6 papers · 1 filter
On -based orthomodular dynamic algebras
Jan Paseka, Juanda Kelana Putra, Richard Smolka
This paper establishes a categorical equivalence between the category of complete orthomodular lattices and the category of -b…
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…
Categories of orthosets and adjointable maps
Jan Paseka, Thomas Vetterlein
An orthoset is a non-empty set together with a symmetric and irreflexive binary relation , called the orthogonality relation. An orthoset with 0 is an orthoset augmented wit…
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 quantales and complete orthomodular lattices
Michal Botur, Jan Paseka, Richard Smolka
Our approach establishes a natural correspondence between complete orthomodular lattices and certain types of quantales. Firstly, given a complete orthomodular lattice X, we associ…
A dagger kernel category of complete orthomodular lattices
Michal Botur, Jan Paseka, Richard Smolka
Dagger kernel categories, a powerful framework for studying quantum phenomena within category theory, provide a rich mathematical structure that naturally encodes key aspects of qu…