Semantic A-translation and Super-consistency entail Classical Cut Elimination

We show that if a theory R defined by a rewrite system is super-consistent, the classical sequent calculus modulo R enjoys the cut elimination property, which was an open question. For such theories it was already known that proofs strongly normalize in natural deduction modulo R, and that cut elimination holds in the intuitionistic sequent calculus modulo R. We first define a syntactic and a semantic version of Friedman's A-translation, showing that it preserves the structure of pseudo-Heyting algebra, our semantic framework. Then we relate the interpretation of a theory in the A-translated algebra and its A-translation in the original algebra. This allows to show the stability of the super-consistency criterion and the cut elimination theorem

A semantic normalization proof for a system with recursors

Semantics methods have been used to prove cut elimination theorems for a long time. It is only recently that they have been extend to prove strong normalization results, in particular for theories in deduction modulo. However such semantic methods did not apply for systems with recursors like Godel system T. We show in this paper how super natural deduction provides a bridge between superconsistency of arithmetic and strong normalization of system T. We then generalize this result to a family of inductive types before discussing the dependant case

A Semantic Normalization Proof for Inductive Types

Abstract. Semantics methods have been used to prove cut elimination theorems for a long time. It is only recently that they have been extended to prove strong normalization results. For instance using the notion of super-consistency that is a semantic criterion for theories expressed in deduction modulo implying strong normalization. However, the strong normalization of System T has always been reluctant to such semantic methods. In this paper we give a semantic normalization proof of system T using the super consistency of some theory. We then extend the result to every strictly positive inductive type and discuss the extension to predicate logic.

Breathlessness and COVID-19: A Call for Research

Breathlessness, also known as dyspnoea, is a debilitating and frequent symptom. Several reports have highlighted the lack of dyspnoea in a subgroup of patients suffering from COVID-19, sometimes referred to as "silent" or "happy hyp-oxaemia." Reports have also mentioned the absence of a clear relationship between the clinical severity of the disease and levels of breathlessness reported by patients. The cerebral complications of COVID-19 have been largely demonstrated with a high prevalence of an acute encephalopathy that could possibly affect the processing of afferent signals or top-down modulation of breathlessness signals. In this review, we aim to highlight the mechanisms involved in breathlessness and summarize the pathophysiology of COVID-19 and its known effects on the brain-lung interaction. We then offer hypotheses for the alteration of breathlessness perception in COVID-19 patients and suggest ways of further researching this phenomenon

Decrease in pain perception during acute SARS-CoV-2 infection: a case series

Many reports have described pain appearance or an increase of chronic pain concomitant to SARS-CoV-2 infection. Here, we describe the cases of three patients with chronic cancer pain, in which COVID-19 was associated with a dramatic reduction/disappearance of pain. Pain reappeared following recovery from COVID-19. Neurological imaging and pathological findings, when available, were inconclusive. To our knowledge, this is the first case series reporting an acute reduction in pain perception in COVID-19. We believe further investigation is mandatory, as it could shed new light on the mechanisms of pain perception and modulation