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… Expand

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… Expand

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… Expand

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… Expand

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 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… Expand

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… Expand

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… Expand