- Publications
- Influence
Share This Author
Ideals and the binary discriminator in universal algebra
- I. Chajda, R. Halaš, I. Rosenberg
- Mathematics
- 1 December 1999
Abstract. We introduce the binary discriminator and the dual binary discriminator and the corresponding universal algebras with 0. The latter are related to permutability and distributivity at 0. For…
Many-valued quantum algebras
Abstract.We deal with algebras $${\bf A} = (A, \oplus, \neg, 0)$$ of the same signature as MV-algebras which are a common extension of MV-algebras and orthomodular lattices, in the sense that (i) A…
ALGEBRAIC PROPERTIES OF PRE-LOGICS
We introduce th e concept of a pre-logic which is an algebra weaker than a Hilbert algebra (an algebraic counterpart of intuitionisti c logic ) but strong enough to have deductive systems. On every…
Residuated relational systems
The aim of the present paper is to generalize the concept of residuated poset, by replacing the usual partial ordering by a generic binary relation, giving rise to relational systems which are…
Congruences in ordered sets
A concept of congruence preserving upper and lower bounds in a poset $P$ is introduced. If $P$ is a lattice, this concept coincides with the notion of lattice congruence.
The Lattice of Deductive Systems on Hilbert Algebras
- I. Chajda
- Mathematics
- 2003
The concept of deductive system on a Hilbert algebra was introduced by A. Diego. We show that the set Ded A of all deductive systems on a Hilbert algebra A forms an algebraic lattice which is…
BASIC ALGEBRAS AND THEIR APPLICATIONS AN OVERVIEW
- I. Chajda
- Mathematics
- 2011
Basic algebras were introduced as a common base for axioma- tization of many-valued propositional logics as well as of the logic of quan- tum mechanics. Since these logics were already axiomatized by…
Semimodular $λ$-lattices
The concept of a λ-lattice was introduced by V. Snášel ([3]) in order to generalize some lattice concepts for directed posets whose elements need not have suprema or infima. We extend the concept of…
...
...