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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
wiley +1 more source
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 ...
Tae Ho Choe, Richard J. Greechie
openaire +1 more source
Qausi-Copulas on Orthomodular Lattice
, 2021 One of the possible mathematical systems to represent non-compatible random events is a quantum logic. In this paper, we propose and illustrate function called quasi-copula on an orthomodular lattice (briefly QO-copula). Also, we compare such function to
A. Al-Adilee, Adel Hashem Nouri
semanticscholar +1 more source
Orthomodular and Skew Orthomodular Posets
Symmetry, 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 ...
I. Chajda, Miroslav Kolarík, H. Länger
semanticscholar +1 more source
Every finite group is the automorphism group of some finite orthomodular lattice [PDF]
, 1976 G. Schrag
semanticscholar +2 more sources
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
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
doaj +1 more source
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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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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