25 citations · 39 across the 40 of their papers we have counts for
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Operators on complemented posets
Michal Botur, Ivan Chajda, Helmut Länger
Given a complemented poset P, we can assign to every element x of P the set x^+ of all its complements. We study properties of the operator ^+ on P, in particular, we are intereste…
Operators Max L and Min U and duals of Boolean posets
Ivan Chajda, Miroslav Kolařík, Helmut Länger
When working with posets which are not necessarily lattices, one has a lack of lattice operations which causes problems in algebraic constructions. This is the reason why we use th…
The variety of complemented lattices where the Sasaki operations form an adjoint pair
Václav Cenker, Ivan Chajda, Helmut Länger
The Sasaki projection was introduced as a mapping from the lattice of closed subspaces of a Hilbert space onto one of its segments. To use this projection and its dual so-called Sa…
Implications in pseudocomplemented and Stone lattices
Ivan Chajda, Helmut Länger
Two kinds of the connective implication are introduced as term operations of a pseudocomplemented lattice. It is shown that they share a lot of properties with the intuitionistic i…
The intuitionistic-like logic based on a poset
Ivan Chajda, Helmut Länger
The aim of the present paper is to show that the concept of intuitionistic logic based on a Heyting algebra can be generalized in such a way that it is formalized by means of a bou…
The logic of effect algebras incorporating time dimension
Ivan Chajda, Helmut Länger
Effect algebras were introduced in order to describe the structure of effects, i.e. events in quantum mechanics. They are partial algebras describing the logic behind the correspon…
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…
The logic with unsharp implication and negation
Ivan Chajda, Helmut Länger
It is well-known that intuitionistic logics can be formalized by means of Brouwerian semilattices, i.e. relatively pseudocomplemented semilattices. Then the logical connective impl…
The logic of quantum mechanics incorporating time dimension
Ivan Chajda, Helmut Länger
Similarly as classical propositional calculus is based algebraically on Boolean algebras, the logic of quantum mechanics was based on orthomodular lattices by G. Birkhoff and J. vo…
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…
Join-semilattices whose principal filters are pseudocomplemented lattices
Ivan Chajda, Helmut Länger
This paper deals with join-semilattices whose sections, i.e. principal filters, are pseudocomplemented lattices. The pseudocomplement of a\vee b in the section [b,1] is denoted by…
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.…
On ring-like structures of lattice-ordered numerical events
Dietmar Dorninger, Helmut Länger
Let S be a set of states of a physical system. The probabilities p(s) of the occurrence of an event when the system is in different states s of S define a function from S to [0,1]…
Properties of the connective implication in effect algebras
Ivan Chajda, Helmut Länger
Effect algebras form a formal algebraic description of the structure of the so-called effects in a Hilbert space which serves as an event-state space for effects in quantum mechani…
How to introduce the connective implication in orthomodular posets
Ivan Chajda, Helmut Länger
Since orthomodular posets serve as an algebraic axiomatization of the logic of quantum mechanics, it is a natural question how the connective of implication can be defined in this…
Unsharp residuation in effect algebras
Ivan Chajda, Helmut Länger
Effect algebras and pseudoeffect algebras were introduced by Foulis, Bennett, Dvurecenskij and Vetterlein as so-called quantum structures which serve as an algebraic axiomatization…
Boolean properties and Bell-like inequalities of numerical events
D. Dorninger, H. Länger, M. J. Mcaczyński
Let S be a set of states of a physical system and p(s) be the probability of the occurrence of an event when the system is in state s. A function p from S to [0,1] is called a nume…
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…
Residuation in modular lattices and posets
Ivan Chajda, Helmut Länger
We show that every complemented modular lattice can be converted into a left residuated lattice where the binary operations of multiplication and residuum are term operations. The…
Residuated operators in complemented posets
Ivan Chajda, Helmut Länger
Using the operators of taking upper and lower cones in a poset with a unary operation, we define operators M(x,y) and R(x,y) in the sense of multiplication and residuation, respect…