Abstract
This paper introduces a rigorous methodology for requirements specification of systems that react to external stimulus by evolving through different operational modes. In each mode different functionalities are provided. Starting from a classical state-machine specification, the envisaged methodology interprets each state as a different mode of operation endowed with an algebraic specification of the corresponding functionality. Specifications are given in an expressive variant of hybrid logic which is, at a later stage, translated into first-order logic to bring into scene suitable tool support. The paper's main contribution is to provide rigorous foundations for the method, framing specification logics as institutions and the translation process as a comorphism between them.

Abstract
The paper discusses the role of interpretations, understood as multifunctions that preserve and reflect logical consequence, as refinement witnesses in the general setting of p -institutions. This leads to a smooth generalization of the "refinement by interpretation" approach, recently introduced by the authors in more specific contexts. As a second, yet related contribution a basis is provided to build up a refinement calculus of structured specifications in and across arbitrary f-institutions. © C.J. Rodrigues, M.A. Martins, A. Madeira & L.S. Barbosa This work is licensed under the Creative Commons Attribution License.

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

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.