Results 11 to 20 of about 428,865 (120)
Orthomodular and Skew Orthomodular Posets [PDF]
, 2023 We present the smallest non-lattice orthomodular poset and show that it is unique up to isomorphism. Since not every Boolean poset is orthomodular, we consider the class of skew orthomodular posets previously introduced by the first and third author ...
Kolařík, Miroslav; orcid: +2 more
core +2 more sources
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
wiley +1 more source
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
wiley +1 more source
Negative Translations of Orthomodular Lattices and Their Logic [PDF]
, 2021 We introduce residuated ortholattices as a generalization of—and environment for the investigation of—orthomodular lattices. We establish a number of basic algebraic facts regarding these structures, characterize orthomodular lattices as those residuated
Fussner, Daniel, St. John, Gavin
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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
doaj +1 more source
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
doaj +1 more source
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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On the properties of spectral effect algebras [PDF]
Quantum, 2019 The aim of this paper is to show that there can be either only one or uncountably many contexts in any spectral effect algebra, answering a question posed in [S. Gudder, Convex and Sequential Effect Algebras, (2018), arXiv:1802.01265].
Anna Jenčová, Martin Plávala
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Quantum-Inspired Uncertainty Quantification
Frontiers in Computer Science, 2022 Reasonable quantification of uncertainty is a major issue of cognitive infocommunications, and logic is a backbone for successful communication. Here, an axiomatic approach to quantum logic, which highlights similarity to and differences to classical ...
Günther Wirsching
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