Ecumenical modal logic

The discussion about how to put together Gentzen's systems for classical and intuitionistic logic in a single unified system is back in fashion. Indeed, recently Prawitz and others have been discussing the so called Ecumenical Systems, where connectives from these logics can co-exist in peace. In Prawitz' system, the classical logician and the intuitionistic logician would share the universal quantifier, conjunction, negation, and the constant for the absurd, but they would each have their own existential quantifier, disjunction, and implication, with different meanings. Prawitz' main idea is that these different meanings are given by a semantical framework that can be accepted by both parties. In a recent work, Ecumenical sequent calculi and a nested system were presented, and some very interesting proof theoretical properties of the systems were established. In this work we extend Prawitz' Ecumenical idea to alethic K-modalities

Eleven strategies for making reproducible research and open science training the norm at research institutions

Reproducible research and open science practices have the potential to accelerate scientific progress by allowing others to reuse research outputs, and by promoting rigorous research that is more likely to yield trustworthy results. However, these practices are uncommon in many fields, so there is a clear need for training that helps and encourages researchers to integrate reproducible research and open science practices into their daily work. Here, we outline eleven strategies for making training in these practices the norm at research institutions. The strategies, which emerged from a virtual brainstorming event organized in collaboration with the German Reproducibility Network, are concentrated in three areas: (i) adapting research assessment criteria and program requirements; (ii) training; (iii) building communities. We provide a brief overview of each strategy, offer tips for implementation, and provide links to resources. We also highlight the importance of allocating resources and monitoring impact. Our goal is to encourage researchers - in their roles as scientists, supervisors, mentors, instructors, and members of curriculum, hiring or evaluation committees - to think creatively about the many ways they can promote reproducible research and open science practices in their institutions

Structures for multiplicative cyclic linear logic: Deepness vs cyclicity

Abstract. The aim of this work is to give an alternative presentation for the multiplicative fragment of Yetter’s cyclic linear logic. The new presentation is inspired by the calculus of structures, and has the interesting feature of avoiding the cyclic rule. The main point in this work is to show how cyclicity can be substituted by deepness, i.e. the possibility of applying an inference rule at any point of a formula. We finally derive, through a new proof technique, the cut elimination property of the calculus