Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Monadic_Boolean_algebra> ?p ?o }
Showing triples 1 to 62 of
62
with 100 triples per page.
- Monadic_Boolean_algebra abstract "In abstract algebra, a monadic Boolean algebra is an algebraic structure A with signature 〈·, +, ', 0, 1, ∃〉 of type 〈2,2,1,0,0,1〉,where 〈A, ·, +, ', 0, 1〉 is a Boolean algebra.The monadic/unary operator ∃ denotes the existential quantifier, which satisfies the identities (using the received prefix notation for ∃): ∃0 = 0 ∃x ≥ x ∃(x + y) = ∃x + ∃y ∃x∃y = ∃(x∃y). ∃x is the existential closure of x. Dual to ∃ is the unary operator ∀, the universal quantifier, defined as ∀x := (∃x' )'. A monadic Boolean algebra has a dual definition and notation that take ∀ as primitive and ∃ as defined, so that ∃x := (∀x ' )' . (Compare this with the definition of the dual Boolean algebra.) Hence, with this notation, an algebra A has signature 〈·, +, ', 0, 1, ∀〉, with 〈A, ·, +, ', 0, 1〉 a Boolean algebra, as before. Moreover, ∀ satisfies the following dualized version of the above identities: ∀1 = 1 ∀x ≤ x ∀(xy) = ∀x∀y ∀x + ∀y = ∀(x + ∀y).∀x is the universal closure of x.".
- Monadic_Boolean_algebra wikiPageID "1018197".
- Monadic_Boolean_algebra wikiPageLength "4065".
- Monadic_Boolean_algebra wikiPageOutDegree "44".
- Monadic_Boolean_algebra wikiPageRevisionID "623204166".
- Monadic_Boolean_algebra wikiPageWikiLink Abstract_algebra.
- Monadic_Boolean_algebra wikiPageWikiLink Algebraic_structure.
- Monadic_Boolean_algebra wikiPageWikiLink Arity.
- Monadic_Boolean_algebra wikiPageWikiLink Boolean_algebra_(structure).
- Monadic_Boolean_algebra wikiPageWikiLink Category:Algebraic_logic.
- Monadic_Boolean_algebra wikiPageWikiLink Category:Boolean_algebra.
- Monadic_Boolean_algebra wikiPageWikiLink Category:Closure_operators.
- Monadic_Boolean_algebra wikiPageWikiLink Clopen_set.
- Monadic_Boolean_algebra wikiPageWikiLink Closure_algebra.
- Monadic_Boolean_algebra wikiPageWikiLink Closure_operator.
- Monadic_Boolean_algebra wikiPageWikiLink Duality_(order_theory).
- Monadic_Boolean_algebra wikiPageWikiLink Existential_quantification.
- Monadic_Boolean_algebra wikiPageWikiLink Existential_quantifier.
- Monadic_Boolean_algebra wikiPageWikiLink First-order_logic.
- Monadic_Boolean_algebra wikiPageWikiLink Interior_algebra.
- Monadic_Boolean_algebra wikiPageWikiLink Interior_operator.
- Monadic_Boolean_algebra wikiPageWikiLink Kuratowski_closure_axioms.
- Monadic_Boolean_algebra wikiPageWikiLink Lindenbaum-Tarski_algebra.
- Monadic_Boolean_algebra wikiPageWikiLink Lindenbaum–Tarski_algebra.
- Monadic_Boolean_algebra wikiPageWikiLink Modal_logic.
- Monadic_Boolean_algebra wikiPageWikiLink Monadic_(arity).
- Monadic_Boolean_algebra wikiPageWikiLink Monadic_logic.
- Monadic_Boolean_algebra wikiPageWikiLink Monadic_predicate_calculus.
- Monadic_Boolean_algebra wikiPageWikiLink Paul_Halmos.
- Monadic_Boolean_algebra wikiPageWikiLink Polyadic_algebra.
- Monadic_Boolean_algebra wikiPageWikiLink Prefix.
- Monadic_Boolean_algebra wikiPageWikiLink Propositional_calculus.
- Monadic_Boolean_algebra wikiPageWikiLink Propositional_logic.
- Monadic_Boolean_algebra wikiPageWikiLink Semisimple_algebra.
- Monadic_Boolean_algebra wikiPageWikiLink Signature_(logic).
- Monadic_Boolean_algebra wikiPageWikiLink Synonym.
- Monadic_Boolean_algebra wikiPageWikiLink Topology.
- Monadic_Boolean_algebra wikiPageWikiLink Unary_operation.
- Monadic_Boolean_algebra wikiPageWikiLink Unary_operator.
- Monadic_Boolean_algebra wikiPageWikiLink Universal_quantification.
- Monadic_Boolean_algebra wikiPageWikiLink Universal_quantifier.
- Monadic_Boolean_algebra wikiPageWikiLink Variety_(universal_algebra).
- Monadic_Boolean_algebra wikiPageWikiLink Łukasiewicz–Moisil_algebra.
- Monadic_Boolean_algebra wikiPageWikiLinkText "Monadic Boolean algebra".
- Monadic_Boolean_algebra wikiPageWikiLinkText "monadic Boolean algebra".
- Monadic_Boolean_algebra hasPhotoCollection Monadic_Boolean_algebra.
- Monadic_Boolean_algebra wikiPageUsesTemplate Template:Logic-stub.
- Monadic_Boolean_algebra subject Category:Algebraic_logic.
- Monadic_Boolean_algebra subject Category:Boolean_algebra.
- Monadic_Boolean_algebra subject Category:Closure_operators.
- Monadic_Boolean_algebra hypernym Structure.
- Monadic_Boolean_algebra type Building.
- Monadic_Boolean_algebra type Theory.
- Monadic_Boolean_algebra comment "In abstract algebra, a monadic Boolean algebra is an algebraic structure A with signature 〈·, +, ', 0, 1, ∃〉 of type 〈2,2,1,0,0,1〉,where 〈A, ·, +, ', 0, 1〉 is a Boolean algebra.The monadic/unary operator ∃ denotes the existential quantifier, which satisfies the identities (using the received prefix notation for ∃): ∃0 = 0 ∃x ≥ x ∃(x + y) = ∃x + ∃y ∃x∃y = ∃(x∃y). ∃x is the existential closure of x. Dual to ∃ is the unary operator ∀, the universal quantifier, defined as ∀x := (∃x' )'.".
- Monadic_Boolean_algebra label "Monadic Boolean algebra".
- Monadic_Boolean_algebra sameAs Monadyczna_algebra_Boolea.
- Monadic_Boolean_algebra sameAs m.03zq6q.
- Monadic_Boolean_algebra sameAs Q6897884.
- Monadic_Boolean_algebra sameAs Q6897884.
- Monadic_Boolean_algebra sameAs 一元布尔代数.
- Monadic_Boolean_algebra wasDerivedFrom Monadic_Boolean_algebra?oldid=623204166.
- Monadic_Boolean_algebra isPrimaryTopicOf Monadic_Boolean_algebra.