Abstract
Lightweight formal methods, of which Alloy is a prime example, combine the rigour of mathematics without compromising simplicity of use and suitable tool support. In some cases, however, the verification of safety or mission critical software entails the need formore sophisticated technologies, typically based on theorem provers. This explains a number of attempts to connect Alloy to specific theorem provers documented in the literature. This chapter, however, takes a different perspective: instead of focusing on one more combination of Alloy with still another prover, it lays out the foundations to fully integrate this system in the Hets platform which supports a huge network of logics, logic translators and provers. This makes possible for Alloy specifications to “borrow” the power of several, non dedicated proof systems. The chapter extends the authors’ previous work on this subject by developing in full detail the semantical foundations for this integration, including a formalisation of Alloy as an institution, and introducing a new, more general translation of the latter to second-order logic.

Abstract
This paper extends the authors' previous work on a formal approach to the specification of reconfigurable systems, introduced in [7], in which configurations are taken as local states in a suitable transition structure. The novelty is the explicit consideration that not only the realisation of a service may change from a configuration to another, but also the set of services provided and even their functionality, may themselves vary. In other words, interfaces may evolve, as well.

Abstract
Boilerplates are simplified, normative English texts, intended to capture software requirements in a controlled way. This paper proposes a pallet of boilerplates as a requirements modelling language for reconfigurable systems, i.e., systems structured in different modes of execution among which they can dynamically commute. The language semantics is given as an hybrid logic, in an institutional setting. The mild use made of the theory of institutions, which, to a large extent, may be hidden from the working software engineer, not only provides a rigorous and generic semantics, but also paves the way to tool-supported validation.

Abstract
Hierarchical transition systems provide a popular mathematical structure to represent state-based software applications in which different layers of abstraction are represented by inter-related state machines. The decomposition of high level states into inner sub-states, and of their transitions into inner sub-transitions is common refinement procedure adopted in a number of specification formalisms. This paper introduces a hybrid modal logic for k-layered transition systems, its first-order standard translation, a notion of bisimulation, and a modal invariance result. Layered and hierarchical notions of refinement are also discussed in this setting.

Abstract
In Computer Science stepwise refinement of algebraic specifications is a well-known formal methodology for rigorous program development. This paper illustrates how techniques from Algebraic Logic, in particular that of interpretation, understood as a multifunction that preserves and reflects logical consequence, capture a number of relevant transformations in the context of software design, reuse, and adaptation, difficult to deal with in classical approaches. Examples include data encapsulation and the decomposition of operations into atomic transactions. But if interpretations open such a new research avenue in program refinement, (conceptual) tools are needed to reason about them. In this line, the paper's main contribution is a study of the correspondence between logical interpretations and morphisms of a particular kind of coalgebras. This opens way to the use of coalgebraic constructions, such as simulation and bisimulation, in the study of interpretations between (abstract) logics.

Abstract
Hybridisation is a systematic process along which the characteristic features of hybrid logic, both at the syntactic and the semantic levels, are developed on top of an arbitrary logic framed as an institution. It also captures the construction of first-order encodings of such hybridised institutions into theories in first-order logic. The method was originally developed to build suitable logics for the specification of reconfigurable software systems on top of whatever logic is used to describe local requirements of each system’s configuration. Hybridisation has, however, a broader scope, providing a fresh example of yet another development in combining and reusing logics driven by a problem from Computer Science. This paper offers an overview of this method, proposes some new extensions, namely the introduction of full quantification leading to the specification of dynamic modalities, and exemplifies its potential through a didactical application. It is discussed how hybridisation can be successfully used in a formal specification course in which students progress from equational to hybrid specifications in a uniform setting, integrating paradigms, combining data and behaviour, and dealing appropriately with systems evolution and reconfiguration. © Springer International Publishing Switzerland 2016.