12 citations · 55 across the 30 of their papers we have counts for
21 papers · 1 filter
Foulis m-semilattices and their modules
Michal Botur, Jan Paseka, Milan Lekár
Building upon the results of Jacobs, we show that the category OMLatLin of orthomodular lattices and linear maps forms a dagger category. For each orthomodular lattice X, we constr…
Tense logics based on posets
Ivan Chajda, Helmut Länger, Antonio Ledda +2
Not all logical systems can be captured using algebras. We see this in classical logic (formalized by Boolean algebras) and many-valued logics (like Lukasiewicz logic with MV-algeb…
Quantum implications in orthomodular posets
Kadir Emir, Jan Paseka
We show that, for every orthogonal lub-complete poset P, we can introduce multiple-valued implications sharing properties with quantum implications presented for orthomodular latti…
Implication in sharply paraorthomodular and relatively paraorthomodular posets
Ivan Chajda, Davide Fazio, Helmut Länger +2
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 qu…
Representability of Kleene posets and Kleene lattices
Ivan Chajda, Helmut Länger, Jan Paseka
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…
Constructions of Kleene lattices
Ivan Chajda, Helmut Laenger, Jan Paseka
We present an easy construction producing a Kleene lattice K from an arbitrary distributive lattice L and a non-empty subset of L. We show that L can be embedded into K and compute…
An algebraic analysis of implication in non-distributive logics
Ivan Chajda, Kadir Emir, Davide Fazio +3
In this paper, we introduce the concept of a (lattice) skew Hilbert algebra as a natural generalization of Hilbert algebras. This notion allows a unified treatment of several struc…
Linear orthogonality spaces as a new approach to quantum logic
Kadir Emir, David Kruml, Jan Paseka +1
The notion of an orthogonality space was recently rediscovered as an effective means to characterise the essential properties of quantum logic. The approach can be considered as mi…
Algebraic properties of paraorthomodular posets
Ivan Chajda, Davide Fazio, Helmut Länger +2
Paraorthomodular posets are bounded partially ordered set with an antitone involution induced by quantum structures arising from the logico-algebraic approach to quantum mechanics.…
Residuated operators and Dedekind-MacNeille completion
Ivan Chajda, Helmut Länger, Jan Paseka
The concept of operator residuation for bounded posets with unary operation was introduced by the first two authors. It turns out that in some cases when these operators are transf…
A representation theorem for quantale valued sup-algebras
Jan Paseka, Radek Šlesinger
With this paper we hope to contribute to the theory of quantales and quantale-like structures. It considers the notion of -sup-algebra and shows a representation theorem for suc…
The groupoid-based logic for lattice effect algebras
I. Chajda, H. Länger, J. Paseka
The aim of the paper is to establish a certain logic corresponding to lattice effect algebras. First, we answer a natural question whether a lattice effect algebra can be represent…
Set Representation of Dynamic De Morgan algebras
Ivan Chajda, Jan Paseka
By a De Morgan algebra is meant a bounded poset equipped with an antitone involution considered as negation. Such an algebra can be considered as an algebraic axiomatization of a p…
Galois connections and tense operators on q-effect algebras
Ivan Chajda, Jan Paseka
For effect algebras, the so-called tense operators were already introduced by Chajda and Paseka. They presented also a canonical construction of them using the notion of a time fra…
Filters on some classes of quantum B-algebras
Michal Botur, Jan Paseka
In this paper, we continue the study of quantum B-algebras with emphasis on filters on integral quantum B-algebras. We then study filters in the setting of pseudo-hoops. First, we…
Transition operators assigned to physical systems
Ivan Chajda, Jan Paseka
By a physical system we recognize a set of propositions about a given system with their truth-values depending on the states of the system. Since every physical system can go from…
On the extensions of Di Nola's Theorem
Michal Botur, Jan Paseka
The main aim of this paper is to present a direct proof of Di Nola's representation Theorem for MV-algebras and to extend his results to the restriction of the standard MV-algebra…
Triple Representation Theorem for orthocomplete homogeneous effect algebras
Josef Niederle, Jan Paseka
The aim of our paper is twofold. First, we thoroughly study the set of meager elements , the set of sharp elements and the center in the setting of meager-ortho…
Triple Representation Theorem for homogeneous effect algebras
Josef Niederle, Jan Paseka
The aim of our paper is to prove the Triple Representation Theorem, which was established by Jenča in the setting of complete lattice effect algebras, for a special class of homoge…
Homogeneous orthocomplete effect algebras are covered by MV-algebras
Josef Niederle, Jan Paseka
The aim of our paper is twofold. First, we thoroughly study the set of meager elements Mea(E) and the set of hypermeager elements HMea(E) in the setting of homogeneous effect algeb…
More about sharp and meager elements in Archimedean atomic lattice effect algebras
Josef Niederle, Jan Paseka
The aim of our paper is twofold. First, we thoroughly study the set of meager elements M(E), the center C(E) and the compatibility center B(E)in the setting of atomic Archimedean l…