Healthiness from Duality

Healthiness is a good old question in program logics that dates back to Dijkstra. It asks for an intrinsic characterization of those predicate transformers which arise as the (backward) interpretation of a certain class of programs. There are several results known for healthiness conditions: for deterministic programs, nondeterministic ones, probabilistic ones, etc. Building upon our previous works on so-called state-and-effect triangles, we contribute a unified categorical framework for investigating healthiness conditions. We find the framework to be centered around a dual adjunction induced by a dualizing object, together with our notion of relative Eilenberg-Moore algebra playing fundamental roles too. The latter notion seems interesting in its own right in the context of monads, Lawvere theories and enriched categories.Comment: 13 pages, Extended version with appendices of a paper accepted to LICS 201

The groupoidal analogue Theta~ to Joyal's category Theta is a test category

We introduce the groupoidal analogue \tilde\Theta to Joyal's cell category \Theta and we prove that \tilde\Theta is a strict test category in the sense of Grothendieck. This implies that presheaves on \tilde\Theta model homotopy types in a canonical way. We also prove that the canonical functor from \Theta to \tilde\Theta is aspherical, again in the sense of Grothendieck. This allows us to compare weak equivalences of presheaves on \tilde\Theta to weak equivalences of presheaves on \Theta. Our proofs apply to other categories analogous to \Theta.Comment: 41 pages, v2: references added, Remark 7.3 added, v3: metadata update

Bunge’s Mathematical Structuralism Is Not a Fiction

In this paper, I explore Bunge’s fictionism in philosophy of mathematics. After an overview of Bunge’s views, in particular his mathematical structuralism, I argue that the comparison between mathematical objects and fictions ultimately fails. I then sketch a different ontology for mathematics, based on Thomasson’s metaphysical work. I conclude that mathematics deserves its own ontology, and that, in the end, much work remains to be done to clarify the various forms of dependence that are involved in mathematical knowledge, in particular its dependence on mental/brain states and material objects

Geometric Logic in Computer Science

We present an introduction to geometric logic and the mathematical structures associated with it, such as categorical logic and toposes. We also describe some of its applications in computer science including its potential as a logic for spec-i cation languages.

A new foundational crisis in mathematics, is it really happening?

The article reconsiders the position of the foundations of mathematics after the discovery of HoTT. Discussion that this discovery has generated in the community of mathematicians, philosophers and computer scientists might indicate a new crisis in the foundation of mathematics. By examining the mathematical facts behind HoTT and their relation with the existing foundations, we conclude that the present crisis is not one. We reiterate a pluralist vision of the foundations of mathematics. The article contains a short survey of the mathematical and historical background needed to understand the main tenets of the foundational issues.Comment: Final versio

The roots of "Western European societal evolution". A concept of Europe by Jenő Szűcs

Jenő Szűcs wrote his essay entitled Sketch on the three regions of Europe in the early 1980s in Hungary. During these years, a historically well-argued opinion emphasising a substantial difference between Central European and Eastern European societies was warmly received in various circles of the political opposition. In a wider European perspective Szűcs used the old “liberty topos” which claims that the history of Europe is no other than the fulfillment of liberty. In his Sketch, Szűcs does not only concentrate on questions concerning the Middle Ages in Western Europe. Yet it is this stream of thought which brought a new perspective to explaining European history. His picture of the Middle Ages represents well that there is a way to integrate all typical Western motifs of post-war self-definition into a single theory. Mainly, the “liberty motif”, as a sign of “Europeanism” – in the interpretation of Bibó’s concept, Anglo-saxon Marxists and Weber’s social theory –, developed from medieval concepts of state and society and from an analysis of economic and social structures. Szűcs’s historical aspect was a typical intellectual product of the 1980s: this was the time when a few Central European historians started to outline non-Marxist aspects of social theory and categories of modernisation theories, but concealing them with Marxist terminology

Towards a ‘smart’ cost–benefit tool: using machine learning to predict the costs of criminal justice policy interventions

BACKGROUND: The Manning Cost–Benefit Tool (MCBT) was developed to assist criminal justice policymakers, policing organisations and crime prevention practitioners to assess the benefits of different interventions for reducing crime and to select those strategies that represent the greatest economic return on investment. DISCUSSION: A challenge with the MCBT and other cost–benefit tools is that users need to input, manually, a considerable amount of point-in-time data, a process that is time consuming, relies on subjective expert opinion, and introduces the potential for data-input error. In this paper, we present and discuss a conceptual model for a ‘smart’ MCBT that utilises machine learning techniques. SUMMARY: We argue that the Smart MCBT outlined in this paper will overcome the shortcomings of existing cost–benefit tools. It does this by reintegrating individual cost–benefit analysis (CBA) projects using a database system that securely stores and de-identifies project data, and redeploys it using a range of machine learning and data science techniques. In addition, the question of what works is respecified by the Smart MCBT tool as a data science pipeline, which serves to enhance CBA and reconfigure the policy making process in the paradigm of open data and data analytics