Modular labelled calculi for relevant logics

In this article, we perform a detailed proof theoretic investigation of a wide number of relevant logics by employing the well-established methodology of labelled sequent calculi to build our intended systems. At the semantic level, we will characterise relevant logics by employing reduced Routley-Meyer models, namely, relational structures with a ternary relation between worlds along with a unique distinct element considered as the real (or actual) world. This paper realizes the idea of building a variety of modular labelled calculi by reflecting, at the syntactic level, semantic informations taken from reduced Routley-Meyer models. Central results include proofs of soundness and completeness, as well as a proof of cut- admissibility

Topics in the Proof Theory of Non-classical Logics. Philosophy and Applications

Chapter 1 constitutes an introduction to Gentzen calculi from two perspectives, logical and philosophical. It introduces the notion of generalisations of Gentzen sequent calculus and the discussion on properties that characterize good inferential systems. Among the variety of Gentzen-style sequent calculi, I divide them in two groups: syntactic and semantic generalisations. In the context of such a discussion, the inferentialist philosophy of the meaning of logical constants is introduced, and some potential objections – mainly concerning the choice of working with semantic generalizations – are addressed. Finally, I’ll introduce the case studies that I’ll be dealing with in part II. Chapter 2 is concerned with the origins and development of Jaśkowski’s discussive logic. The main idea of this chapter is to systematize the various stages of the development of discussive logic related researches from two different angles, i.e., its connections to modal logics and its proof theory, by highlighting virtues and vices. Chapter 3 focuses on the Gentzen-style proof theory of discussive logic, by providing a characterization of it in terms of labelled sequent calculi. Chapter 4 deals with the Gentzen-style proof theory of relevant logics, again by employing the methodology of labelled sequent calculi. This time, instead of working with a single logic, I’ll deal with a whole family of them. More precisely, I’ll study in terms of proof systems those relevant logics that can be characterised, at the semantic level, by reduced Routley-Meyer models, i.e., relational structures with a ternary relation between states and a unique base element. Chapter 5 investigates the proof theory of a modal expansion of intuitionistic propositional logic obtained by adding an ‘actuality’ operator to the connectives. This logic was introduced also using Gentzen sequents. Unfortunately, the original proof system is not cut-free. This chapter shows how to solve this problem by moving to hypersequents. Chapter 6 concludes the investigations and discusses the future of the research presented throughout the dissertation

Discussive Logic. A Short History of the First Paraconsistent Logic

In this paper we present an overview, with historical and critical remarks, of two articles by S. Jaśkowski ([20, 21] 1948 and [22, 23] 1949), which contain the oldest known formulation of a paraconsistent logic. Jaśkowski has built the logic – he termed discussive (D2) – by defining two new connectives and by introducing a modal translation map from D2 systems into Lewis’ modal logic S5. Discussive systems, for their formal details and their original philosophical justification, have attracted discrete attention among experts. Indeed, in what follows, after having introduced Jaśkowski methodology of building D2 and his main philosophical motivations for providing such a system, we will explore some of the main contributions to the development of D2

Beyond semantic pollution: Towards a practice-based philosophical analysis of labelled calculi

This paper challenges the negative attitudes towards labelled proof systems, usually referred to as semantic pollution, by arguing that such critiques overlook the full potential of labelled calculi. The overarching objective is to develop a practice-based philosophical analysis of labelled calculi to provide insightful considerations regarding their proof-theoretic and philosophical value. To achieve this, successful applications of labelled calculi and related results will be showcased, and comparisons with other relevant works will be discussed. The paper ends by advocating for a more practice-based approach towards the philosophical understanding of proof systems and their role in structural proof theory

Fusion, fission, and Ackermann’s truth constant in relevant logics: A proof-theoretic investigation

The aim of this paper is to provide a proof-theoretic characterization of relevant logics including fusion and fission connectives, as well as Ackermann’s truth constant. We achieve this by employing the well-established methodology of labelled sequent calculi. After having introduced several systems, we will conduct a detailed proof-theoretic analysis, show a cut-admissibility theorem, and establish soundness and completeness. The paper ends with a discussion that contextualizes our current work within the broader landscape of the proof theory of relevant logics

Blockade and Counterflow Supercurrent in exciton-condensate Josephson junctions

We demonstrate that perfect conversion between charged supercurrents in superconductors and neutral supercurrents in electron-hole pair condensates is possible via a new Andreev-like scattering mechanism. As a result, when two superconducting circuits are coupled through a bilayer exciton condensate, the superflow in both layers is drastically modified. Depending on the phase biases the supercurrents can be completely blocked or exhibit perfect drag.Comment: 4 pages, 2 figure

Nodular lymphocyte predominant hodgkin lymphoma and T cell/histiocyte rich large B cell lymphoma : endpoints of a spectrum of one disease?

In contrast to the commonly indolent clinical behavior of nodular lymphocyte predominant Hodgkin lymphoma (NLPHL), T cell/histiocyte rich large B cell lymphoma (THRLBCL) is frequently diagnosed in advanced clinical stages and has a poor prognosis. Besides the different clinical presentations of these lymphoma entities, there are variants of NLPHL with considerable histopathologic overlap compared to THRLBCL. Especially THRLBCL-like NLPHL, a diffuse form of NLPHL, often presents a histopathologic pattern similar to THRLBCL, suggesting a close relationship between both lymphoma entities. To corroborate this hypothesis, we performed gene expression profiling of microdissected tumor cells of NLPHL, THRLBCL-like NLPHL and THRLBCL. In unsupervised analyses, the lymphomas did not cluster according to their entity. Moreover, even in supervised analyses, very few consistently differentially expressed transcripts were found, and for these genes the extent of differential expression was only moderate. Hence, there are no clear and consistent differences in the gene expression of the tumor cells of NLPHL, THRLBCL-like NLPHL and THRLBCL. Based on the gene expression studies, we identified BAT3/BAG6, HIGD1A, and FAT10/UBD as immunohistochemical markers expressed in the tumor cells of all three lymphomas. Characterization of the tumor microenvironment for infiltrating T cells and histiocytes revealed significant differences in the cellular composition between typical NLPHL and THRLBCL cases. However, THRLBCL-like NLPHL presented a histopathologic pattern more related to THRLBCL than NLPHL. In conclusion, NLPHL and THRLBCL may represent a spectrum of the same disease. The different clinical behavior of these lymphomas may be strongly influenced by differences in the lymphoma microenvironment, possibly related to the immune status of the patient at the timepoint of diagnosis