4 citations · 13 across the 28 of their papers we have counts for
18 papers · 1 filter
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…
Operators on complemented lattices
Ivan Chajda, Helmut Länger
The present paper deals with complemented lattices where, however, a unary operation of complementation is not explicitly assumed. This means that an element can have several compl…
Tense logic based on finite orthomodular posets
Ivan Chajda, Helmut Länger
It is widely accepted that the logic of quantum mechanics is based on orthomodular posets. However, such a logic is not dynamic in the sense that it does not incorporate time dimen…
Operator residuation in orthomodular posets of finite height
Ivan Chajda, Helmut Länger
We show that for every orthomodular poset P of finite height there can be defined two operators forming an adjoint pair with respect to an order-like relation defined on the power…
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…
Implication in finite posets with pseudocomplemented sections
Ivan Chajda, Helmut Länger
It is well-known that relatively pseudocomplemented lattices can serve as an algebraic semantics of intuitionistic logic. To extend the concept of relative pseudocomplementation to…
Logical and algebraic properties of generalized orthomodular posets
Ivan Chajda, Helmut Länger
Generalized orthomodular posets were introduced recently by D. Fazio, A. Ledda and the first author of the present paper in order to establish a useful tool for studying the logic…
Filters and congruences in sectionally pseudocomplemented lattices and posets
Ivan Chajda, Helmut Länger
In our previous papers, together with J. Paseka we introduced so-called sectionally pseudocomplemented lattices and posets and illuminated their role in algebraic constructions. We…
Consistent posets
Ivan Chajda, Helmut Länger
We introduce so-called consistent posets which are bounded posets with an antitone involution ' where the lower cones of x,x' and of y,y' coincide provided x,y are different form 0…
The logic of orthomodular posets of finite height
Ivan Chajda, Helmut Länger
Orthomodular posets form an algebraic formalization of the logic of quantum mechanics. The question is how to introduce the connective implication in such a logic. We show that thi…
The logic induced by effect algebras
Ivan Chajda, Radomír Halaš, Helmut Länger
Effect algebras form an algebraic formalization of the logic of quantum mechanics. For lattice effect algebras E we investigate a natural implication and prove that the implication…
Residuation in finite posets
Ivan Chajda, Helmut Länger
When an algebraic logic based on a poset instead of a lattice is investigated then there is a natural problem how to introduce the connective implication to be everywhere defined a…
Residuation in lattice effect algebras
Ivan Chajda, Helmut Länger
We introduce the concept of a quasiresiduated lattice and prove that every lattice effect algebra can be organized into a commutative quasiresiduated lattice with divisibility. Als…
Relatively residuated lattices and posets
Ivan Chajda, Helmut Länger
It is known that every relatively pseudocomplemented lattice is residuated and, moreover, it is distributive. Unfortunately, non-distributive lattices with a unary operation satisf…
Left residuated operators induced by posets with a unary operation
Ivan Chajda, Helmut Länger
The concept of operator left residuation has been introduced by the authors in a previous paper. Modifications of so-called quantum structures, in particular orthomodular posets, l…
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…
Residuation in non-associative MV-algebras
Ivan Chajda, Helmut Länger
It is well known that every MV-algebra can be converted into a residuated lattice satisfying divisibility and the double negation law. In our previous papers we introduced the conc…