A syntactic realization theorem for justification logics

Justification logics are refinements of modal logics where modalities are replaced by justification terms. They are connected to modal logics via so-called realization theorems. We present a syntactic proof of a single realization theorem that uniformly connects all the normal modal logics formed from the axioms \$mathsfd\$, \$mathsft\$, \$mathsfb\$, \$mathsf4\$, and \$mathsf5\$ with their justification counterparts. The proof employs cut-free nested sequent systems together with Fitting's realization merging technique. We further strengthen the realization theorem for \$mathsfKB5\$ and \$mathsfS5\$ by showing that the positive introspection operator is superfluous.

Bayesian Approach to Spectral Function Reconstruction for Euclidean Quantum Field Theories

We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set of axioms is postulated for the prior probability, leading to an improved expression, which is devoid of the asymptotically flat directions present in the Shanon-Jaynes entropy. Hyperparameters are integrated out explicitly, liberating us from the Gaussian approximations underlying the evidence approach of the maximum entropy method. We present a realistic test of our method in the context of the nonperturbative extraction of the heavy quark potential. Based on hard-thermal-loop correlator mock data, we establish firm requirements in the number of data points and their accuracy for a successful extraction of the potential from lattice QCD. Finally we reinvestigate quenched lattice QCD correlators from a previous study and provide an improved potential estimation at T2.33TC.

The Swiss Schools have been Governed by Local Lay Authorities

After the introduction of the liberal-democratic constitutions in the Swiss cantons in the first half of the 1830ies the grid of existing schools has been systemized and broadly expanded. The school systems have ever since been characterized by one key element: a special local authority type called „Schulkommission“ or „Schulpflege“. They take the form of committees consisting of laymen that are appointed by democratic elections like all the other executive bodies on the different federal levels in Switzerland. When it comes to their obligations and activities these community level school committees conform very much to the school boards in the American and Canadian school systems. They are accountable for the selection and supervision of the teachers. They approve decisions about the school careers of pupils and about curricular matters like the choice of school books. Normally their members are elected by the local voters for four year terms of office (reelection remains possible) and with regard to pedagogics they normally are non-professionals. The board members are responsible for classes and teachers assigned to them and they have to go to see them periodically. These visitations and the board meetings each month together with the teachers enable the board members to attain a deep insight into what happens in their schools over the course of their term of office. But they are confronted as laymen with a professional teaching staff and with educational experts in the public administration. Nevertheless this form of executive power by non-professionals is constitutive for the state governance in the Swiss as well as in other national political environments. It corresponds to the principles of subsidiarity and militia and therefore allows for a strong accentuation of liberty and the right of self-determination, two axioms at the very base of democratic federalist ideology. This governance architecture with this strong accent on local anchorage features substantial advantages for the legitimacy and acceptability of political and administrative decisions. And this is relevant especially in the educational area because the rearing of the offspring is a project of hope and, besides, quite costly. In the public opinion such supervision bodies staffed by laymen seem to have certain credibility advances in comparison with the professional administration. They are given credit to be capable of impeding the waste of common financial resources and of warranting the protection and the fostering of the community’s children at once. Especially because of their non-professional character they are trusted to be reliably immune against organizational blindness and they seem to be able to defend the interests of the local community against the standardization and centralization aspirations originating from the administrational expertocracy. In the paper these common rationales will be underpinned by results of a comprehensive historical analysis of the Session protocols of three Bernese school commissions from 1835 to 2005.

A feasible theory of truth over combinatory algebra

We define an applicative theory of truth TPT which proves totality exactly for the polynomial time computable functions. TPT has natural and simple axioms since nearly all its truth axioms are standard for truth theories over an applicative framework. The only exception is the axiom dealing with the word predicate. The truth predicate can only reflect elementhood in the words for terms that have smaller length than a given word. This makes it possible to achieve the very low proof-theoretic strength. Truth induction can be allowed without any constraints. For these reasons the system TPT has the high expressive power one expects from truth theories. It allows embeddings of feasible systems of explicit mathematics and bounded arithmetic. The proof that the theory TPT is feasible is not easy. It is not possible to apply a standard realisation approach. For this reason we develop a new realisation approach whose realisation functions work on directed acyclic graphs. In this way, we can express and manipulate realisation information more efficiently.

Penetrability of the inner mucus layer: who is out there?

Large numbers of microorganisms colonise the skin and mucous membranes of animals, with their highest density in the lower gastrointestinal tract. The impact of these microbes on the host can be demonstrated by comparing animals (usually mice) housed under germ-free conditions, or colonised with different compositions of microbes. Inbreeding and embryo manipulation programs have generated a wide variety of mouse strains with a fixed germ-line (isogenic) and hygiene comparisons robustly show remarkably strong interactions between the microbiota and the host, which can be summarised in three axioms. (I) Live microbes are largely confined to their spaces at body surfaces, provided the animal is not suffering from an infection. (II) There is promiscuous molecular exchange throughout the host and its microbiota in both directions [1]. (III) Every host organ system is profoundly shaped by the presence of body surface microbes. It follows that one must draw a line between live microbial and host “spaces” (I) to understand the crosstalk (II and III) at this interesting interface of the host-microbial superorganism. Of course, since microbes can adapt to very different niches, there has to be more than one line. In this issue of EMBO Reports, Johansson and colleagues have studied mucus, which is the main physical frontier for most microbes in the intestinal tract: they report how different non-pathogenic microbiota compositions affect its permeability and the functional protection of the epithelial surface [2].