In the early months of 2020, the deadly Covid-19 disease spread rapidly around the world. In response, national and regional governments implemented a range of emergency lockdown measures, curtailing citizens’ movements and greatly limiting economic activity. More recently, as restrictions begin to be loosened or lifted entirely, the use of so-called contact tracing apps has figured prominently in many jurisdictions’ plans to reopen society. Critics have questioned the utility of such technologies on a number of fronts, both practical and ethical. (...) However, little has been said about the ways in which the normative design choices of app developers, and the products that result therefrom, might contribute to ethical reflection and wider political debate. Drawing from scholarship in critical design and human–computer interaction, this paper examines the development of a QR code-based tracking app called Zwaai (‘Wave’ in Dutch), where its designers explicitly positioned the app as an alternative to the predominant Bluetooth and GPS-based approaches. Through analyzing these designers’ choices, this paper argues that QR code infrastructures can work to surface a set ofethical–political seams, two of which are discussed here—responsibilizationandnetworked (im)permanence—that more ‘seamless’ protocols like Bluetooth actively aim to bypass, and which may go otherwise unnoticed by existing ethical frameworks. (shrink)

Martin-Löf's constructive type theory forms the basis of this paper. His central notions of category and set, and their relations with Russell's type theories, are discussed. It is shown that addition of an axiom - treating the category of propositions as a set and thereby enabling higher order quantification - leads to inconsistency. This theorem is a variant of Girard's paradox, which is a translation into type theory of Mirimanoff's paradox (concerning the set of all well-founded sets). The occurrence of (...) the contradiction is explained in set theoretical terms. Crucial here is the way a proof-object of an existential proposition is understood. It is shown that also Russell's paradox can be translated into type theory. The type theory extended with the axiom mentioned above contains constructive higher order logic, but even if one only adds constructive second order logic to type theory the contradictions arise. (shrink)

Medical research data is sensitive personal data that needs to be protected from unauthorized access and unintentional disclosure. In a research setting, sharing of data within the scientific community is necessary in order to make progress and maximize scientific benefits derived from valuable and costly data. At the same time, convincingly protecting the privacy of people participating in medical research is a prerequisite for maintaining trust and willingness to share. In this commentary, we will address this issue and the pitfalls (...) involved in the context of the PEP project1 that provides the infrastructure for the Personalized Parkinson’s Project,2 a large cohort study on Parkinson’s disease from Radboud University Medical Center, in cooperation with Verily life Sciences, an Alphabet subsidiary. (shrink)

The shriek modality \s! of linear logic performs two tasks: it restores in annotated from both weakening and contraction. We separate these tasks by introducing two modalities: for weakening and for contraction. These give rise to two logics which are “inbetween” linear and intuitionistic logic: in affine logic one always has a weakening and a for contraction and in relevant logic one always has a contraction and a weakening. The semantics of these logics is obtained from special kinds of monads, (...) introduced by Anders Kock in the early seventies. As subtle point is how to retrieve the \s! of linear logic from and . Technically this will be achieved in terms of distributive laws—introduced by Jon Beck. We find models where one has \s! = and also models with \s! = . It will be shown that on the category of complete lattices one has comonads and with = \s!=. (shrink)

Within the context of an involutive monoidal category the notion of a comparison relation ${\mathsf{cp} : \overline{X} \otimes X \rightarrow \Omega}$ is identified. Instances are equality = on sets, inequality ${\leq}$ on posets, orthogonality ${\perp}$ on orthomodular lattices, non-empty intersection on powersets, and inner product ${\langle {-}|{-} \rangle}$ on vector or Hilbert spaces. Associated with a collection of such (symmetric) comparison relations a dagger category is defined with “tame” relations as morphisms. Examples include familiar categories in the foundations of quantum (...) mechanics, such as sets with partial injections, or with locally bifinite relations, or with formal distributions between them, or Hilbert spaces with bounded (continuous) linear maps. Of one particular example of such a dagger category of tame relations, involving sets and bifinite multirelations between them, the categorical structure is investigated in some detail. It turns out to involve symmetric monoidal dagger structure, with biproducts, and dagger kernels. This category may form an appropriate universe for discrete quantum computations, just like Hilbert spaces form a universe for continuous computation. (shrink)

This paper develops the basics of the theory of involutive categories and shows that such categories provide the natural setting in which to describe involutive monoids. It is shown how categories of Eilenberg-Moore algebras of involutive monads are involutive, with conjugation for modules and vector spaces as special case. A part of the so-called Gelfand–Naimark–Segal (GNS) construction is identified as an isomorphism of categories, relating states on involutive monoids and inner products. This correspondence exists in arbritrary involutive symmetric monoidal categories.

Expectation Maximisation (EM) and Latent Dirichlet Allocation (LDA) are two frequently used inference algorithms, for finding an appropriate mixture of latent variables, and for finding an allocation of topics for a collection of documents. A recent insight in probabilistic learning is that Jeffrey’s update rule gives a decrease of Kullback-Leibler divergence. Its logic is error correction. It is shown that this same rule and divergence decrease logic is at the heart of EM and LDA, ensuring that successive iterations are decreasingly (...) wrong. (shrink)

Various generalizations of Boolean algebras are being studied in algebraic quantum logic, including orthomodular lattices, orthomodular po-sets, orthoalgebras and effect algebras. This paper contains a systematic study of the structure in and between categories of such algebras. It does so via a combination of totalization (of partially defined operations) and transfer of structure via coreflections.

Multisets are ‘sets’ in which elements may occur multiple times. Discrete probability distributions capture states in which elements may occur with probabilities that add up to one. This paper describes how the interaction between multisets and distributions lies at the heart of some basic constructions in probability theory, especially in distributions arising from drawing from an urn with multiple balls and in learning distributions from multiple occurrences of data. Drawing multiple balls from an urn is described uniformly in terms of (...) Kleisli iteration for a monad, covering the four standard distinctions of ordered/unordered draws, with/without replacement. In probabilistic learning the paper distinguishes two forms of likelihood, based on also on iteration, with corresponding forms of learning. Both of these forms occur in the literature, but they are not clearly distinguished, even though they lead to different outcomes. (shrink)