A language for multiplicative-additive linear logic

A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive categories with additives. It is also shown that proof equivalence is decidable by showing that the cut elimination rewrites supply a confluent rewriting system modulo equations.Comment: 16 pages without appendices, 30 with appendice

Complete Positivity for Mixed Unitary Categories

In this article we generalize the \CP^\infty-construction of dagger monoidal categories to mixed unitary categories. Mixed unitary categories provide a setting, which generalizes (compact) dagger monoidal categories and in which one may study quantum processes of arbitrary (infinite) dimensions. We show that the existing results for the \CP^\infty-construction hold in this more general setting. In particular, we generalize the notion of environment structures to mixed unitary categories and show that the \CP^\infty-construction on mixed unitary categories is characterized by this generalized environment structure.Comment: Lots of figure

Measuring brand image: Shopping centre case studies

'Branding' is well known for consumer products but power has shifted from manufacturers' brands towards retailers'. The term 'image' is more common than 'brand' in the context of shopping centres, but 'branding' may become more important. In this study, the authors first investigated qualitatively, asking shoppers to describe centres in 'personality' terms and eliciting clear descriptive differences between centres. For example, one in-town centre was 'dull, boring and old-fashioned . . . not exciting, just OK'; a larger regional centre was 'trendy, prestigious . . . strong, vibrant, big and colourful'. Second, the authors evaluated six UK shopping centres quantitatively using a questionnaire survey (n = 287). The 'strong and vibrant' centre scored significantly higher than the 'dull and boring' one. Despite 'branding' being little used by shopping centres, those with the better 'brand images' tended to have larger catchment areas, sales and rental incomes. The authors contend that brand management could pay rewards in terms of customer numbers, sales turnover and rental income

There Is Only One Notion of Differentiation

Differential linear logic was introduced as a syntactic proof-theoretic approach to the analysis of differential calculus. Differential categories were subsequently introduce to provide a categorical model theory for differential linear logic. Differential categories used two different approaches for defining differentiation abstractly: a deriving transformation and a coderiliction. While it was thought that these notions could give rise to distinct notions of differentiation, we show here that these notions, in the presence of a monoidal coalgebra modality, are completely equivalent