14 papers · 1 filter
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…
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…