Abstract This paper introduces Pgeon, a meta-prover framework that generates tableau-based automated theorem provers from declarative specifications. In Pgeon, the syntax of a given calculus, its tableau inference rules, and the proof-search strategy are described in a small domain-specific language that closely follows textbook presentations. From such a specification, Pgeon instantiates a fully functional prover, handling tableau construction, rule instantiation, branching, and backtracking in a logic-agnostic manner. Proof-search is driven by a strategy engine that gives users explicit control over exploration order while keeping logical content separate from operational concerns. Pgeon supports first-order reasoning through binders, capture-avoiding substitution, and extensible term generators required for Skolemization and free variable introduction. We describe the design of the specification language, the execution model of the tool, and the strategy mechanism, and illustrate the approach on case studies covering classical first-order tableau calculus and intuitionistic propositional calculus.

International audience

An important issue of software architecture evolution is the capability for architects to keep a trace of the evolution of their work.This paper states that existing research on versioning does not cope well with software architectures.Indeed, it does not propose any adapted solutions to manage the co-evolution of the different architecture representations produced during the development process.We base our work on a three-level architecture description language (ADL) named Dedal, which represents architectures at three abstraction levels.Moreover, Dedal provides a formal base for managing version propagation.It is based on component substitutability that generalizes Liskov's substitutability principle.We propose a set of rules to support the prediction of version compatibility in terms of impact on the different architecture levels.

We propose an automatic transformation of Focal specifications to UML class diagrams. The main motivation for this work lies within the framework of the EDEMOI project, which aims to integrate and apply several requirements engineering and formal methods techniques to analyze regulations in the domain of airport security. The idea is to provide a graphical documentation of formal models for developers, and in the long-term, for certification authorities. The transformation is formally described and an implementation has been designed. We also provide a concrete example coming from the EDEMOI project.

We present the validation of regulations intended to ensure airport security in the framework of civil aviation. In particular, we describe the proofs of correctness/completeness for two standards, one at the international level and the other at the European level, and we show how the properties of the European level refines those of the international level. These models are expressed using the Focal environment, an object-oriented specification and proof system, and the proofs described by means of a declarative-like language are processed by the automated theorem prover Zenon. We show how Zenon appears quite appropriate when dealing with abstract specifications like our case study, but also how it should be controlled to present readable proofs.