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

A System of Interaction and Structure

This paper introduces a logical system, called BV, which extends multiplicative linear logic by a non-commutative self-dual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved therein. It becomes very natural in a new formalism, called the calculus of structures, which is the main contribution of this work. Structures are formulae submitted to certain equational laws typical of sequents. The calculus of structures is obtained by generalising the sequent calculus in such a way that a new top-down symmetry of derivations is observed, and it employs inference rules that rewrite inside structures at any depth. These properties, in addition to allow the design of BV, yield a modular proof of cut elimination.Comment: This is the authoritative version of the article, with readable pictures, in colour, also available at . (The published version contains errors introduced by the editorial processing.) Web site for Deep Inference and the Calculus of Structures at <http://alessio.guglielmi.name/res/cos

Towards a Combinatorial Proof Theory

International audienceThe main part of a classical combinatorial proof is a skew fi-bration, which precisely captures the behavior of weakening and contraction. Relaxing the presence of these two rules leads to certain substruc-tural logics and substructural proof theory. In this paper we investigate what happens if we replace the skew fibration by other kinds of graph homomorphism. This leads us to new logics and proof systems that we call combinatorial

On the Length of Medial-Switch-Mix Derivations

International audienceSwitch and medial are two inference rules that play a central role in many deep inference proof systems. In specific proof systems, the mix rule may also be present. In this paper we show that the maximal length of a derivation using only the inference rules for switch, medial, and mix, modulo associativity and commutativity of the two binary con-nectives involved, is quadratic in the size of the formula at the conclusion of the derivation. This shows, at the same time, the termination of the rewrite system

On the Concept of a Notational Variant

In the study of modal and nonclassical logics, translations have frequently been employed as a way of measuring the inferential capabilities of a logic. It is sometimes claimed that two logics are “notational variants” if they are translationally equivalent. However, we will show that this cannot be quite right, since first-order logic and propositional logic are translationally equivalent. Others have claimed that for two logics to be notational variants, they must at least be compositionally intertranslatable. The definition of compositionality these accounts use, however, is too strong, as the standard translation from modal logic to first-order logic is not compositional in this sense. In light of this, we will explore a weaker version of this notion that we will call schematicity and show that there is no schematic translation either from first-order logic to propositional logic or from intuitionistic logic to classical logic

Adaptation of plasminogen activator sequences to known protease structures

AbstractThe sequences of urokinase (UK) and tissue-type plasminogen activator (TPA) were aligned with those of chymotrypsin, trypsin, and elastase according to their ‘structurally conserved regions’. In spite of its trypsin-like specificity UK was model-built on the basis of the chymotrypsin structure because of a corresponding disulfide pattern. The extra disulfide bond falls to cysteines 50 and 111d. Insertions can easily be accommodated at the surface. As they occur similarly in both, UK and TPA, a role in plasminogen recognition may be possible. Of the functional positions known to be involved in substrate or inhibitor binding, Asp 97, Lys 143 and Arg 217 (Leu in TPA) may contribute to plasminogen activating specificity. PTI binding may in part be impaired by structural differences at the edge of the binding pocket

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

Across disciplines, researchers increasingly recognize that open science and reproducible research practices may accelerate scientific progress by allowing others to reuse research outputs and by promoting rigorous research that is more likely to yield trustworthy results. While initiatives, training programs, and funder policies encourage researchers to adopt reproducible research and open science practices, these practices are uncommon inmanyfields. Researchers need training to integrate these practicesinto their daily work. We organized a virtual brainstorming event, in collaboration with the German Reproducibility Network, to discuss strategies for making reproducible research and open science training the norm at research institutions. Here, weoutline eleven strategies, concentrated in three areas:(1)offering training, (2)adapting research assessment criteria and program requirements, and (3) building communities. We provide a brief overview of each strategy, offer tips for implementation,and provide links to resources. Our goal is toencourage members of the research community to think creatively about the many ways they can contribute and collaborate to build communities,and make reproducible research and open sciencetraining the norm. Researchers may act in their roles as scientists, supervisors, mentors, instructors, and members of curriculum, hiring or evaluation committees. Institutionalleadership and research administration andsupport staff can accelerate progress by implementing change across their institution

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

Across disciplines, researchers increasingly recognize that open science and reproducible research practices may accelerate scientific progress by allowing others to reuse research outputs and by promoting rigorous research that is more likely to yield trustworthy results. While initiatives, training programs, and funder policies encourage researchers to adopt reproducible research and open science practices, these practices are uncommon inmanyfields. Researchers need training to integrate these practicesinto their daily work. We organized a virtual brainstorming event, in collaboration with the German Reproducibility Network, to discuss strategies for making reproducible research and open science training the norm at research institutions. Here, weoutline eleven strategies, concentrated in three areas:(1)offering training, (2)adapting research assessment criteria and program requirements, and (3) building communities. We provide a brief overview of each strategy, offer tips for implementation,and provide links to resources. Our goal is toencourage members of the research community to think creatively about the many ways they can contribute and collaborate to build communities,and make reproducible research and open sciencetraining the norm. Researchers may act in their roles as scientists, supervisors, mentors, instructors, and members of curriculum, hiring or evaluation committees. Institutionalleadership and research administration andsupport staff can accelerate progress by implementing change across their institution