Renato Neves

Hybridisation at Work

This paper presents the encoding of the hybridisation method proposed in [MMDB11, DM13] into the Hets platform.

Proof theory for hybrid(ised) logics

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. In a series of papers this process has been detailed and taken as a basis for a specification methodology for reconfigurable systems. The present paper extends this work by showing how a proof calculus (in both a Hilbert and a tableau based format) for the hybridised version of a logic can be systematically generated from a proof calculus for the latter. Such developments provide the basis for a complete proof theory for hybrid(ised) logics, and thus pave the way to the development of (dedicated) proof support. Decidability results for hybrid(ised) logics.Generation of Hilbert calculi for hybrid(ised) logics.Generation of Tableau systems for hybrid(ised) logics.

Continuity as a computational effect

The original purpose of component-based development was to provide techniques to master complex software, through composition, reuse and parametrisation. However, such systems are rapidly moving towards a level in which software becomes prevalently intertwined with (continuous) physical processes. A possible way to accommodate the latter in component calculi relies on a suitable encoding of continuous behaviour as (yet another) computational effect. This paper introduces such an encoding through a monad which, in the compositional development of hybrid systems, may play a role similar to the one played by the 1+, powerset, and distribution monads in the characterisation of partial, non deterministic and probabilistic components, respectively. This monad and its Kleisli category provide a setting in which the effects of continuity over (different forms of) composition can be suitably studied.

Completeness and Decidability Results for Hybrid(ised) Logics

Adding to the modal description of transition structures the ability to refer to specific states, hybrid(ised) logics provide an interesting framework for the specification of reconfigurable systems. The qualifier ‘hybrid(ised)’ refers to a generic method of developing, on top of whatever specification logic is used to model software configurations, the elements of an hybrid language, including nominals and modalities. In such a context, this paper shows how a calculus for a hybrid(ised) logic can be generated from a calculus of the base logic and that, moreover, it preserves soundness and completeness. A second contribution establishes that hybridising a decidable logic also gives rise to a decidable hybrid(ised) one. These results pave the way to the development of dedicated proof tools for such logics used in the design of reconfigurable systems.

An Institution for Alloy and Its Translation to Second-Order Logic

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 for more 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.

Hybrid Automata as Coalgebras

Able to simultaneously encode discrete transitions and continuous behaviour, hybrid automata are the de facto framework for the formal specification and analysis of hybrid systems. The current paper revisits hybrid automata from a coalgebraic point of view. This allows to interpret them as state-based components, and provides a uniform theory to address variability in their definition, as well as the corresponding notions of behaviour, bisimulation, and observational semantics.

An exercise on the generation of many-valued dynamic logics

Abstract In the last decades, dynamic logics have been used in different domains as a suitable formalism to reason about and specify a wide range of systems. On the other hand, logics with many-valued semantics are emerging as an interesting tool to handle devices and scenarios where uncertainty is a prime concern. This paper contributes towards the combination of these two aspects through the development of a method for the systematic construction of many-valued dynamic logics. Technically, the method is parameterised by an action lattice that defines both the computational paradigm and the truth space (corresponding to the underlying Kleene algebra and residuated lattices, respectively).

A method for rigorous design of reconfigurable systems

Reconfigurability, understood as the ability of a system to behave differently in different modes of operation and commute between them along its lifetime, is a cross-cutting concern in modern Software Engineering. This paper introduces a specification method for reconfigurable software based on a global transition structure to capture the systems reconfiguration space, and a local specification of each operation mode in whatever logic (equational, first-order, partial, fuzzy, probabilistic, etc.) is found expressive enough for handling its requirements.In the method these two levels are not only made explicit and juxtaposed, but formally interrelated. The key to achieve such a goal is a systematic process of hybridisation of logics through which the relationship between the local and global levels of a specification becomes internalised in the logic itself.

Giving Alloy a family

Lightweight formal methods ought to provide to the end user the rigorousness of mathematics, without compromising simplicity and intuitiveness. Alloy is a powerful tool, particularly successful on this mission. Limitations on the verification side, however, are known to prevent its wider use in the development of safety or mission critical applications. A number of researchers proposed ways to connect Alloy to other tools in order to meet such challenges. This papers proposal, however, is not establishing a link from Alloy to another single tool, but rather to “plunge” it into the HETS network of logics, logic translators and provers. This makes possible for Alloy specifications to “borrow” the power of several, non dedicated proof systems. Semantical foundations for this integration are discussed in detail.

A Dynamic Logic for Every Season

This paper introduces a method to build dynamic logics with a graded semantics. The construction is parametrized by a structure to support both the spaces of truth and of the domain of computations. Possible instantiations of the method range from classical (assertional) dynamic logic to less common graded logics suitable to deal with programs whose transitional semantics exhibits fuzzy or weighted behaviour. This leads to the systematic derivation of program logics tailored to specific program classes.