In this paper we describe an approach, implemented in a system named REFINER, to combining Boolean information retrieval and content-based navigation with concept lattices. When REFINER is presented with a Boolean query, it builds and displays a portion of the concept lattice associated with the documents being searched centered around the user query. The cluster network displayed by REFINER sh...

Heribert Vollmer : Boolean functions and Post’s lattice with applications to complexity theory. A Boolean functions f can be obtained from a set B of Boolean functions by superposition, if f can be written as a nested composition of functions from B. In the 1940’s, Emil Post determined the complete list of all sets of Boolean functions closed under superposition, and for each of them, he constr...

The main result of this paper is the following theorem: If a projective Boolean algebra B is generated by its sublattice L, then there is a projective distributive lattice D which is a sublattice of L and generates B.

‎The notion of (Boolean) uni-soft filters‎ ‎in MTL-algebras is introduced‎, ‎and several properties of them are‎ ‎investigated‎. ‎Characterizations of (Boolean) uni-soft filters are discussed‎, ‎and some (necessary and sufficient) conditions‎ ‎for a uni-soft filter to be Boolean are provided‎. ‎The condensational property for a Boolean uni-soft filter is established.

Stonean residuated lattices are closely related to Stone algebras since the bounded lattice reduct of a distributive Stonean residuated lattice is a Stone algebra. In the present work we follow the ideas presented by Chen and Grätzer and try to apply them for the case of Stonean residuated lattices. Given a Stonean residuated lattice, we consider the triple formed by its Boolean skeleton, its a...

We show that the automorphism group of the countable universal distributive lattice has strong uncountable cofinality, and we adapt the method to deduce the strong uncountable cofinality of the automorphism group of the countable universal generalized boolean algebra.