A Note on the Use of Sum in the Logic of Proofs

The Logic of Proofs~LP, introduced by Artemov, encodes the same reasoning as the modal logic~S4 using proofs explicitly present in the language. In particular, Artemov showed that three operations on proofs (application~$\cdot$, positive introspection~!, and sum~+) are sufficient to mimic provability concealed in S4~modality. While the first two operations go back to G{\"o}del, the exact role of~+ remained somewhat unclear. In particular, it was not known whether the other two operations are sufficient by themselves. We provide a positive answer to this question under a very weak restriction on the axiomatization of LP.

Item Sum: A New Technique for Asking Quantitative Sensitive Questions

This article contributes to an ongoing debate about how to measure sensitive topics in population surveys. We propose a novel technique that can be applied to the measurement of quantitative sensitive variables: the item sum technique (IST). This method is closely related to the item count technique, which was developed for the measurement of dichotomous sensitive items. First, we provide a description of our new technique and discuss how data collected by the IST can be analyzed. Second, we present the results of a CATI survey on undeclared work in Germany, in which the IST has been applied. Using an experimental design, we compare the IST to direct questioning. Our empirical results indicate that the IST is a promising data-collection technique for sensitive questions. We conclude by discussing the limitations of the new technique and outlining possible improvements for future studies.

The bottom-quark mass from non-relativistic sum rules at NNNLO

We determine the mass of the bottom quark from high moments of the bbproduction cross section in e+e−annihilation, which are dominated by the threshold region. On the theory side next-to-next-to-next-to-leading order (NNNLO) calculations both for the resonances and the continuum cross section are used for the first time. We find mPSb(2GeV) =4.532+0.013−0.039GeVfor the potential-subtracted mass and mMSb(mMSb) =4.193+0.022−0.035GeVfor the MSbottom-quark mass.

Linguista sum... sed lingua non definio. Absence de définition de la langue et circularité de la construction structurale

This article analyzes the Jakobsonian classification of aphasias. It aims to show on the one hand the non-linguistic character of this classification and on the other hand its asymmetry, in spite of the fact that its author had conceived his structural construction as symmetrical. The non-linguistic character of Jakobson’s formulation is due to the absence of any definition of language, this absence being the main characteristic of Jakobsonian linguistics: concerning the aphasia problem, the Jakobsonian formulation is linguistic solely by virtue of its object, aphasia, which is already considered as a linguistic concern because it belongs to the field of « language », but which is not defined as such (as linguistic). As for asymmetry, it demonstrates first the circularity of the Jakobsonian representation of language (the duality between structure and functioning), and secondly the non-linguistic character – in the Saussurean sense of the term – of the aphasia problem. Thus it appears that breaking (in the sense of Gaston Bachelard) with idiom is the prerequisite of a scientific apprehension of language, and therefore of any interdisciplinarity, this being one of Jakobson’s favorite topics but one that this linguist failed to render fruitful because he did not offer a real definition of language.