Results 11 to 20 of about 131 (121)
Topological duality for orthomodular lattices
Mathematical Logic Quarterly, 2023 AbstractA 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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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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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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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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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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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
Choe, Tae Ho, Greechie, Richard J.
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Generalized Rough Sets via Quantum Implications on Quantum Logic
Axioms, 2021 This paper introduces some new concepts of rough approximations via five quantum implications satisfying Birkhoff–von Neumann condition. We first establish rough approximations via Sasaki implication and show the equivalence between distributivity of ...
Songsong Dai
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Between quantum logic and concurrency [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 We start from two closure operators defined on the elements of a special kind of partially ordered sets, called causal nets. Causal nets are used to model histories of concurrent processes, recording occurrences of local states and of events. If every
Luca Bernardinello +2 more
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Orthomodular Lattices Induced by the Concurrency Relation [PDF]
Electronic Proceedings in Theoretical Computer Science, 2009 We apply to locally finite partially ordered sets a construction which associates a complete lattice to a given poset; the elements of the lattice are the closed subsets of a closure operator, defined starting from the concurrency relation. We show that,
Luca Bernardinello +2 more
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Towards a Paraconsistent Quantum Set Theory [PDF]
Electronic Proceedings in Theoretical Computer Science, 2015 In this paper, we will attempt to establish a connection between quantum set theory, as developed by Ozawa, Takeuti and Titani, and topos quantum theory, as developed by Isham, Butterfield and Döring, amongst others.
Benjamin Eva
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