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    Arithmetic lattices and weak spectral geometry

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    This note is an expansion of three lectures given at the workshop "Topology, Complex Analysis and Arithmetic of Hyperbolic Spaces" held at Kyoto University in December of 2006 and will appear in the proceedings for this workshop.Comment: To appear in workshop proceedings for "Topology, Complex Analysis and Arithmetic of Hyperbolic Spaces". Comments welcom

    Formal concept analysis and structures underlying quantum logics

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    A Hilbert space HH induces a formal context, the Hilbert formal context H‾\overline H, whose associated concept lattice is isomorphic to the lattice of closed subspaces of HH. This set of closed subspaces, denoted C(H)\mathcal C(H), is important in the development of quantum logic and, as an algebraic structure, corresponds to a so-called ``propositional system'', that is, a complete, atomistic, orthomodular lattice which satisfies the covering law. In this paper, we continue with our study of the Chu construction by introducing the Chu correspondences between Hilbert contexts, and showing that the category of Propositional Systems, PropSys, is equivalent to the category of ChuCorsH\text{ChuCors}_{\mathcal H} of Chu correspondences between Hilbert contextsUniversidad de Málaga. Campus de Excelencia Internacional Andalucía Tech
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