Apartness and the elimination of strong forms of extensionality

We introduce a new version of arithmetic in all finite types which extends the usual versions with primitive notions of extensionality and extensional equality. This new hybrid version allows us to formulate a strong form of extensionality, which we call converse extensionality. Inspired by Brouwer's notion of apartness, we show that converse extensionality can be eliminated in a way which improves on results from our previous work. We also explain how standard proof-theoretic interpretations, like realizability and functional interpretations, can be extended to such hybrid systems, and how that might be relevant to proof-mining

Unifying Functional Interpretations: Past and Future

This article surveys work done in the last six years on the unification of various functional interpretations including G\"odel's dialectica interpretation, its Diller-Nahm variant, Kreisel modified realizability, Stein's family of functional interpretations, functional interpretations "with truth", and bounded functional interpretations. Our goal in the present paper is twofold: (1) to look back and single out the main lessons learnt so far, and (2) to look forward and list several open questions and possible directions for further research.Comment: 18 page

The curious case of the refrigerator-TV: similarity and hybridization

This paper examines the role of similarity in the hybridization of concepts, focusing on hybrid products as an applied test case. Hybrid concepts found in natural language, such as singer songwriter, typically combine similar concepts, whereas dissimilar concepts rarely form hybrids. The hybridization of dissimilar concepts in products such as jogging shoe mp3 player, and refrigerator TV thus poses a challenge for understanding the process of conceptual combination. It is proposed that models of conceptual combination can throw light on the judged future success and desirability of hybrid products in general. The composite prototype model proposes two stages of conceptual combination. In the first stage, the concepts are aggregated into an additive hybrid, simply by forming the union of the two sets of attributes. In the second stage, any conflicting attributes are identified and resolved, often with the introduction of emergent attributes, resulting in an integrative hybrid. Across four studies that varied the similarity and type of hybrid products, similar and integrative hybrids were valued more than dissimilar and additive hybrids. Critically, though, dissimilar hybrids were also highly valued if they were integrative. Results supported the two stages proposed by the composite prototype model, and implications for other models of hybrid formation are discussed

Identity ambiguity and the promises and practices of hybrid e-HRM project teams

The role of IS project team identity work in the enactment of day-to-day relationships with their internal clients is under-researched. We address this gap by examining the identity work undertaken by an electronic human resource management (e-HRM) 'hybrid' project team engaged in an enterprise-wide IS implementation for their multi-national organisation. Utilising social identity theory, we identify three distinctive, interrelated dimensions of project team identity work (project team management, team 'value propositions' (promises) and the team's 'knowledge practice'). We reveal how dissonance between two perspectives of e-HRM project identity work (clients' expected norms of project team's service and project team's expected norms of themselves) results in identity ambiguity. Our research contributions are to identity studies in the IS project management, HR and hybrid literatures and to managerial practice by challenging the assumption that hybrid experts are the panacea for problems associated with IS projects

The New Keynesian Phillips Curve and Inflation Expectations: Re-Specification and Interpretation

A theoretical analysis of the new Keynesian Phillips curve (NKPC) is provided, formulating the conditions under which the NKPC coincides with a real-world relation that is not spurious or misspecified. A time-varying-coefficient (TVC) model, involving only observed variables, is shown to exactly represent the underlying “true” NKPC under certain conditions. In contrast, “hybrid” NKPC models, which add lagged-inflation and supply-shock variables, are shown to be spurious and misspecified. We also show how to empirically implement the NKPC under the assumption that expectations are formed rationally.Time-varying-coefficient model; Inflation-unemployment trade-off; “Objective” probability; Spurious correlation; Rational expectation; Coefficient driver

Charge disproportionation and Jahn-Teller distortion in LiNiO2 and NaNiO2: A density functional theory study

Density functional theory calculations have been performed on three potential ground-state configurations of LiNiO2 and NaNiO2. These calculations show that, whereas NaNiO2 shows the expected cooperative Jahn-Teller distortion (and therefore a crystal structure with C2/m symmetry), LiNiO2 shows at least two possible crystal structures very close in energy (within 3 meV/f.u.): P21/c and P2/c. Moreover, one of them (P2/c) shows charge disproportionation of the (expected) Ni3+ cations into Ni2+ and Ni4+. We discuss the implications of this complex ground state for the interpretation of the available electron and neutron structure data, its electronic and complex magnetic behaviour

Unraveling the Jahn-Teller effect in Mn doped GaN using the Heyd-Scuseria-Ernzerhof hybrid functional

We present an ab-initio study of the Mn substitution for Ga in GaN using the Heyd-Scuseria-Ernzerhof hybrid functional (HSE). Contrary to semi-local functionals, the majority Mn t$_{2}$ manifold splits into an occupied doublet and an unoccupied singlet well above the Fermi-level resulting in an insulating groundstate, which is further stabilized by a sizeable Jahn-Teller distortion. The predictions are confirmed using $GW$ calculations and are in agreement with experiment. A transition from a localized to a delocalized Mn hole state is predicted from GaN to GaAs.Comment: 5 pages; 3 figures; to be published in Physical Review B: Rapid Communication