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- Action_algebra abstract "In algebraic logic, an action algebra is an algebraic structure which is both a residuated semilattice and a Kleene algebra. It adds the star or reflexive transitive closure operation of the latter to the former, while adding the left and right residuation or implication operations of the former to the latter. Unlike dynamic logic and other modal logics of programs, for which programs and propositions form two distinct sorts, action algebra combines the two into a single sort. It can be thought of as a variant of intuitionistic logic with star and with a noncommutative conjunction whose identity need not be the top element. Unlike Kleene algebras, action algebras form a variety, which furthermore is finitely axiomatizable, the crucial axiom being a•(a → a)* ≤ a. Unlike models of the equational theory of Kleene algebras (the regular expression equations), the star operation of action algebras is reflexive transitive closure in every model of the equations.".
- Action_algebra wikiPageID "12415190".
- Action_algebra wikiPageLength "7859".
- Action_algebra wikiPageOutDegree "22".
- Action_algebra wikiPageRevisionID "653330426".
- Action_algebra wikiPageWikiLink Algebraic_logic.
- Action_algebra wikiPageWikiLink Algebraic_structure.
- Action_algebra wikiPageWikiLink Algebraic_variety.
- Action_algebra wikiPageWikiLink Boolean_algebra.
- Action_algebra wikiPageWikiLink Boolean_algebra_(structure).
- Action_algebra wikiPageWikiLink Category:Algebraic_logic.
- Action_algebra wikiPageWikiLink Category:Algebraic_structures.
- Action_algebra wikiPageWikiLink Category:Formal_languages.
- Action_algebra wikiPageWikiLink Dynamic_logic_(modal_logic).
- Action_algebra wikiPageWikiLink Formal_language.
- Action_algebra wikiPageWikiLink Heyting_algebra.
- Action_algebra wikiPageWikiLink John_Horton_Conway.
- Action_algebra wikiPageWikiLink Kleene_algebra.
- Action_algebra wikiPageWikiLink Kleene_star.
- Action_algebra wikiPageWikiLink Regular_expression.
- Action_algebra wikiPageWikiLink Relation_algebra.
- Action_algebra wikiPageWikiLink Residuated_lattice.
- Action_algebra wikiPageWikiLinkText "Action algebra".
- Action_algebra wikiPageWikiLinkText "action algebra".
- Action_algebra date "June 2014".
- Action_algebra reason "These are properties of binary relations. Explain why a* can be considered as a binary relation.".
- Action_algebra wikiPageUsesTemplate Template:Cite_book.
- Action_algebra wikiPageUsesTemplate Template:Clarify.
- Action_algebra wikiPageUsesTemplate Template:Reflist.
- Action_algebra subject Category:Algebraic_logic.
- Action_algebra subject Category:Algebraic_structures.
- Action_algebra subject Category:Formal_languages.
- Action_algebra hypernym Structure.
- Action_algebra type Building.
- Action_algebra type Language.
- Action_algebra type Combinatoric.
- Action_algebra type Language.
- Action_algebra comment "In algebraic logic, an action algebra is an algebraic structure which is both a residuated semilattice and a Kleene algebra. It adds the star or reflexive transitive closure operation of the latter to the former, while adding the left and right residuation or implication operations of the former to the latter. Unlike dynamic logic and other modal logics of programs, for which programs and propositions form two distinct sorts, action algebra combines the two into a single sort.".
- Action_algebra label "Action algebra".
- Action_algebra sameAs Q4677173.
- Action_algebra sameAs m.02w4cqk.
- Action_algebra sameAs Q4677173.
- Action_algebra sameAs 作用代数.
- Action_algebra wasDerivedFrom Action_algebra?oldid=653330426.
- Action_algebra isPrimaryTopicOf Action_algebra.