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- Q4677173 subject Q7142640.
- Q4677173 subject Q8234740.
- Q4677173 subject Q8234762.
- Q4677173 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.".
- Q4677173 wikiPageWikiLink Q1005222.
- Q4677173 wikiPageWikiLink Q1617044.
- Q4677173 wikiPageWikiLink Q173183.
- Q4677173 wikiPageWikiLink Q185612.
- Q4677173 wikiPageWikiLink Q192161.
- Q4677173 wikiPageWikiLink Q205464.
- Q4677173 wikiPageWikiLink Q2634506.
- Q4677173 wikiPageWikiLink Q268961.
- Q4677173 wikiPageWikiLink Q3836453.
- Q4677173 wikiPageWikiLink Q4973304.
- Q4677173 wikiPageWikiLink Q5965969.
- Q4677173 wikiPageWikiLink Q648995.
- Q4677173 wikiPageWikiLink Q7142640.
- Q4677173 wikiPageWikiLink Q8234740.
- Q4677173 wikiPageWikiLink Q8234762.
- Q4677173 wikiPageWikiLink Q849775.
- Q4677173 wikiPageWikiLink Q9462417.
- Q4677173 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.".
- Q4677173 label "Action algebra".