In a recent paper [7], J. W. Pelletier and J. Rosický published a characterization of *-simple *-quantales. Their results were adapted for the case of simple quantales by J. Paseka in [5]. In this paper we present similar characterizations which do not use a notion of discrete quantale. We also show a completely new characterization based on separating and cyclic sets. Further we explain a link...

We establish a close and previously unknown relation between quantales and groupoids, in terms of which the notion of étale groupoid is subsumed in a natural way by that of quantale. In particular, to each étale groupoid, either localic or topological, there is associated a unital involutive quantale. We obtain a bijective correspondence between localic étale groupoids and their quantales, whic...

While the study of quantale-like structures goes back up to the 1930’s (notwithstanding that the term itself was introduced in [2] in connection with certain aspects of C∗-algebras), there has recently been much interest in quantales in a variety of contexts. The most important connection probably is with Girard’s linear logic. In particular, one can enunciate the following slogan: Quantales ar...

We propose various methods for combining or amalgamating propositional languages and deductive systems. make heavy use of quantales quantale modules in the wake previous works by present other authors. also describe quite extensively relationships among algebraic order-theoretic constructions corresponding ones based on a purely logical approach.

We present a trajectory-based model for describing hybrid systems. For this we use left quantales and left semirings, thus providing a new application for these algebraic structures. Furthermore, we sketch a connection between game theory and hybrid systems.

We illustrate the idea that quantales can be regarded as algebras of experimental observations on physical systems, and we give a survey of some research in computer science where this idea has been used. We extend the mathematical framework hitherto available so that it can be applied to more general systems than before, in particular to quantum systems and systems whose behaviour is partially...

The theory of metric spaces provides an elementary introduction to topology and unies many branches of classical analysis. Using it, the intuitive notions of continuity, limit and Cauchy sequence can be developed in a very general setting. Moreover, since metric techniques are frequently much more powerful than topological ones, they make possible simpler and more elegant solutions to many prob...