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. (shrink)

A movement asking to take race out of medicine is growing in the US. While we agree with the necessity to get rid of flawed assumptions about biological race that pervade automatic race correction in medical algorithms, we urge caution about insisting on a blanket eliminativism about race in medicine. If we look at racism as a fundamental cause, in the sense that this notion has been introduced in epidemiological studies by Bruce Link and Jo Phelan, we must conclude that (...) race is indispensable to consider, investigate, and denounce the health effects of multilevel racism, and cannot be eliminated by addressing more specific risk factors in socially responsible epidemiology and clinical medicine. This does not mean that realism about human races is vindicated. While maintaining that there are no human races, we show how it is that a non-referring concept can nonetheless turn out indispensable for explaining real phenomena. (shrink)

In this paper, we argue for the centrality of prediction in the use of computational models in science. We focus on the consequences of the irreversibility of computational models and on the conditional or ceteris paribus, nature of the kinds of their predictions. By irreversibility, we mean the fact that computational models can generally arrive at the same state via many possible sequences of previous states. Thus, while in the natural world, it is generally assumed that physical states have a (...) unique history, representations of those states in a computational model will usually be compatible with more than one possible history in the model. We describe some of the challenges involved in prediction and retrodiction in computational models while arguing that prediction is an essential feature of non-arbitrary decision making. Furthermore, we contend that the non-predictive virtues of computational models are dependent to a significant degree on the predictive success of the models in question. (shrink)

The aim of this article is to explore the impact of Darwinism in metaethics and dispel some of the confusion surrounding it. While the prospects for a Darwinian metaethics appear to be improving, some underlying epistemological issues remain unclear. We will focus on the so-called Evolutionary Debunking Arguments (EDAs) which, when applied in metaethics, are defined as arguments that appeal to the evolutionary origins of moral beliefs so as to undermine their epistemic justification. The point is that an epistemic disanalogy (...) can be identified in the debate on EDAs between moral beliefs and other kinds of beliefs, insofar as only the former are regarded as vulnerable to EDAs. First, we will analyze some significant debunking positions in metaethics in order to show that they do not provide adequate justification for such an epistemic disanalogy. Then, we will assess whether they can avoid the accusation of being epistemically incoherent by adopting the same evolutionary account for all kinds of beliefs. In other words, once it is argued that Darwinism has a corrosive impact on metaethics, what if its universal acid cannot be contained? (shrink)

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.

The present article aims to utilize some insights from behavioral and happiness economics to discuss the consequences that the introduction of an unconditional basic income to cope with technological unemployment may hold for well-being. The impact of 21st-century technological progress on employment has only just begun to make itself felt and it will take time to realize its full extent. However, the main innovation is already common knowledge: robots are finding their way into the production process. According to several recent (...) contributions, the phenomenon is radically different from past technological revolutions and could generate high levels of unemployment, calling for innovative redistributive public policies. The present article, building on Keynes’ short essay and referring to some of the principles and models of behavioral and happiness economics, focuses on the best-known of these policies, namely provision of an unconditional basic income. A series of factors – loss aversion and hedonic adaptation, the impossibility of escalating to higher-grade consumption behaviors, social interaction in the form of active and passive envy, loss of self-esteem and social stigma – are all likely to have a negative impact on well-being if an unconditional basic income that remains unchanging over time is implemented. A policy mix combining a rising basic income with other measures is therefore proposed. (shrink)

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. (shrink)

The book answers long-standing questions on scientific modeling and inference across multiple perspectives and disciplines, including logic, mathematics, physics and medicine. The different chapters cover a variety of issues, such as the role models play in scientific practice; the way science shapes our concept of models; ways of modeling the pursuit of scientific knowledge; the relationship between our concept of models and our concept of science. The book also discusses models and scientific explanations; models in the semantic view of theories; (...) the applicability of mathematical models to the real world and their effectiveness; the links between models and inferences; and models as a means for acquiring new knowledge. It analyzes different examples of models in physics, biology, mathematics and engineering. Written for researchers and graduate students, it provides a cross-disciplinary reference guide to the notion and the use of models and inferences in science. (shrink)

