Normalization in Supernatural deduction and in Deduction modulo

Deduction modulo and Supernatural deduction are two extentions of predicate logic with computation rules. Whereas the application of computation rules in deduction modulo is transparent, these rules are used to build non-logical deduction rules in Supernatural deduction. In both cases, adding computation rules may jeopardize proof normalization, but various conditions have been given in both cases, so that normalization is preserved. We prove in this paper that normalization in Supernatural deduction and in Deduction modulo are equivalent, i.e. the set of computation rules for which one system strongly normalizes is the same as the set of computation rules for which the other is

Un calcul des séquents extensible

Ce rapport présente un calcul des séquents où les théories exprimées sous la forme de systèmes de réécriture sont traduites en règles ad hoc pour le calcul des séquents. Cela permet à la fois de réduire la taille des démonstrations en vue de la mise en oeuvre d'un assistant et de raisonner dans la théorie vide, ce qui ramène la preuve de la cohérence d'une théorie à une démonstration d'élimination des coupures dans le système de déduction dérivé de cette théorie. Le rapport expose différentes versions classiques et intuitionnistes du système, ainsi que l'ébauche d'un langage de termes de preuve. Après quelques exemples d'application du système, un prototype d'assistant à la démonstration fondé sur la version classique y est présenté

A semantic normalization proof for a system with recursors

Semantics methods have been used to prove cut elimination theorems for a long time. It is only recently that they have been extend to prove strong normalization results, in particular for theories in deduction modulo. However such semantic methods did not apply for systems with recursors like Godel system T. We show in this paper how super natural deduction provides a bridge between superconsistency of arithmetic and strong normalization of system T. We then generalize this result to a family of inductive types before discussing the dependant case

Principles of Superdeduction

International audienceIn predicate logic, the proof that a theorem P holds in a theory Th is typically conducted in natural deduction or in the sequent calculus using all the information contained in the theory in a uniform way. Introduced ten years ago, Deduction modulo allows us to make use of the computational part of the theory Th for true computations modulo which deductions are performed. Focussing on the sequent calculus, this paper presents and studies the dual concept where the theory is used to enrich the deduction system with new deduction rules in a systematic, correct and complete way. We call such a new deduction system "superdeduction''. We introduce a proof-term language and a cut-elimination procedure both based on Christian Urban's work on classical sequent calculus. Strong normalisation is proven under appropriate and natural hypothesis, therefore ensuring the consistency of the embedded theory and of the deduction system. The proofs obtained in such a new system are much closer to the human intuition and practice. We consequently show how superdeduction along with deduction modulo can be used to ground the formal foundations of new extendible proof assistants. We finally present lemuridae, our current implementation of superdeduction modulo

Defense Mechanisms of Hepatocytes Against Burkholderia pseudomallei

The Gram-negative facultative intracellular rod Burkholderia pseudomallei causes melioidosis, an infectious disease with a wide range of clinical presentations. Among the observed visceral abscesses, the liver is commonly affected. However, neither this organotropism of B. pseudomallei nor local hepatic defense mechanisms have been thoroughly investigated so far. Own previous studies using electron microscopy of the murine liver after systemic infection of mice indicated that hepatocytes might be capable of killing B. pseudomallei. Therefore, the aim of this study was to further elucidate the interaction of B. pseudomallei with these cells and to analyze the role of hepatocytes in anti-B. pseudomallei host defense. In vitro studies using the human hepatocyte cell line HepG2 revealed that B. pseudomallei can invade these cells. Subsequently, B. pseudomallei is able to escape from the vacuole, to replicate within the cytosol of HepG2 cells involving its type 3 and type 6 secretion systems, and to induce actin tail formation. Furthermore, stimulation of HepG2 cells showed that IFNγ can restrict growth of B. pseudomallei in the early and late phase of infection whereas the combination of IFNγ, IL-1β, and TNFα is required for the maximal antibacterial activity. This anti-B. pseudomallei defense of HepG2 cells did not seem to be mediated by inducible nitric oxide synthase-derived nitric oxide or NADPH oxidase-derived superoxide. In summary, this is the first study describing B. pseudomallei intracellular life cycle characteristics in hepatocytes and showing that IFNγ-mediated, but nitric oxide- and reactive oxygen species-independent, effector mechanisms are important in anti-B. pseudomallei host defense of hepatocytes

Inductive Proof Search Modulo

International audienceWe present an original narrowing-based proof search method for inductive theorems in equational rewrite theories given by a rewrite system R and a set E of equalities. It has the specificity to be grounded on deduction modulo and to rely on narrowing to provide both induction variables and instantiation schemas. Whenever the equational rewrite system (R, E) has good properties of termination, sufficient completeness, and when E is constructor and variable preserving, narrowing at defined- innermost positions leads to consider only unifiers which are constructor substitutions. This is especially interesting for associative and associative-commutative theories for which the general proof search system is refined. The method is shown to be sound and refutationaly correct and complete. A major feature of our approach is to provide a constructive proof in deduction modulo for each successful instance of the proof search procedure

100,000 lumens to treat seasonal affective disorder: a proof of concept RCT of Bright, whole-ROom, All-Day (BROAD) light therapy

Background: Seasonal affective disorder (SAD) is common and debilitating. The standard of care includes light therapy provided by a light box; however, this treatment is restrictive and only moderately effective. Advances in LED technology enable lighting solutions that emit vastly more light than traditional light boxes. Here, we assess the feasibility of BROAD (Bright, whole-ROom, All-Day) light therapy and get a first estimate for its potential effectiveness. Methods: Patients were randomly assigned to a treatment for 4 weeks; either a very brightly illuminated room in their home for at least 6 h per day (BROAD light therapy) or 30 min in front of a standard 10,000 lux SAD light box. Feasibility was assessed by monitoring recruitment, adherence, and side effects. SAD symptoms were measured at baseline and after 2 and 4 weeks, with the Hamilton Depression Rating Scale-Seasonal Affective Disorders 29-items, self-report version. Results: All 62 patients who started treatment were available at 4-week follow-up and no significant adverse effects were reported. SAD symptoms of both groups improved similarly and considerably, in line with previous results. Exploratory analyses indicate that a higher illuminance (lux) is associated with a larger symptom improvement in the BROAD light therapy group. Conclusions: BROAD light therapy is feasible and seems similarly effective as the standard of care while not confining the participants to 30 min in front of a light box. In follow-up trials, BROAD light therapy could be modified for increased illuminance, which would likely improve its effectiveness

Extensional and Intensional Strategies

This paper is a contribution to the theoretical foundations of strategies. We first present a general definition of abstract strategies which is extensional in the sense that a strategy is defined explicitly as a set of derivations of an abstract reduction system. We then move to a more intensional definition supporting the abstract view but more operational in the sense that it describes a means for determining such a set. We characterize the class of extensional strategies that can be defined intensionally. We also give some hints towards a logical characterization of intensional strategies and propose a few challenging perspectives