Results 1 to 10 of about 672,721 (195)

Rough Approximation Operators on a Complete Orthomodular Lattice [PDF]

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
doaj   +3 more sources

Residuated Structures and Orthomodular Lattices [PDF]

Studia Logica, 2021
The variety of (pointed) residuated lattices includes a vast proportion of the classes of algebras that are relevant for algebraic logic, e.g., ℓ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage ...
D. Fazio, A. Ledda, F. Paoli
semanticscholar   +5 more sources

Note on p-ideals set of orthomodular lattices

AIMS Mathematics
This paper mainly discusses the problems raised in Kalmbach's book: When are the $ p $-ideals of an irreducible orthomodular lattice well ordered under set inclusion?
Ziteng Zhao, Jing Wang, Yali Wu
doaj   +3 more sources

Connecting the free energy principle with quantum cognition [PDF]

Frontiers in Neurorobotics, 2022
It appears that the free energy minimization principle conflicts with quantum cognition since the former adheres to a restricted view based on experience while the latter allows deviations from such a restricted view.
Yukio-Pegio Gunji, Shuji Shinohara, Vasileios Basios   +2 more
doaj   +2 more sources

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
doaj   +2 more sources

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.
europepmc   +2 more sources

Residuation in orthomodular lattices

Topological Algebra and its Applications, 2017
We show that every idempotent weakly divisible residuated lattice satisfying the double negation law can be transformed into an orthomodular lattice. The converse holds if adjointness is replaced by conditional adjointness.
Chajda Ivan, Länger Helmut
doaj   +3 more sources

The near center of an orthomodular lattice [PDF]

Journal of the Australian Mathematical Society, 1972
The results described herein were obtained in connection with the development of some lattice theoretic machinery needed by Randall and Foulis in their treatment of the so-called “logic of empirical science” (See [3] for an introduction to this subject).
M. Janowitz
semanticscholar   +3 more sources

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
doaj   +1 more source

Orthogonality and complementation in the lattice of subspaces of a finite vector space [PDF]

Mathematica Bohemica, 2022
We investigate the lattice $ L( V)$ of subspaces of an $m$-dimensional vector space $ V$ over a finite field ${\rm GF}(q)$ with a prime power $q=p^n$ together with the unary operation of orthogonality.
Ivan Chajda, Helmut Länger
doaj   +1 more source