We introduce the notion of relative co-annihilator in lattice equality algebras and investigate some important properties of it. Then, we obtain some interesting relations among -irreducible filters, positive implicative filters, prime filters and relative co-annihilators. Given a lattice equality algebra and a filter of , we define the set of all -involutive filters of and show that by defining some operations on it, it makes a BL-algebra.
In this paper, we present the representation for uni-nullnorms with disjunctive underlying uninorms on bounded lattices. It is shown that our method can cover the representation of nullnorms on bounded lattices and some of existing construction methods for uni-nullnorms on bounded lattices. Illustrative examples are presented simultaneously. In addition, the representation of null-uninorms with conjunctive underlying uninorms on bounded lattices is obtained dually.
In the field of automatic proving, the study of the sets of prime implicants or implicates of a formula has proven to be very important. If we focus on non-classical logics and, in particular, on temporal logics, such study is useful even if it is restricted to the set of unitary implicants/implicates [P. Cordero, M. Enciso, and I. de Guzmán: Structure theorems for closed sets of implicates/implicants in temporal logic. (Lecture Notes in Artificial Intelligence 1695.) Springer–Verlag, Berlin 1999]....
As a generalization of filters in lattice implication algebras, the notion of rough filters in lattice implication algebras is introduced, and some of their properties are considered.