Karim Berkani

Tableaux modulo theories using superdeduction: an application to the verification of B proof rules with the zenon automated theorem prover

We propose a method which allows us to develop tableaux modulo theories using the principles of superdeduction, among which the theory is used to enrich the deduction system with new deduction rules. This method is presented in the framework of the Zenon automated theorem prover, and is applied to the set theory of the B method. This allows us to provide another prover to Atelier B, which can be used to verify B proof rules in particular. We also propose some benchmarks, in which this prover is able to automatically verify a part of the rules coming from the database maintained by Siemens IC-MOL.

Validation des règles de base de l'Atelier B

The B method enables us to build a correct program from an abstract specification expressing the requirements, by refining step by step the abstract specification. Each step must be validated by proof with the help, for example, of the Atelier B proof tool. The Atelier B proof tool uses proof tactics and basic rules. Several years ago, experts proved these rules manually. Our objective is to validate the basic rules in a formal way. This article provides a formalization of a subset of the B language within the Coq system. Then we propose a methodology to validate the basic rules of the Atelier B or more precisely a convenient subset of these rules.

Modeling the CBTC Railway System of Siemens with ScOLa

Considering their increasing complexity, industrial systems are, in general, specified in a natural language. In railway systems, the design phase results an ambiguous and laborious system specification. The objective of this paper is to present ScOLa, a formal modeling language based on scenarios and built for railway system specifications. Its novelty resides in its restriction to a small set of concepts and its multiple representations (textual and graphical). The language offers means to understand what the system is supposed to do and to be as well as to support a dialog with experts so to be sure that they got everything correctly. The language is depicted on the railway automation solution Trainguard MT CBTC of Siemens.

Tableaux Modulo Theories Using Superdeduction

We propose a method which allows us to develop tableaux modulo theories using the principles of superdeduction, among which the theory is used to enrich the deduction system with new deduction rules. This method is presented in the framework of the Zenon automated theorem prover, and is applied to the set theory of the B method. This allows us to provide another prover to Atelier B, which can be used to verify B proof rules in particular. We also propose some benchmarks, in which this prover is able to automatically verify a part of the rules coming from the database maintained by Siemens IC-MOL.

Tableaux Modulo Theories using Superdeduction - An Application to the Veri fication of B Proof Rules with the Zenon Automated Theorem Prover

We propose a method which allows us to develop tableaux modulo theories using the principles of superdeduction, among which the theory is used to enrich the deduction system with new deduction rules. This method is presented in the framework of the Zenon automated theorem prover, and is applied to the set theory of the B method. This allows us to provide another prover to Atelier B, which can be used to verify B proof rules in particular. We also propose some benchmarks, in which this prover is able to automatically verify a part of the rules coming from the database maintained by Siemens IC-MOL.