Abstract
Often in Software Engineering a modelling formalism has to support scenarios of inconsistency in which several requirements either reinforce or contradict each other. Paraconsistent transition systems are proposed in this paper as one such formalism: states evolve through two accessibility relations capturing weighted evidence of a transition or its absence, respectively. Their weights come from a specific residuated lattice. A category of these systems, and the corresponding algebra, is defined providing a formal setting to model different application scenarios. One of them, dealing with the effect of quantum decoherence in quantum programs, is used for illustration purposes.

Abstract

Abstract
Event/data-based systems are controlled by events, their local data state may change in reaction to events. Numerous methods and notations for specifying such reactive systems have been designed, though with varying focus on the different development steps and their refinement relations. We first briefly review some of such methods, like temporal/modal logic, TLA, UML state machines, symbolic transition systems, CSP, synchronous languages, and Event-B with their support for parallel composition and refinement. We then present E. -logic for covering a broad range of abstraction levels of event/data-based systems from abstract requirements to constructive specifications in a uniform foundation. E. -logic uses diamond and box modalities over structured events adopted from dynamic logic, for recursive process specifications it offers (control) state variables and binders from hybrid logic. The semantic interpretation relies on event/data transition systems; specification refinement is defined by model class inclusion. Constructive operational specifications given by state transition graphs can be characterised by a single E. -sentence. Also a variety of implementation constructors is available in E. -logic to support, among others, event refinement and parallel composition. Thus the whole development process can rely on E. -logic and its semantics as a common basis.

Abstract
This paper introduces a class of automata and associated languages, suitable to model a computational paradigm of fuzzy systems, in which both vagueness and simultaneity are taken as first-class citizens. This requires a weighted semantics for transitions and a precise notion of a synchronous product to enforce the simultaneous occurrence of actions. The usual relationships between automata and languages are revisited in this setting, including a specific Kleene theorem.

Abstract