Results 31 to 40 of about 428,865 (120)

A groupoid characterization of orthomodular lattices [PDF]

, 2005
summary:We prove that an orthomodular lattice can be considered as a groupoid with a distinguished element satisfying simple ...
Chajda, Ivan
core   +1 more source

Quantum logic [PDF]

ریاضی و جامعه
This article employs a descriptive-analytical method with an algebraic and axiomatic approach to address quantum logic. Through several thought experiments, it is demonstrated that the distributive law for propositions does not hold in quantum mechanics.
Alireza Moazzen
doaj   +1 more source

On Quantum-MV Algebras - Part I: The Orthomodular Algebras

Scientific Annals of Computer Science, 2021
We prove that almost all the properties of quantum-MV algebras are verified by orthomodular algebras, the new algebras introduced in a previous paper. We put a special insight on transitive antisymmetric orthomodular (taOM) algebras, generalizations of ...
Afrodita Iorgulescu
doaj   +1 more source

Orthomodular lattices with almost orthogonal sets of atoms [PDF]

, 1991
summary:The set $A$ of all atoms of an atomic orthomodular lattice is said to be almost ortho\-go\-nal if the set $\{b\in A:b\nleq a'\}$ is finite for every $a\in A$.
Pulmannová, Sylvia, Rogalewicz, Vladimír   +1 more
core   +1 more source

Axioms for the category of Hilbert spaces and linear contractions

Bulletin of the London Mathematical Society, Volume 56, Issue 4, Page 1532-1549, April 2024.
Abstract The category of Hilbert spaces and linear contractions is characterised by elementary categorical properties that do not refer to probabilities, complex numbers, norm, continuity, convexity or dimension.
Chris Heunen, Andre Kornell, Nesta van der Schaaf   +2 more
wiley   +1 more source

A remark on $\lambda$-regular orthomodular lattices

, 1989
summary:A finite orthomodular lattice in which every maximal Boolean subalgebra (block) has the same cardinality $k$ is called $\lambda$-regular, if each atom is a member of just $\lambda$ blocks.
Rogalewicz, Vladimír
core   +1 more source

Modularity, Atomicity and States in Archimedean Lattice Effect Algebras

Symmetry, Integrability and Geometry: Methods and Applications, 2010
Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra E that is not an orthomodular lattice there exists an (o ...
Jan Paseka
doaj   +1 more source

A measure-theoretic characterization of Boolean algebras among orthomodular lattices [PDF]

, 1994
summary:We investigate subadditive measures on orthomodular lattices. We show as the main result that an orthomodular lattice has to be distributive (=Boolean) if it possesses a unital set of subadditive probability measures.
Pulmannová, Sylvia, Pták, Pavel
core   +1 more source

Matrix Semantics for Classical Logic: The Case of the Lattice O6

Bulletin of the Section of Logic
It is well established that classical propositional logic is Boolean. However, this view has recently been challenged. In their paper Non-Orthomodular Models for Both Standard Quantum Logic and Standard Classical Logic: Repercussions for Quantum ...
Ela Drozdowska
doaj   +1 more source

An 𝑚-orthocomplete orthomodular lattice is 𝑚-complete

, 1970
We call an orthomodular lattice L m \mathcal {L}\;m -orthocomplete for an infinite cardinal m m if every orthogonal family of ≦ m \leqq m ...
Samuel S. Holland
core   +1 more source