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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…
The intuitionistic-like logic based on a poset
Ivan Chajda, Helmut Länger
The aim of the present paper is to show that the concept of intuitionistic logic based on a Heyting algebra can be generalized in such a way that it is formalized by means of a bou…
The logic of effect algebras incorporating time dimension
Ivan Chajda, Helmut Länger
Effect algebras were introduced in order to describe the structure of effects, i.e. events in quantum mechanics. They are partial algebras describing the logic behind the correspon…