Fixedpoint theorems play a fundamental role in denotational semantics of programming languages. In 1955, Tarski [6] and Davis [l] showed that a lattice L is complete if and only if every monotonic function f: L + L has a fixedpoint. Since then, other fixedpoint properties are considered, by imposing either the function to be o-continuous or the fixedpoint to be the least fixedpoint. The key que...

Several relation-algebraic algorithms for computing the cut completion of a partially ordered set are formally developed and afterwards generalized to the case of concept lattices. It is shown how the algorithms can be translated into the programming language of RelView and executed using this system. Furthermore, it is demonstrated how to obtain and draw Hasse diagrams of concept lattices as l...

In this paper the author gives necessary and sufficient conditions under which to a stable weak isometry f in a directed group G there exists a direct decomposition G = A × B of G such that f(x) = x(A) − x(B) for each x ∈ G. Further, some results on weak isometries in partially ordered groups are established. Isometries in an abelian lattice ordered group (l-group) have been introduced and inve...