6 papers · 1 filter
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…
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…
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…