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  1.  7
    Implication in Sharply Paraorthomodular and Relatively Paraorthomodular Posets.Ivan Chajda, Davide Fazio, Helmut Länger, Antonio Ledda & Jan Paseka - 2024 - In Jacek Malinowski & Rafał Palczewski (eds.), Janusz Czelakowski on Logical Consequence. Springer Verlag. pp. 419-446.
    In this paper we show that several classes of partially ordered structures having paraorthomodular reducts, or whose sections may be regarded as paraorthomodular posets, admit a quite natural notion of implication, that admits a suitable notion of adjointness. Within this framework, we propose a smooth generalization of celebrated Greechie’s theorems on amalgams of finite Boolean algebras to the realm of Kleene lattices.
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  2.  4
    Representability of Kleene Posets and Kleene Lattices.Ivan Chajda, Helmut Länger & Jan Paseka - forthcoming - Studia Logica:1-37.
    A Kleene lattice is a distributive lattice equipped with an antitone involution and satisfying the so-called normality condition. These lattices were introduced by J. A. Kalman. We extended this concept also for posets with an antitone involution. In our recent paper (Chajda, Länger and Paseka, in: Proceeding of 2022 IEEE 52th International Symposium on Multiple-Valued Logic, Springer, 2022), we showed how to construct such Kleene lattices or Kleene posets from a given distributive lattice or poset and a fixed element of (...)
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  3.  11
    Algebraic Properties of Paraorthomodular Posets.Ivan Chajda, Davide Fazio, Helmut Länger, Antonio Ledda & Jan Paseka - 2022 - Logic Journal of the IGPL 30 (5):840-869.
    Paraorthomodular posets are bounded partially ordered sets with an antitone involution induced by quantum structures arising from the logico-algebraic approach to quantum mechanics. The aim of the present work is starting a systematic inquiry into paraorthomodular posets theory both from algebraic and order-theoretic perspectives. On the one hand, we show that paraorthomodular posets are amenable of an algebraic treatment by means of a smooth representation in terms of bounded directoids with antitone involution. On the other, we investigate their order-theoretical features (...)
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  4.  27
    How to Produce S-Tense Operators on Lattice Effect Algebras.Ivan Chajda, Jiří Janda & Jan Paseka - 2014 - Foundations of Physics 44 (7):792-811.
    Tense operators in effect algebras play a key role for the representation of the dynamics of formally described physical systems. For this, it is important to know how to construct them on a given effect algebra \( E\) and how to compute all possible pairs of tense operators on \( E\) . However, we firstly need to derive a time frame which enables these constructions and computations. Hence, we usually apply a suitable set of states of the effect algebra \( (...)
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  5.  38
    Considerable Sets of Linear Operators in Hilbert Spaces as Operator Generalized Effect Algebras.Jan Paseka & Zdenka Riečanová - 2011 - Foundations of Physics 41 (10):1634-1647.
    We show that considerable sets of positive linear operators namely their extensions as closures, adjoints or Friedrichs positive self-adjoint extensions form operator (generalized) effect algebras. Moreover, in these cases the partial effect algebraic operation of two operators coincides with usual sum of operators in complex Hilbert spaces whenever it is defined. These sets include also unbounded operators which play important role of observables (e.g., momentum and position) in the mathematical formulation of quantum mechanics.
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