Effect algebras and unsharp quantum logics

1994/10/01 by D. J. Foulis, David J. Foulis, M. K. Bennett · 869 citations
Computer Science · Mathematics · #Advanced Algebra and Logic #Algebra over a field #Computer science #Discrete mathematics #Division algebra #Group (periodic table) #Logic, Reasoning, and Knowledge #Mathematics #Morphism #Non-associative algebra #Partially ordered set #Physics #Pure mathematics #Quadratic algebra #Quantum #Quantum group #Quantum mechanics #Rough Sets and Fuzzy Logic #Set (abstract data type) #Subalgebra #Universal enveloping algebra #Vector space

paper · doi:10.1007/bf02283036

published in Foundations of Physics 24(10), 1331-1352 (Springer Science+Business Media)

openalex publication_date 1994/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Cited by

• Effect algebras with the maximality property
• Foundations of Quantum Granular Computing with Effect-Based Granules, Algebraic Properties and Reference Architectures
• Observables on Quantum Structures
• Effect-valued measurement models and contextuality
• Dimension theory for generalized effect algebras
• On the Nature of Continuous Physical Quantities in Classical and Quantum Mechanics
• Simplicial Perspectives on (Pseudo) Effect Algebras
• Effect test spaces
• Influence-free states on compound quantum systems
• Effectuses in Categorical Quantum Foundations
• *-Autonomous categories in quantum theory
• Algebraic hierarchy of logics unifying fuzzy logic and quantum logic
• Homogeneous orthocomplete effect algebras are covered by MV-algebras
• Observables on synaptic algebras
• Quantum information processing and quantum logic: toward mutual illumination
• Spectral order on synaptic algebras
• Dagger and Dilation in the Category of Von Neumann algebras
• On a New Construction of Pseudo Effect Algebras
• Quantum information processing, operational quantum logic, convexity, and the foundations of physics
• Discrete (n+1)-valued states and n-perfect pseudo-effect algebras
• More about sharp and meager elements in Archimedean atomic lattice effect algebras
• Finite-Dimensional Convex Effect Algebras
• Properties of the connective implication in effect algebras
• Lexicographic Product vs \mathbb Q-perfect and \mathbb H-perfect Pseudo Effect Algebras
• AF inverse monoids and the structure of countable MV-algebras
• Quantum Physics and Classical Physics - in the Light of Quantum Logic
• Finite homogeneous effect algebras with trivial sharp elements
• \mathbb H-perfect Pseudo MV-algebras and Their Representations
• Distributive PBZ^*-lattices
• Logic and Partially Ordered Abelian Groups
• Compression Bases in Unital Groups
• Modularity, Atomicity and States in Archimedean Lattice Effect Algebras
• On the consistent effect histories approach to quantum mechanics
• Lattice pseudo-effect algebras as double residuated structures
• Sharp and Fuzzy Observables on Effect Algebras
• On Realization of Generalized Effect Algebras
• Convexity, Duality and Effects
• Can the World Beshown to be Indeterministic after all?
• No-cloning theorem on quantum logics
• Smearing of Observables and Spectral Measures on Quantum Structures
• Lattice uniformities on effect algebras
• Effect Algebras are the Eilenberg-Moore Category for the Kalmbach Monad
• An Algebraic Theory for Data Linkage
• Efficient Formal Verification of Quantum Error Correcting Programs
• The logic induced by effect algebras. [europepmc]
• Logical Divergence, Logical Entropy, and Logical Mutual Information in Product MV-Algebras. [europepmc]
• R -Norm Entropy and R -Norm Divergence in Fuzzy Probability Spaces. [europepmc]