It is of concern that, until now, Western and Southern theories have not been able to provide a full conceptual understanding of the complicity of the elites and states of former colonies outside the West with the political domination they suffer from their Western counterparts. Decolonial thought, by exploring global epistemic designs, can fully explain such political dependency, which, for Aníbal Quijano, results from the local elites’ goal to racially identify with their Western peers (self-humanization), obstructing local nationalization. We explore (...) why the racially dehumanized local elites believe they can humanize themselves. Our claim is that this happens because of modernity’s pretense that everyone can become civilized and, thereby, human, hiding the fact that hu(man)s are only heterosexual men that are simultaneously Western, white and Christian. Only by focusing on the enunciation of Western knowledge, instead of on its enunciated content, can we make that argument. (shrink)

As Artificial Intelligence (AI) becomes more and more pervasive in our everyday life, new questions arise about its ethical and social impacts. Such issues concern all stakeholders involved in or committed to the design, implementation, deployment, and use of the technology. The present document addresses these preoccupations by introducing and discussing a set of practical obligations and recommendations for the development of applications and systems based on AI techniques. With this work we hope to contribute to spreading awareness on the (...) many social challenges posed by AI and encouraging the establishment of good practices throughout the relevant social areas. As points of novelty, the paper elaborates on an integrated view that combines both human rights and ethical concepts to reap the benefits of the two approaches. Moreover, it proposes innovative recommendations, such as those on redress and governance, which add further insight to the debate. Finally, it incorporates a specific focus on the Italian Constitution, thus offering an example of how core legislations of Member States might contribute to further specify and enrich the EU normative framework on AI. (shrink)

The article reviews some analyses of temporal language in logical approaches to natural language semantics. It considers some asymmetries between past and future, manifested in language, which motivate the “standard view” of the non-reversibility of time and the persistence of the past. It concludes with a puzzle about the changing past which challenges the standard view.

El propósito del presente trabajo es ofrecer una contextualización de “Las implicancias del pragmatismo para la educación”, que traducimos en este número de la revista. El artículo está compuesto de tres partes que John Dewey escribe en diciembre de 1908, febrero y marzo de 1909. Nuestra hipótesis interpretativa es que este texto es fundamental en dos sentidos: en primer lugar, para entender los lazos de Dewey con la tradición pragmatista; en segundo lugar, para comprender su conceptualización del vínculo entre pragmatismo (...) y educación. (shrink)

All around the world in March, due to COVID-19, competitive sport calendars were suddenly canceled, jeopardizing the training programs of athletes. Moreover, in Italy, the government banned all non-essential travel across the entire country from the beginning of March. Consequently, Italian cyclists were banned from leaving their homes and therefore unable to perform their ordinary training activities. The Italian Association of Professional Cyclists early on during that period noticed that several cyclists were experiencing a worrying decrease in their mental well-being (...) and asked the authors to set up an online Sport Psychology Intervention during lockdown to enhance the athletes' mental health. Through a number of unprecedented events and considerations, the aim of the current investigation was to assess the Italian cyclists' mental health during the lockdown and its changes after the SPI. We validated the Italian version of the Sport Mental Health Continuum Short Form —presented in Study 1—and then applied it to a sample of Italian professional cyclists—presented in Study 2—prior to and after the SPI. To achieve these objectives, the reliability and construct validity of the Italian version of the Sport MHC-SF were tested in Study 1. RM-MANOVA tests were run to evaluate the effect of SPI on cyclists in Study 2. A total of 185 Italian athletes were involved in the validation of the MHC in Study 1 and 38 professional cyclists in Study 2. Results from Study 1 suggested a three-factor higher order model of Sport MHC-SF [Model fit: χ2 = 471.252, p < 0.000; CFI = 0.951; RMSEA = 0.049; RMR= 0.048]. MCFA showed that the default model kept invariance among groups of athletes. Results from Study 2 highlighted that professional cyclists who followed the SPI were able to cope better with psychological stressors, showing improved well-being compared to the athletes that did not. No significant differences were found for emotional and social well-being. The present multi-study paper contributes to the theoretical field with a validated measure of Sport MHC-SF translated in the Italian language and culture. It also provides practical implications related to cases of reduced mental health due to injury, illness, or similar situations of home confinement in the future. (shrink)

