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Conditional probabilities on orthomodular lattices
Reports on Mathematical Physics, 1984A definition of generalized probability on an orthomodular lattice which includes as particular cases the classical probability space and non- commutative probability theory on a von Neumann algebra is proposed. In this generalized structure the problem of conditioning with respect to Boolean \(\sigma\)-subalgebras is examined.
CASSINELLI, GIOVANNI, P. Truini:
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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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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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Decision problem for orthomodular lattices
Algebra Universalis, 1997The author partially solves the problem of H. P. Sankappanavar and S. Burris whether the theory of orthomodular lattices is recursively inseparable and which varieties of orthomodular lattices are finitely decidable. Results: -- The variety of orthomodular lattices has a finitely inseparable first order theory.
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Decidability in Orthomodular Lattices
International Journal of Theoretical Physics, 2005We discuss the possibility of automatic simplification of formulas in orthomodular lattices. We describe the principles of a program which decides the validity of equalities and inequalities, as well as implications between them and other important relations significant in quantum mechanics.
Mirko Navara, Marek Hyčko
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Boolean factors of orthomodular lattices [PDF]
Algebra Universalis, 1988 Bruns, Greechie, and Herman have shown that an orthomodular lattice whose commutator set is the commuting set of a finite set has to be a direct product of a Boolean algebra and a lattice without Boolean factor. The converse is refuted by a counterexample in this note.
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Block-Finite Orthomodular Lattices
Canadian Journal of Mathematics, 1979Introduction. Every orthomodular lattice (abbreviated : OML) is the union of its maximal Boolean subalgebras (blocks). The question thus arises how conversely Boolean algebras can be amalgamated in order to obtain an OML of which the given Boolean algebras are the blocks.
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Projective orthomodular lattices II
Algebra Universalis, 1997The authors continue the study of projectivity in orthomodular lattices started in Part I [Can. Math. Bull. 37, No. 2, 145-153 (1994; Zbl 0819.06007)]. The main results: Theorem 1.1. No uncountable Boolean algebra is projective in the variety of all orthomodular lattices. Corollary 1.3. Every Boolean subalgebra of a free orthomodular lattice is at most
Micheale S. Roddy, Günter Bruns
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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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Orthomodular Symmetric Lattices
1970Let J be an ideal of a lattice L, and assume that every element of J is modular. If x,y∈J and x ≦a ∨ y in L, then there exists an element u ∈ J such that x≦u ∨ y andu≦a.
Shûichirô Maeda, Fumitomo Maeda
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