Results 1 to 10 of about 112 (103)
Non-Deterministic Semantics for Quantum States [PDF]
Entropy, 2020 In this work, we discuss the failure of the principle of truth functionality in the quantum formalism. By exploiting this failure, we import the formalism of N-matrix theory and non-deterministic semantics to the foundations of quantum mechanics. This is
Juan Pablo Jorge, Federico Holik
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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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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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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).
Mirko Navara +2 more
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Weakly Orthomodular and Dually Weakly Orthomodular Lattices [PDF]
Order, 2018 The authors study the varieties of lattices with a unary operation~\('\) satisfying one or two or the following equations: \begin{align*} x= & (x\land y) \lor (x\land (x\land y)')\\ x= & (x\lor y) \land (x\lor (x\lor y)')\,. \end{align*} In ortholattices, any of these equations is equivalent to orthomodularity.
Helmut Langer +2 more
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On Quantum-MV algebras - Part II: Orthomodular Lattices, Softlattices and Widelattices [PDF]
Transactions on Fuzzy Sets and Systems, 2022 Orthomodular lattices generalize the Boolean algebras; they have arisen in the study of quantum logic. Quantum-MV algebras were introduced as non-lattice theoretic generalizations of MV algebras and as non-idempotent generalizations of ...
Afrodita Iorgulescu
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Residuated Structures and Orthomodular Lattices [PDF]
Studia Logica, 2021 AbstractThe variety of (pointed) residuated lattices includes a vast proportion of the classes of algebras that are relevant for algebraic logic, e.g., $$\ell $$ ℓ -groups, Heyting algebras, MV-algebras, or De Morgan monoids.
fazio, davide +2 more
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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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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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