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An Extended Epistemic Framework Beyond Probability for Quantum Information Processing with Applications in Security, Artificial Intelligence, and Financial Computing. [PDF]
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Skew Boolean algebras derived from generalized Boolean algebras
Algebra universalis, 2008Every skew Boolean algebra S has a maximal generalized Boolean algebra image given by S/\({\mathcal{D}}\) where \({\mathcal{D}}\) is the Green’s relation defined initially on semigroups. In this paper we study skew Boolean algebras \(\omega({\bf B})\) constructed from generalized Boolean algebras B by a twisted product construction for which \(\omega({\
Jonathan Leech, Matthew Spinks
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Minimally generated Boolean algebras
Order, 1989A Boolean algebra is minimally generated iff it is the union of a continuous well-ordered chain of subalgebras, where each \(B_{\alpha +1}\) is minimally generated over \(B_{\alpha}\). This paper proves basic theorems about minimally generated algebras. For example: Theorem. Interval algebras and superatomic algebras are minimally generated.
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Generalized Boolean Algebras in Lattice-Ordered Groups
Order, 1997In this paper lattice-ordered groups and lattice-ordered modules generated by a generalized Boolean algebra (i.e., relatively complemented distributive lattice) are investigated and (complete) extensions of \(l\)-groups based on generalized Boolean algebras are studied. The main results deal with Specker \(l\)-groups, i.e., \(l\)-groups \(G\) which are
Conrad, Paul F., Darnel, Michael R.
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Continuum cardinals generalized to Boolean algebras
Journal of Symbolic Logic, 2001A number of specific cardinal numbers have been defined in terms of /fin or ωω. Some have been generalized to higher cardinals, and some even to arbitrary Boolean algebras. Here we study eight of these cardinals, defining their generalizations to higher cardinals, and then defining them for Boolean algebras. We then attempt to completely describe their
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Generalized Boolean Algebras and Applications
2018A new notion of a lattice valued Boolean algebra is introduced. It is based on an algebra with two binary, a unary and two nullary operations, which is not a crisp Boolean algebra in general. The classical equality is replaced by a lattice valued equivalence so that the Boolean algebra identities are correspondingly satisfied.
O. S. A. Bleblou +2 more
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