Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we initiate the study of soft normed rings by soft set theory. The notions of soft normed rings, soft normed ideals, soft complete normed rings are introduced and also several related properties and examples are given.

Recent studies reveal that branching bisimilarity is decidable for both nBPP (normed Basic Parallel Processes) and nBPA (normed Basic Process Algebras). These results lead to the question if there are any other models in the hierarchy of PRS (Process Rewrite Systems) whose branching bisimilarity is decidable. It is shown in this paper that the branching bisimilarity for both nOCN (normed One Co...

We propose a model of full propositional linear logic based on topological vector spaces. The essential feature is that we consider partially ordered vector spaces, or, rather, positive cones in such spaces. Thus we introduce a category whose objects are dual pairs of normed cones satisfying certain specific completeness properties, such as existence of norm-bounded monotone suprema, and whose ...

We consider the problem of deciding regularity of normed BPP and normed BPA processes. A process is regular if it is bisimilar to a process with finitely many states. We show that regularity of normed BPP and normed BPA processes is decidable in polynomial time and we present constructive regularity tests. Combining these two results we obtain a rich subclass of normed PA processes (called sPA)...

Definition 1.3 (Banach Spaces). It is easy to show that any convergent sequence in a normed linear space is a Cauchy sequence. However, it may or may not be true in an arbitrary normed linear space that all Cauchy sequences are convergent. A normed linear space X which does have the property that all Cauchy sequences are convergent is said to be complete. A complete normed linear space is calle...