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.

Kyzylkumite, Ti2V3+O5(OH): new structure type, modularity and revised formula

The crystal structure of kyzylkumite, ideally Ti2V3+O5(OH), from the Sludyanka complex in South Baikal, Russia was solved and refined (including the hydrogen atom position) to an agreement index, R1, of 2.34 using X-ray diffraction data collected on a twinned crystal. Kyzylkumite crystallizes in space group P21/c, with a = 8.4787(1), b = 4.5624(1), c = 10.0330(1) Å, β = 93.174(1)°, V = 387.51(1) Å3 and Z = 4. Tivanite, TiV3+O3OH, and kyzylkumite have modular structures based on hexagonal close packing of oxygen, which are made up of rutile TiO2 and montroseite V3+O(OH) slices. In tivanite the rutile:montroseite ratio is 1:1, in kyzylkumite the ratio is 2:1. The montroseite module may be replaced by the isotypic paramontroseite V4+O2 module, which produces a phase with the formula Ti2V4+O6. In the metamorphic rocks of the Sludyanka complex, vanadium can be present as V4+ and V3+ within the same mineral (e.g. in batisivite, schreyerite and berdesinskiite). Kyzylkumite has a flexible composition with respect to the M4+/M3+ ratio. The relationship between kyzylkumite and a closely related Be-bearing kyzylkumite-like mineral with an orthorhombic norbergite-type structure from Byrud mine, Norway is discussed. Both minerals have similar X-ray powder diffraction patterns.

“50+L2”: una formula utile dopo il pensionamento?

In diesem Artikel möchten wir anhand eigener Untersuchungen und der Präsentation bereits vorhandener Studien einerseits einen Einblick in die Welt der 50+ Sprachkurse geben und andererseits mögliche Lösungen für eine an das Zielpublikum angepasste Didaktik vorstellen. Bei den erforschten Sprachkursen handelt es sich um drei unterschiedliche Kurstypen mit den dazugehörigen Kursteilnehmertypologien. Das erste Forschungsfeld umfasst Sprachkurse, die von der Berner Volkshochschule angeboten und teilweise von Personen im Alter von 50 und älter besucht werden. Zum zweiten Kurstyp gehören solche Kurse, die im Ausland besucht werden. Im vorliegenden Fall ein Italienischkurs in Sizilien mit einem expliziten Freizeitprogramm für Personen ab 50. Das dritte Untersuchungsfeld betrifft einen etwas anderen Typ von Kursteilnehmern, da es sich um einen Deutschkurs für pensionierte italienische MigrantInnen in Bern handelt. Die abschliessenden Vorschläge für eine an die älteren Kursteilnehmer angepasste Didaktik sollen dabei nicht als allgemeingültige Rezepte betrachtet werden, sondern als erste Anregungspunkte.

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.

Censors for Boolean Description Logic

Protecting different kinds of information has become an important area of research. One aspect is to provide effective means to avoid that secrets can be deduced from the answers of legitimate queries. In the context of atomic propositional databases several methods have been developed to achieve this goal. However, in those databases it is not possible to formalize structural information. Also they are quite restrictive with respect to the specification of secrets. In this paper we extend those methods to match the much greater expressive power of Boolean description logics. In addition to the formal framework, we provide a discussion of various kinds of censors and establish different levels of security they can provide.

Effects of colostrum versus formula feeding on hepatic glucocorticoid and α1- and β2-adrenergic receptors in neonatal calves and their effect on glucose and lipid metabolism

Neonatal energy metabolism in calves has to adapt to extrauterine life and depends on colostrum feeding. The adrenergic and glucocorticoid systems are involved in postnatal maturation of pathways related to energy metabolism and calves show elevated plasma concentrations of cortisol and catecholamines during perinatal life. We tested the hypothesis that hepatic glucocorticoid receptors (GR) and α₁- and β₂-adrenergic receptors (AR) in neonatal calves are involved in adaptation of postnatal energy metabolism and that respective binding capacities depend on colostrum feeding. Calves were fed colostrum (CF; n=7) or a milk-based formula (FF; n=7) with similar nutrient content up to d 4 of life. Blood samples were taken daily before feeding and 2h after feeding on d 4 of life to measure metabolites and hormones related to energy metabolism in blood plasma. Liver tissue was obtained 2 h after feeding on d 4 to measure hepatic fat content and binding capacity of AR and GR. Maximal binding capacity and binding affinity were calculated by saturation binding assays using [(3)H]-prazosin and [(3)H]-CGP-12177 for determination of α₁- and β₂-AR and [(3)H]-dexamethasone for determination of GR in liver. Additional liver samples were taken to measure mRNA abundance of AR and GR, and of key enzymes related to hepatic glucose and lipid metabolism. Plasma concentrations of albumin, triacylglycerides, insulin-like growth factor I, leptin, and thyroid hormones changed until d 4 and all these variables except leptin and thyroid hormones responded to feed intake on d 4. Diet effects were determined for albumin, insulin-like growth factor I, leptin, and thyroid hormones. Binding capacity for GR was greater and for α₁-AR tended to be greater in CF than in FF calves. Binding affinities were in the same range for each receptor type. Gene expression of α₁-AR (ADRA1) tended to be lower in CF than FF calves. Binding capacity of GR was related to parameters of glucose and lipid metabolism, whereas β₂-AR binding capacity was negatively associated with glucose metabolism. In conclusion, our results indicate a dependence of GR and α₁-AR on milk feeding immediately after birth and point to an involvement of hepatic GR and AR in postnatal adaptation of glucose and lipid metabolism in calves.