Results 11 to 20 of about 1,569 (137)

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

Orthomodular Lattices and Quantales [PDF]

International Journal of Theoretical Physics, 2005
Let $L$ be a complete orthomodular lattice. There is a one to one correspondence between complete boolean subalgebras of $L$ contained in the center of $L$ and endomorphisms $j$ of $L$ satisfying the Borceux-Van den Bossche conditions.
Leopoldo Román
openaire   +5 more sources

Cyclic atoms in orthomodular lattices [PDF]

Proceedings of the American Mathematical Society, 1971
Let P ( H ) P(H) denote the projection lattice of a separable Hilbert space H. For each x ∈ H {\text {x}} \in H , let P x {P_{\text {x}}} denote the projection onto the one ...
Donald E. Catlin
  +5 more sources

Conditioning maps on orthomodular lattices [PDF]

Glasgow Mathematical Journal, 1971
Let (χ Σ, μ) be a probability space, so that X is a non-empty set, Σ is a Boolean a-algebra of subsets of X, and μ is a probability measure defined on Σ. If D Ε S is such that μ(D)≠0, then one traditionally associates with D a new probability measure μD, called the conditional probability measure determined by D, and defined by μD(E)= μ(D∩E)/μ(D), for ...
C. H. Randall, David J. Foulis
openaire   +3 more sources

Hypersubstitutions in orthomodular lattices

Discussiones Mathematicae - General Algebra and Applications, 2001
Let \(\tau\) be a type of algebras. By a hypersubstitution of type \(\tau\) there is either meant a mapping assigning to every fundamental operation symbol of type \(\tau\) a term of type \(\tau\) of the same arity or there is meant the obvious extension of this mapping to the set of all terms of type \(\tau\).
Helmut Länger, Ivan Chajda
openaire   +4 more sources

On Locally Finite Orthomodular Lattices [PDF]

Mathematica Slovaca, 2023
Abstract Let us denote by ℒ ℱ $[\mathcal{L}\mathcal{F}$ the ...
Burešová, Dominika, Pták, Pavel
openaire   +3 more sources

Equivalences, Identities, Symmetric Differences, and Congruences in Orthomodular Lattices [PDF]

, 2003
It is shown that operations of equivalence cannot serve for building algebras which would induce orthomodular lattices as the operations of implication can. Several properties of equivalence operations have been investigated.
Megill, Norman D., Pavicic, Mladen
core   +3 more sources

Orthomodular Lattices and a Quantum Algebra [PDF]

International Journal of Theoretical Physics, 2001
We show that one can formulate an algebra with lattice ordering so as to contain one quantum and five classical operations as opposed to the standard formulation of the Hilbert space subspace algebra. The standard orthomodular lattice is embeddable into the algebra.
Mladen Pavicic, Norman D. Megill
openaire   +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   +2 more sources

Congruence relations on orthomodular lattices [PDF]

Journal of the Australian Mathematical Society, 1966
We denote lattice join and meet by ∨ and ∧ respectively and the associated partial order by ≧. A lattice L with 0 and I is said to be orthocomplemented if it admits a dual automorphism x → x′, that is a one-one mapping of L onto itself such that which is involutive, so that for each x in L and, further, is such that for each x in L.
П. Д. Финч
openaire   +4 more sources