Results 11 to 20 of about 399 (126)
Classical Logic and Quantum Logic with Multiple and Common Lattice Models
Advances in Mathematical Physics, 2016 We consider a proper propositional quantum logic and show that it has multiple disjoint lattice models, only one of which is an orthomodular lattice (algebra) underlying Hilbert (quantum) space.
Mladen Pavičić
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Topological duality for orthomodular lattices
Mathematical Logic Quarterly, Volume 69, Issue 2, Page 174-191, May 2023., 2023 Abstract A class of ordered relational topological spaces is described, which we call orthomodular spaces. Our construction of these spaces involves adding a topology to the class of orthomodular frames introduced by Hartonas, along the lines of Bimbó's topologization of the class of orthoframes employed by Goldblatt in his representation of ...
Joseph McDonald, Katalin Bimbó
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Roughness in lattice ordered effect algebras. [PDF]
ScientificWorldJournal, 2014 Many authors have studied roughness on various algebraic systems. In this paper, we consider a lattice ordered effect algebra and discuss its roughness in this context. Moreover, we introduce the notions of the interior and the closure of a subset and give some of their properties in effect algebras. Finally, we use a Riesz ideal induced congruence and
Xin XL, Hua XJ, Zhu X.
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Rough Approximation Operators on a Complete Orthomodular Lattice
Axioms, 2021 This paper studies rough approximation via join and meet on a complete orthomodular lattice. Different from Boolean algebra, the distributive law of join over meet does not hold in orthomodular lattices. Some properties of rough approximation rely on the
Songsong Dai
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On interval homogeneous orthomodular lattices
, 2001 Summary: An orthomodular lattice \(L\) is said to be interval homogeneous (respectively centrally interval homogeneous) if it is \(\sigma \)-complete and satisfies the following property: Whenever \(L\) is isomorphic to an interval, \([a,b]\), in \(L\) then \(L\) is isomorphic to each interval \([c,d]\) with \(c\leq a\) and \(d\geq b\) (respectively ...
Anna De Simone +2 more
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Profinite orthomodular lattices [PDF]
Proceedings of the American Mathematical Society, 1993 We prove that any compact topological orthomodular lattice L L is zero dimensional. This leads one to show that L L is profinite iff it is the product of finite orthomodular lattices with their discrete topologies. We construct a completion L ¯ \overline L of a residually finite ...
Choe, Tae Ho, Greechie, Richard J.
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The paraunitary group of a von Neumann algebra
Bulletin of the London Mathematical Society, Volume 54, Issue 4, Page 1220-1231, August 2022., 2022 Abstract It is proved that the pure paraunitary group over a von Neumann algebra coincides with the structure group of its projection lattice. The structure group of an arbitrary orthomodular lattice (OML) is a group with a right invariant lattice order, and as such it is known to be a complete invariant of the OML.
Carsten Dietzel, Wolfgang Rump
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Orthomodular lattices, Foulis Semigroups and Dagger Kernel Categories [PDF]
Logical Methods in Computer Science, 2010 This paper is a sequel to arXiv:0902.2355 and continues the study of quantum logic via dagger kernel categories. It develops the relation between these categories and both orthomodular lattices and Foulis semigroups.
Bart Jacobs
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Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 The main goal of this paper is to introduce and investigate the related theory on monadic effect algebras. First, we design the axiomatic system of existential quantifiers on effect algebras and then use it to give the definition of the universal quantifier and monadic effect algebras.
Yuxi Zou, Xiaolong Xin, Li Guo
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Subalgebras of Orthomodular Lattices [PDF]
Order, 2010 Sachs showed that a Boolean algebra is determined by its lattice of subalgebras. We establish the corresponding result for orthomodular lattices. We show that an orthomodular lattice L is determined by its lattice of subalgebras Sub(L), as well as by its poset of Boolean subalgebras BSub(L).
Harding, John, Navara, Mirko
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