| dbo:abstract | In mathematical logic, algebraic semantics is a formal semantics based on algebras studied as part of algebraic logic. For example, the modal logic S4 is characterized by the class of topological boolean algebras—that is, boolean algebras with an interior operator. Other modal logics are characterized by various other algebras with operators. The class of boolean algebras characterizes classical propositional logic, and the class of Heyting algebras propositional intuitionistic logic. MV-algebras are the algebraic semantics of Łukasiewicz logic. (en) En logique mathématique, la sémantique algébrique est une sémantique formelle basé sur les algèbres étudiés dans le cadre de la logique algébrique. Par exemple, la logique modale S4 se caractérise par la classe des —à savoir, des algèbres booléennes possédants un . D'autres logiques modales sont caractérisées par diverses autres algèbres avec des opérateurs. La classe des algèbres booléennes caractérise la logique propositionnelle classique, et la classe des algèbres d'Heyting de la logique intuitionniste. (fr) |
| dbo:wikiPageExternalLink | http://projecteuclid.org/euclid.lnl/1235416965 https://www.jstor.org/stable/3094793 |
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| dbo:wikiPageWikiLink | dbr:Modal_logic dbr:MV-algebra dbr:Algebraic_semantics_(computer_science) dbr:Interior_algebra dbr:Intuitionistic_logic dbr:Universal_algebra dbr:Lindenbaum–Tarski_algebra dbr:Mathematical_logic dbr:Order_theory dbr:Algebraic_logic dbr:Formal_semantics_(logic) dbr:Project_Euclid dbr:Heyting_algebra dbr:Łukasiewicz_logic dbc:Mathematical_logic dbr:Association_for_Symbolic_Logic dbr:Boolean_algebra_(structure) dbr:Non-classical_logic dbr:Classical_propositional_logic dbr:Interior_operator |
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| rdfs:comment | In mathematical logic, algebraic semantics is a formal semantics based on algebras studied as part of algebraic logic. For example, the modal logic S4 is characterized by the class of topological boolean algebras—that is, boolean algebras with an interior operator. Other modal logics are characterized by various other algebras with operators. The class of boolean algebras characterizes classical propositional logic, and the class of Heyting algebras propositional intuitionistic logic. MV-algebras are the algebraic semantics of Łukasiewicz logic. (en) En logique mathématique, la sémantique algébrique est une sémantique formelle basé sur les algèbres étudiés dans le cadre de la logique algébrique. Par exemple, la logique modale S4 se caractérise par la classe des —à savoir, des algèbres booléennes possédants un . D'autres logiques modales sont caractérisées par diverses autres algèbres avec des opérateurs. La classe des algèbres booléennes caractérise la logique propositionnelle classique, et la classe des algèbres d'Heyting de la logique intuitionniste. (fr) |
| rdfs:label | Algebraic semantics (mathematical logic) (en) Sémantique algébrique (logique mathématique) (fr) |
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