The paper defends the thesis that future tensed statements have truth values that can change over time. In relativistic approaches to the evaluation of future contingents (MacFarlane, 2003, 2007), only changes in the truth status of such statements from neither-true-nor-false to definitely true (or definitely false) are taken into consideration. More precisely, given the monotonicity property of the model of historical possibilities, for which historical alternatives to a world w at a time t increase moving backward and shrink moving forward (...) in time with respect to t (Thomason, 1984), only such changes are predicted to be possible. I will consider the theoretical possibility of truth value transitions for future contingents from true to false and from false to true, as well as some potential linguistic evidence for such transitions - drawn from certain uses of phase adverbs like still, no longer, and always in English and Romance. To deal with the natural language data, I will propose a situation-based version of Branching Time which accommodates partiality of information, and a revision of the Kaplanian notion of truth-in-context. (shrink)

According to the actualist view, what is essential to the truth conditions of a future-tensed sentence ‘it will be the case that ϕ’ is reference to the unique course of events that will become actual. On the other hand, the modal view has it that the truth conditions of such a sentence require that the truth of ϕ be already “settled” at the time of utterance, where “being settled at time t” is defined by universal quantification over a domain of (...) courses of events, the futures compatible with what has happened up to time t. On the proposal we discuss in this paper, the actualist view and the modal view are seen as two related attitudes that speakers can have when they evaluate future-tensed sentences, and the corresponding interpretations undergo a unified semantic treatment based on a contextual notion of settledness. A central feature of our approach is a dynamic view of contexts of utterance, whereby the world of the utterance is not fixed once and for all, as different worlds, by the passing of time, can play this role in turn. Finally, one major goal of the paper is to show how the unified analysis we propose accounts for a particularly interesting interpretation of future-tensed sentences, often referred to as ‘epistemic reading’. (shrink)

An open question in the semantics of modality is what relations there are among different modal flavours. In this article, we consider the thorny issue of whether ascribing to an agent the obligation to φ implies that it is possible for the agent to φ. Traditionally, this issue has been interpreted as whether ‘ought’ implies ‘can’. But another linguistic interpretation is available as well, namely, whether ‘must’ implies ‘can’ (MIC). We show that ‘must’ does imply ‘can’ via a convergent argument. (...) The first strand of the argument is theoretical: it consists in proving MIC from a well-established theory of modality in natural language, i.e., that proposed by Kratzer. The second strand is empirical: we present novel acceptability judgment studies showing that MIC predicts and explains the linguistic behaviour of native English speakers. (shrink)

Este artículo presenta una interpretación del ser-para-otro en la ontología fenomenológica de Sartre. A partir de un análisis contextual de la fenomenología de la mirada en El ser y la nada, formulamos el problema del ser-para-otro como tercera ek-stasis. Si admitimos que el ser-para-otro surge de una profundización de la segunda ek-stasis (reflexión) y que, por tanto, está siempre condicionado por ella, corremos el riesgo de caer en la ilusión de la primacía del ser-para-sí. En oposición a esta interpretación, presentamos (...) la hipótesis de que el ser para otro tiene una estructura inmediata, y no sólo reflexiva, basada en El ser y la nada y, de manera auxiliar, en el Idiota da familia. (shrink)

The scope and mission of the history of science have been constant objects of reflection and debate within the profession. Recently, Lorraine Daston has called for a shift of focus: from the history of science to the history of knowledge. Such a move is an attempt at broadening the field and ridding it of the contradictions deriving from its modernist myth of origin and principle of demarcation. Taking the move from a pluralistic concept of medicine, the present paper explores the (...) actual and possible contributions that a history of knowledge can offer to the history of medicine in particular. As we will argue, the history of medicine has always been a history of knowledge, but for good reasons has always stuck to the concept of medicine as its object and problem throughout the ages, including the modern, scientific one. We argue that, in the history of medicine, the demarcation between scientific and non‐scientific represents an accident, but is not foundational as in the case of natural science. Furthermore, the history of medicine programmatically played a role in at least two academic domains (history proper and medical education), adjusting historical narratives of medical knowledge to its audience. Accordingly, we underscore that the history of both science and medicine, as traditionally defined, already provides room for almost the whole spectrum of approaches to history. Moreover, their different myths of origin can, and indeed must, be included in the reflexivity of the historical gaze. We argue that the position towards a history of science, medicine, or knowledge is not a question of narrative or theory, rather, it is a question of relevance and awareness of extant contexts. (shrink)

