Two ways to common knowledge

It is not clear what a system for evidence-based common knowledge should look like if common knowledge is treated as a greatest fixed point. This paper is a preliminary step towards such a system. We argue that the standard induction rule is not well suited to axiomatize evidence-based common knowledge. As an alternative, we study two different deductive systems for the logic of common knowledge. The first system makes use of an induction axiom whereas the second one is based on co-inductive proof theory. We show the soundness and completeness for both systems.

[Serological and clinical proof of freedom from Equine Infectious Anemia (EIA) in imported and domestic horses in Switzerland]

Since 1991, no cases of Equine Infectious Anemia (EIA) have been reported in Switzerland. Risk factors for introduction of the virus into Switzerland are still present or have even increased as frequent inapparent infections, large numbers of imported horses, (since 2003) absence of compulsory testing prior to importation, EIA cases in surrounding Europe, possible illegal importation of horses, frequent short-term stays, poor knowledge of the disease among horse owners and even veterinarians. The aim of this study was to provide evidence of freedom from EIA in imported and domestic horses in Switzerland. The serum samples from 434 horses imported since 2003 as well as from 232 domestic horses fifteen years of age or older (since older horses have naturally had a longer time of being exposed to the risk of infection) were analysed using a commercially available ELISA test. All samples were seronegative, indicating that the maximum possible prevalence that could have been missed with this sample was 0.5% (95% confidence).

Canonical proof nets for classical logic

Proof nets provide abstract counterparts to sequent proofs modulo rule permutations; the idea being that if two proofs have the same underlying proof-net, they are in essence the same proof. Providing a convincing proof-net counterpart to proofs in the classical sequent calculus is thus an important step in understanding classical sequent calculus proofs. By convincing, we mean that (a) there should be a canonical function from sequent proofs to proof nets, (b) it should be possible to check the correctness of a net in polynomial time, (c) every correct net should be obtainable from a sequent calculus proof, and (d) there should be a cut-elimination procedure which preserves correctness. Previous attempts to give proof-net-like objects for propositional classical logic have failed at least one of the above conditions. In Richard McKinley (2010) [22], the author presented a calculus of proof nets (expansion nets) satisfying (a) and (b); the paper defined a sequent calculus corresponding to expansion nets but gave no explicit demonstration of (c). That sequent calculus, called LK∗ in this paper, is a novel one-sided sequent calculus with both additively and multiplicatively formulated disjunction rules. In this paper (a self-contained extended version of Richard McKinley (2010) [22]), we give a full proof of (c) for expansion nets with respect to LK∗, and in addition give a cut-elimination procedure internal to expansion nets – this makes expansion nets the first notion of proof-net for classical logic satisfying all four criteria.

Proof internalization in generalized Frege systems for classical logic

We present a general method for inserting proofs in Frege systems for classical logic that produces systems that can internalize their own proofs.

First-in-Human Proof-of-Concept Study: Intralesional Administration of BQ788, an Endothelin Receptor B Antagonist, to Melanoma Skin Metastases

BACKGROUND This first-in-human proof-of-concept study aimed to check whether safety and preclinical results obtained by intratumoral administration of BQ788, an endothelin receptor B (EDNRB) antagonist, can be repeated in human melanoma patients. METHODS Three patients received a single intralesional BQ788 application of 3 mg. After 3-7 days, the lesions were measured and removed for analysis. The administered dose was increased to a cumulative dosage of 8 mg in patient 4 (4 × 2.0 mg, days 0-3; lesion removed on day 4) and to 10 mg in patient 5 (3 × 3.3 mg, days 0, 3, and 10; lesion removed after 14 days). Control lesions were simultaneously treated with phosphate-buffered saline (PBS). All samples were processed and analyzed without knowledge of the clinical findings. RESULTS No statistical evaluation was possible because of the number of patients (n = 5) and the variability in the mode of administration. No adverse events were observed, regardless of administered dose. All observations were in accordance with results obtained in preclinical studies. Accordingly, no difference in degree of tumor necrosis was detected between BQ788- and PBS-treated samples. In addition, both EDNRB and Ki67 showed decreased expression in patients 2 and 5 and, to a lesser extent, in patient 1. Similarly, decreased expression of EDNRB mRNA in patients 2 and 5 and of BCL2A1 and/or PARP3 in patients 2, 3, and 5 was found. Importantly, semiquantitatively scored immunohistochemistry for CD31 and CD3 revealed more blood vessels and lymphocytes, respectively, in BQ788-treated tumors of patients 2 and 4. Also, in all patients, we observed inverse correlation in expression levels between EDNRB and HIF1A. Finally, in patient 5 (the only patient treated for longer than 1 week), we observed inhibition in lesion growth, as shown by size measurement. CONCLUSION The intralesional applications of BQ788 were well tolerated and showed signs of directly and indirectly reducing the viability of melanoma cells.

A Proof-Theoretic Analysis of Theories for Stratified Inductive Definitions

In this article we study subsystems SIDᵥ of the theory ID₁ in which fixed point induction is restricted to properly stratified formulas.