8 papers · 1 filter
Quantales carrying ortholattice structure
Michal Botur, David Kruml, Jan Paseka
This paper investigates the intersection of residuated structures from many-valued logic and orthomodular lattices from quantum logic. We explore whether non-Boolean structures can…
A new representation of finite Hoops using a new type of product of structures
Michal Botur
In this paper we show that a new type of products hoops can be defined which, in the case of finite hoops, can describe an arbitrary hoop as the product of its arbitrar…
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…
Kites and representations of pseudo MV-algebras
Michal Botur, Tomasz Kowalski
We investigate the structure of perfect residuated lattices, focussing especially on perfect pseudo MV-algebras. We show that perfect pseudo MV-algebras can be represented as a gen…
Many-valued aspects of tense an related operators
Michal Botur, Jan Paseka, Richard Smolka
Our research builds upon Halmos's foundational work on functional monadic Boolean algebras and our previous work on tense operators to develop three essential constructions, includ…
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…