Effect systems are lightweight extensions to type that can verify a wide range of important properties with modest developer burden. But our general understanding effect is limited primarily where the order effects irrelevant. Understanding such in terms semilattice grounds essential issues and provides guidance when designing new systems. By contrast, sequential systems—where important—lack an...

We study functorial properties of the quantale spectrum MaxA of an arbitrary unital C*-algebra A. In particular we show that the spatialization of MaxA with respect to one of the notions of spatiality in the literature yields the locale of closed ideals of A when A is commutative. We study under general conditions functors with this property, in addition requiring that inductive limits be prese...

Various notions of observing and testing processes are placed in a uniform algebraic framework in which observations are taken as constituting a quantale. General completeness criteria are stated, and proved in our applications. 2 67("/89:&",;&<+*91(8=&>)",#"3185&.781(2"#+.,"3&3.?+*&",;&0(.*188&81/",#+*8

This paper is about a generalization of Scott’s domain theory in such a way that its definitions and theorems become meaningful in quasimetric spaces. The generalization is achieved by a change of logic: the fundamental concepts of original domain theory (order, way-below relation, Scott-open sets, continuous maps, etc.) are interpreted as predicates that are valued in an arbitrary completely d...

Preface This document is the report of my final degree project. The project consisted of an initiation to research: an unsolved mathematical problem was presented to me by my project tutor Pedro Resende, and my task was to help find a solution for it. This eventually led to writing a scientific paper with him as a co-author. This paper is currently in preparation and once finished it will be su...

Abstract We show how modal quantales arise as convolution algebras $$Q^X$$ Q X of functions from catoids X , multisemigroups equipped with source and target maps, into value or weight Q . In the tradition boolean operators we study correspondences between algebraic laws...