Complete Lattices Represent Complete Heyting Algebras (Or: Quantum Logic With An Intuitionistic Implication) Export

@misc{citeulike:1286414, abstract = {Via the introduction of (infinitary) disjunctions on any complete lattice while inheriting the meet as a conjunction, we construct a bijective correspondence (up to isomorphism) between complete lattices L and complete Heyting algebras DI(L) equipped with a so called disjunctive join dense closure operator RL . If L is itself a complete Heyting algebra then DI(L) \# = L and RL = id DI(L) . Ortholattices can similarly be represented bijectively (up to isomorphism) by complete Heyting...}, author = {Coecke, Bob}, citeulike-article-id = {1286414}, citeulike-linkout-0 = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.40.1550}, keywords = {atomisticity, closure-structures, commutativity, complete, concept-lattice, conceptual-structures, formal-science, frames, heyting-algebra, hyperdoctrine, inquiry-calculus, intuitionistic-logic, lattice, lattice-of-properties, locales, operational, ortholattice, probability-theory, property-lattice, quantum-logic, stone-duality, topos-theory, unified-concept-theory}, posted-at = {2007-05-09 22:41:14}, priority = {2}, title = {Complete Lattices Represent Complete Heyting Algebras (Or: Quantum Logic With An Intuitionistic Implication)}, url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.40.1550} }

TY - GEN ID - citeulike:1286414 L3 - citeulike-article-id:1286414 N2 - Via the introduction of (infinitary) disjunctions on any complete lattice while inheriting the meet as a conjunction, we construct a bijective correspondence (up to isomorphism) between complete lattices L and complete Heyting algebras DI(L) equipped with a so called disjunctive join dense closure operator RL . If L is itself a complete Heyting algebra then DI(L) # = L and RL = id DI(L) . Ortholattices can similarly be represented bijectively (up to isomorphism) by complete Heyting... TI - Complete Lattices Represent Complete Heyting Algebras (Or: Quantum Logic With An Intuitionistic Implication) KW - atomisticity KW - closure-structures KW - commutativity KW - complete KW - concept-lattice KW - conceptual-structures KW - formal-science KW - frames KW - heyting-algebra KW - hyperdoctrine KW - inquiry-calculus KW - intuitionistic-logic KW - lattice KW - lattice-of-properties KW - locales KW - operational KW - ortholattice KW - probability-theory KW - property-lattice KW - quantum-logic KW - stone-duality KW - topos-theory KW - unified-concept-theory AU - Coecke, Bob UR - http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.40.1550 ER -