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.

Social Work in an Ethnically Diverse Europe: The Shifting Challenges of Difference

This article addresses the inherently politicised context of social work practice located within the contested logics and values of national social policy and professional values and identities. Noting the key role of social work in delivering the state’s promise of social citizenship, it is argued that the increasing neo-nationalist sentiments and politics in European states generate significant pressures upon the universalist, inclusive, values of social work in a multiethnic Europe. The academic and policy debate around social cohesion is explored to illustrate how an assimilationist drift in multicultural state policies undermines the capacity of social work services to deliver appropriate, ethnically sensitive, services. It is further argued that the pervasive spread of populist counter-narratives to multiculturalism erode support for anti-racist and transcultural social work practice. In this context it is argued that social work must acknowledge its compromised situation and explicitly develop a political agenda committed to guaranteeing substantive equality in service delivery.

Extrapolated difference technique for the determination of atomization energies of Sm, Eu, and Yb bromides

An approach for the determination of atomization energies based on the extrapolated difference technique in the framework of Knudsen effusion mass spectrometry is proposed. Its essence is the use of thermodynamic data for the determination of the appearance energy of fragment ions of a reference and a special mathematical treatment of the ionization efficiency functions. The advantages of this approach are demonstrated for the cases of incongruently vaporizing lanthanide bromides that suffer from decomposition or disproportionation at high temperatures. The atomization energies for SmBr2 (7.78±0.12 eV), EuBr2 (7.51±0.11 eV), YbBr2 (7.25±0.13 eV), SmBr3 (11.09±0.10 eV), and YbBr3 (10.23±0.09 eV) molecules have been determined for the first time.

A case of distinct difference between the measured blood Ethanol concentration and the concentration estimated by Widmark's equation

In the last century, several mathematical models have been developed to calculate blood ethanol concentrations (BAC) from the amount of ingested ethanol and vice versa. The most common one in the field of forensic sciences is Widmark's equation. A drinking experiment with 10 voluntary test persons was performed with a target BAC of 1.2 g/kg estimated using Widmark's equation as well as Watson's factor. The ethanol concentrations in the blood were measured using headspace gas chromatography/flame ionization and additionally with an alcohol Dehydrogenase (ADH)-based method. In a healthy 75-year-old man a distinct discrepancy between the intended and the determined blood ethanol concentration was observed. A blood ethanol concentration of 1.83 g/kg was measured and the man showed signs of intoxication. A possible explanation for the discrepancy is a reduction of the total body water content in older people. The incident showed that caution is advised when using the different mathematical models in aged people. When estimating ethanol concentrations, caution is recommended with calculated results due to potential discrepancies between mathematical models and biological systems

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.