A modal theorem-preserving translation of a class of three-valued logics of incomplete information

International audienceThere are several three-valued logical systems that form a scattered landscape, even if all reasonable connectives in three-valued logics can be derived from a few of them. Most papers on this subject neglect the issue of the relevance of such logics in relation with the intended meaning of the third truth-value. Here, we focus on the case where the third truth-value means unknown, as suggested by Kleene. Under such an understanding, we show that any truth-qualified formula in a large range of three-valued logics can be translated into KD as a modal formula of depth 1, with modalities in front of literals only, while preserving all tautologies and inference rules of the original three-valued logic. This simple information logic is a two-tiered classical propositional logic with simple semantics in terms of epistemic states understood as subsets of classical interpretations. We study in particular the translations of Kleene, Gödel, ᴌukasiewicz and Nelson logics. We show that Priest’s logic of paradox, closely connected to Kleene’s, can also be translated into our modal setting, simply by exchanging the modalities possible and necessary. Our work enables the precise expressive power of three-valued logics to be laid bare for the purpose of uncertainty management

Intracellular calcium leak as a therapeutic target for RYR1-related myopathies

Contains fulltext : 220671.pdf (Publisher’s version ) (Closed access)RYR1 encodes the type 1 ryanodine receptor, an intracellular calcium release channel (RyR1) on the skeletal muscle sarcoplasmic reticulum (SR). Pathogenic RYR1 variations can destabilize RyR1 leading to calcium leak causing oxidative overload and myopathy. However, the effect of RyR1 leak has not been established in individuals with RYR1-related myopathies (RYR1-RM), a broad spectrum of rare neuromuscular disorders. We sought to determine whether RYR1-RM affected individuals exhibit pathologic, leaky RyR1 and whether variant location in the channel structure can predict pathogenicity. Skeletal muscle biopsies were obtained from 17 individuals with RYR1-RM. Mutant RyR1 from these individuals exhibited pathologic SR calcium leak and increased activity of calcium-activated proteases. The increased calcium leak and protease activity were normalized by ex-vivo treatment with S107, a RyR stabilizing Rycal molecule. Using the cryo-EM structure of RyR1 and a new dataset of > 2200 suspected RYR1-RM affected individuals we developed a method for assigning pathogenicity probabilities to RYR1 variants based on 3D co-localization of known pathogenic variants. This study provides the rationale for a clinical trial testing Rycals in RYR1-RM affected individuals and introduces a predictive tool for investigating the pathogenicity of RYR1 variants of uncertain significance