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.

A new model construction by making a detour via intuitionistic theories II: Interpretability lower bound of Feferman's explicit mathematics T0

We partially solve a long-standing problem in the proof theory of explicit mathematics or the proof theory in general. Namely, we give a lower bound of Feferman’s system T0 of explicit mathematics (but only when formulated on classical logic) with a concrete interpretat ion of the subsystem Σ12-AC+ (BI) of second order arithmetic inside T0. Whereas a lower bound proof in the sense of proof-theoretic reducibility or of ordinalanalysis was already given in 80s, the lower bound in the sense of interpretability we give here is new. We apply the new interpretation method developed by the author and Zumbrunnen (2015), which can be seen as the third kind of model construction method for classical theories, after Cohen’s forcing and Krivine’s classical realizability. It gives us an interpretation between classical theories, by composing interpretations between intuitionistic theories.

Pro-inflammatory biomarkers during experimental gingivitis in patients with type 1 diabetes mellitus: a proof-of-concept study

To compare gingival crevicular fluid (GCF) biomarker levels and microbial distribution in plaque biofilm (SP) samples for subjects with type 1 diabetes (T1DM) versus healthy subjects without diabetes during experimental gingivitis (EG).

A smooth transition protocol for patients with multifocal motor neuropathy going from intravenous to subcutaneous immunoglobulin therapy: an open-label proof-of-concept study

Intravenous immunoglobulin (IVIG) is the first-line therapy for multifocal motor neuropathy (MMN). This open-label multi-centre study (NCT00701662) assessed the efficacy, safety, and convenience of subcutaneous immunoglobulin (SCIG) in patients with MMN over 6 months, as an alternative to IVIG. Eight MMN patients (42-66 years), on stable IVIG dosing, received weekly SCIG at doses equivalent to previous IVIG using a "smooth transition protocol". Primary efficacy endpoint was the change from baseline to week 24 in muscle strength. Disability, motor function, and health-related quality of life (HRQL) endpoints were also assessed. One patient deteriorated despite dose increase and was withdrawn. Muscle strength, disability, motor function, and health status were unchanged in all seven study completers who rated home treatment as extremely good. Four experienced 18 adverse events, of which only two were moderate. This study suggests that MMN patients with stable clinical course on regular IVIG can be switched to SCIG at the same monthly dose without deterioration and with a sustained overall improvement in HRQL.

Orexin receptor antagonism, a new sleep-enabling paradigm: a proof-of-concept clinical trial

The orexin system is a key regulator of sleep and wakefulness. In a multicenter, double-blind, randomized, placebo-controlled, two-way crossover study, 161 primary insomnia patients received either the dual orexin receptor antagonist almorexant, at 400, 200, 100, or 50 mg in consecutive stages, or placebo on treatment nights at 1-week intervals. The primary end point was sleep efficiency (SE) measured by polysomnography; secondary end points were objective latency to persistent sleep (LPS), wake after sleep onset (WASO), safety, and tolerability. Dose-dependent almorexant effects were observed on SE , LPS , and WASO . SE improved significantly after almorexant 400 mg vs. placebo (mean treatment effect 14.4%; P < 0.001). LPS (–18 min (P = 0.02)) and WASO (–54 min (P < 0.001)) decreased significantly at 400 mg vs. placebo. Adverse-event incidence was dose-related. Almorexant consistently and dose-dependently improved sleep variables. The orexin system may offer a new treatment approach for primary insomnia.