Focused labeled proof systems for modal logic

International audienceFocused proofs are sequent calculus proofs that group inference rules into alternating positive and negative phases. These phases can then be used to define macro-level inference rules from Gentzen's original and tiny introduction and structural rules. We show here that the inference rules of labeled proof systems for modal logics can similarly be described as pairs of such phases within the LKF focused proof system for first-order classical logic. We consider the system G3K of Negri for the modal logic K and define a translation from labeled modal formulas into first-order polarized formulas and show a strict correspondence between derivations in the two systems, i.e., each rule application in G3K corresponds to a bipole—a pair of a positive and a negative phases—in LKF. Since geometric axioms (when properly polarized) induce bipoles, this strong correspondence holds for all modal logics whose Kripke frames are characterized by geometric properties. We extend these results to present a focused labeled proof system for this same class of modal logics and show its soundness and completeness. The resulting proof system allows one to define a rich set of normal forms of modal logic proofs

A Distributed and Trusted Web of Formal Proofs

International audienceMost computer checked proofs are tied to the particular technology of a prover's software. While sharing results between proof assistants is a recognized and desirable goal, the current organization of theorem proving tools makes such sharing an exception instead of the rule. In this talk, I argue that we need to turn the current architecture of proof assistants and formal proofs inside-out. That is, instead of having a few mature theorem provers include within them their formally checked theorems and proofs, I propose that proof assistants should sit on the edge of a web of formal proofs and that proof assistant should be exporting their proofs so that they can exist independently of any theorem prover. While it is necessary to maintain the dependencies between definitions, theories, and theorems, no explicit library structure should be imposed on this web of formal proofs. Thus a theorem and its proofs should not necessarily be located at a particular URL or within a particular prover's library. While the world of symbolic logic and proof theory certainly allows for proofs to be seen as global and permanent objects, there is a lot of research and engineering work that is needed to make this possible. I describe some of the required research and development that must be done to achieve this goal

Automating the Verification of Floating-Point Programs

International audienceIn the context of deductive program verification, handling floating-point computations is challenging. The level of proof success and proof automation highly depends on the way the floating-point operations are interpreted in the logic supported by back-end provers. We address this challenge by combining multiple techniques to separately prove different parts of the desired properties. We use abstract interpretation to compute numerical bounds of expressions, and we use multiple automated provers, relying on different strategies for representing floating-point computations. One of these strategies is based on the native support for floating-point arithmetic recently added in the SMT-LIB standard. Our approach is implemented in the Why3 environment and its front-end SPARK 2014 for the development of safety-critical Ada programs. It is validated experimentally on several examples originating from industrial use of SPARK 2014

Comportamento de cura de adesivo epoxídico contendo grupo mercaptana avaliado por espectroscopia no infravermelho (MIR/NIR) e calorimetria exploratória diferencial (DSC) Cure behavior of epoxy adhesive containig mercaptan group evaluated by infrared spectroscopy (MIR/NIR) and differential scanning calorimetry (DSC)

No presente trabalho, a flexibilidade de um adesivo epoxídico contendo diglicidiléter de bisfenol A (DGEBA) e dietilenotriamina (DETA) como agente de cura foi modificada pela adição de um segundo componente contendo grupos mercaptana (CAPCURE). A adição de amianto ao adesivo contendo CAPCURE também foi avaliada. As reações entre os grupos epoxídicos e os grupos amina, assim como entre os grupos epoxídicos e os grupos mercaptana, foram estudadas nas regiões espectrais do infravermelho médio (MIR) e próximo (NIR). Observou-se que o amianto não interfere nas reações de cura e que a espectroscopia FT-NIR evidencia melhor as alterações espectrométricas ocorridas durante as reações em relação à análise FT-MIR. O tempo das reações de cura foi monitorado por calorimetria exploratória diferencial (DSC), observando-se que a introdução do CAPCURE acelerou a cura da resina. A energia de ativação (Ea) das reações de cura foi obtida pelos métodos de Barrett e Borchardt-Daniels. Os adesivos contendo CAPCURE mostraram Ea em torno de 30 kJ.mol-1, enquanto o adesivo DGEBA/DETA apresentou Ea de 46 kJ.mol-1, ambas calculadas pelo método de Barrett.<br>In the present work, the flexibility of an epoxy adhesive containing diglycidylether of bisphenol-A (DGEBA) and diethylenetriamine (DETA) as curing agent was changed by the addition of a second component containing mercaptan groups (CAPCURE). The addition of asbestos as a filler in the adhesive containing CAPCURE was also evaluated. Epoxy-amine and epoxy-mercaptan reactions were studied in NIR and MIR spectral regions. The filler addition did not cause influence on the cure reactions and spectrometric changes of cure reactions could be better observed by FT-NIR than FT-MIR analysis. The cure reaction time was monitored by DSC experiments and it was observed that the introduction of CAPCURE accelerated the cure reaction. The activation energies (Ea) of curing reactions were obtained using Barrett and Borchardt-Daniels methods. The adhesives containing CAPCURE showed Ea around 30 kJ.mol-1, while DGEBA/DETA adhesive presented Ea of 46 kJ.mol-1 calculated by Barrett method