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.

Marginalized Youth, the ‘Modern’ Professional and the ‘Modern’ Workplace: A note on the Need for a Critical Approach to ‘Modernizing’ Strategies

This paper briefly examines plans to ‘transform’ social work services for socially marginalized children and young people in England. More specifically, it will focus on moves to privatize social work services for children and young people who are in public care, or ‘looked after’. In what follows, the focus will be on how the promotion of ‘social work practices’ (SWPs) – the name of these envisaged new structures – is discursively embedded in the idea the idea that ‘liberation’ and worker fulfillment can only be delivered within a privatized sphere. In this context, it will be maintained, the work of Boltanski and Chiapello may help to illuminate how the government and other primary definers are seeking to ‘win hearts and minds’ for further neoliberal ‘transformations’ within Children’s Services in England.