Results 111 to 120 of about 399 (126)
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Three Classes of Orthomodular Lattices
International Journal of Theoretical Physics, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Greechie, Richard J., Legan, Bruce J.
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International Journal of Theoretical Physics, 1995
For two classes of algebras \(C_2\subseteq C_1\) (minimal) exclusion systems \(\Sigma\subseteq C_1- C_2\) are discussed, for \(C_1\): all orthomodular lattices OML, \(C_2\): all modular ortholattices. A negative answer is given to the question of a finite \(\Sigma\) consisting of finite OML: Every such \(\Sigma\) contains an infinite OML. A minimal OML
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For two classes of algebras \(C_2\subseteq C_1\) (minimal) exclusion systems \(\Sigma\subseteq C_1- C_2\) are discussed, for \(C_1\): all orthomodular lattices OML, \(C_2\): all modular ortholattices. A negative answer is given to the question of a finite \(\Sigma\) consisting of finite OML: Every such \(\Sigma\) contains an infinite OML. A minimal OML
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Orthomodular Lattices in Occurrence Nets
2009In this paper, we study partially ordered structures associated to occurrence nets. An occurrence net is endowed with a symmetric, but in general non transitive, concurrency relation. By applying known techniques in lattice theory, from any such relation one can derive a closure operator, and then an orthocomplemented lattice.
BERNARDINELLO, LUCA +2 more
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Algebra Universalis, 1992
Let \({\mathcal C}(X)\) be the \(\perp\)-closed subsets of a set \(X\) with a binary relation \(\perp\) which is irreflexive, symmetric and satisfies \(x^{\perp\perp}=\{x\}\). For \(A,B\in{\mathcal C}(X)\) the relation \(A\theta B\) holds iff \([A\cap B,\;A\vee B]\) is of finite height.
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Let \({\mathcal C}(X)\) be the \(\perp\)-closed subsets of a set \(X\) with a binary relation \(\perp\) which is irreflexive, symmetric and satisfies \(x^{\perp\perp}=\{x\}\). For \(A,B\in{\mathcal C}(X)\) the relation \(A\theta B\) holds iff \([A\cap B,\;A\vee B]\) is of finite height.
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Finitely Generated Free Orthomodular Lattices. III
International Journal of Theoretical Physics, 2000For all \(k\in N\), the authors give a description of finitely generated free algebras in the variety generated by the horizontal sum of one three-atomic block \(2^3\) and \(k-1\) two-atomic blocks \(2^2\). This extends the results obtained in Part I [\textit{M. Haviar, P. Konôpka, H. A. Priestley} and \textit{C. B. Wegener}, Int. J. Theor. Phys.
Haviar, M., Konôpka, P.
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Generalized Orthomodular Lattices
1985Let ‵G = (G, ∨, ∧) be a lattice with the least element 0. For any a∈G, define P(a): [0,a]→[0,a],to be a unary operation on [O,a] such that P(a):x↦xP(a). We shall say that ‵G is a generalized orthomodular lattice if and only if it satisfies the following conditions: (G 1) The algebra ([O,a], ∨, ∧,P(a), 0,a) is an orthomodular lattice for every a ...
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Completions of orthomodular lattices
Order, 1990zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bruns, Günter +3 more
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Remarks on Concrete Orthomodular Lattices
International Journal of Theoretical Physics, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Completions of orthomodular lattices II
Order, 1993zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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1990
The paper On complemented lattices was the third paper in the new theory of orthomodular lattices which started in 1936 with Birkhoff and von Neumann’s idea of developing a new many-valued logic for quantum mechanics by using the lattice of closed subspaces C(H) of a Hilbert space H as the valuation lattice.
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The paper On complemented lattices was the third paper in the new theory of orthomodular lattices which started in 1936 with Birkhoff and von Neumann’s idea of developing a new many-valued logic for quantum mechanics by using the lattice of closed subspaces C(H) of a Hilbert space H as the valuation lattice.
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