We study relations between predicate transformers and mul-tifunctions in a topological setting based on closure operators. We give topological deenitions of safety and liveness predicates and using these predicates we deene predicate transformers. State transformers are mul-tifunctions with values in the collection of xed points of a closure operator. We derive several isomorphisms between pred...

When closure operators are deened over gures in the plane, they are normally deened with respect to convex closure in the Euclidean plane. This report concentrates on discrete closure operators deened over the discrete, rectilinear plane. Basic to geometric convexity is the concept of a geodesic, or shortest path. Such geodesics can be regarded as the closure of two points. But, given the usual...

It is well known that closure operators on a complete lattice, ordered pointwise, give rise to a complete lattice, and this basic fact plays an important rôle in many fields of the semantics area, notably in domain theory and abstract interpretation. We strengthen that result by showing that closure operators on any directed-complete partial order (CPO) still form a complete lattice. An example...

In this paper we highlight the specific meaning of images of fuzzy sets under fuzzy relations in the context of fuzzy topology. More precisely we show that fuzzy modifiers taking direct and superdirect images of fuzzy sets under fuzzy pre-orderings are respectively closure and interior operators, inducing fuzzy topologies. Furthermore we investigate under which conditions the same applies to th...

We present a term rewriting system to solve a class of open problems that are generalisations of Kuratowski’s closure-complement theorem. The problems are concerned with finding the number of distinct sets that can be obtained by applying combinations of axiomatically defined set operators. While the original problem considers only closure and complement of a topological space as operators, it ...