The 3sg pronouns “he” and “she” impose descriptive gender conditions on their referents. These conditions are standardly analysed as presuppositions. Cooper argues that, when 3sg pronouns occur free, they have indexical presuppositions: the gender condition must be satisfied by the pronoun’s referent in the actual world. In this paper, we consider the behaviour of free 3sg pronouns in conditionals and focus on cases in which the pronouns’ gender presuppositions no longer seem to be indexical and project locally instead. We compare (...) these cases to previously reported shifty readings of indexicals in so-called “epistemic conditionals” :359–406, 2012) and propose a unified account of locally projected gender presuppositions and shifty indexicals based on the idea that indicative conditionals are Kaplanian monsters. (shrink)

Italian irrealis conditionals with a double imperfect (Imperfetto Irrealis) have puzzling temporal and aspectual properties: unlike well-known core uses (continuative, progressive, habitual/generic) of Romance imperfects to describe an eventuality as past, they allow for the whole range of temporal interpretations, namely, the events described by the protasis and the apodosis can be past, present or future; in addition, the ongoingness condition characteristic of those core uses is not relevant anymore, since the events described by the protasis and the apodosis are (...) seen as culminated. Imperfetto Irrealis are also puzzling for their modal properties: unlike the other indicative conditionals, which are generally interpreted as epistemic, they express counterfactual meaning. By relying on data of mixed CFs (in which an Imperfetto combines with a past Subjunctive or a past Conditional), we show that Imperfetto Irrealis are closer to two pasts CFs than to one past CFs. The data suggest that, in spite of the latitude of their temporal interpretations, Imperfetto Irrealis preserve the true past tense active in core uses of Romance imperfects. Building on a previous analysis of imperfective sentences in Del Prete (2013), combined with crucial insights on CF semantics from Ippolito (2004, 2006), Arregui (2005) and Anand and Hacquard (2010), we propose a formal account of Imperfetto Irrealis which allows a partially unified view of the semantics of the Imperfetto across conditional and non-conditional uses. The main insight making this partial unification possible bears on the morphosyntactic structure of Imperfetto Irrealis and is inspired by previous formal analyses of CFs (Iatridou 2000, Ippolito 2006, Ferreira 2016): the two realizations of the Imperfetto found in this type of conditional are the morphosyntactic reflexes of a single higher PAST+IPFV, therefore the true semantically active Imperfetto is not situated where one can see/hear the Imperfetto morphology but higher in the syntactic structure. (shrink)

O problema lógico do mal é a alegação de que a existência de Deus e a existência de mal no mundo são logicamente inconsistentes. Neste artigo, descrevemos o sistema N3, baseado em partes na contribuição de Nieznański (2007, 2008), que oferece uma resposta ao problema lógico do mal através da refutação de uma versão do determinismo religioso. Argumentamos especificamente que, dados os resultados de N3, a existência de Deus não é contraditória com a do mal, e portanto, o teísmo clássico (...) não pode ser considerado irracional com base no problema lógico do mal. Nossa abordagem pode ser considerada um caso de lógica da religião, ou seja, de lógica aplicada ao discurso religioso. (shrink)

This article explores the ways in which suspects attempt to make putative victims/complainants at least partially responsible for the incidents for which they are investigated, transforming themselves into the victim and the other into the perpetrator. Drawing upon conversation analysis, I examine audio-recorded police interviews for low-level crimes in England and in which suspects have constructed what I refer as counter-denunciations. I argue that suspects accomplish these counter-denunciations through discursive practices that involve, for example (a) contrasting the complainant’s actions with (...) their own innocent conduct; (b) historicizing the event being investigated; and (c) discrediting the complainant’s character—stigmatizing. These practices have in common the suspects’ reliance on the relational and contextual character of the categories ‘offender’ and ‘victim’. (shrink)

This article aims at discussing an interesting variant of scientific realism recently proposed and defended by Sandra Mitchell (forthcoming), namely an affordances-based and pragmatist variant of scientific realism. We firstly place Mitchell’s proposal in the context of the current state of the debate over scientific realism. Secondly, we summarize the salient features of Mitchell’s proposal. Thirdly, we point out some aspects of that proposal that might require some further refinement and clarification in order to make it less prone to criticisms (...) by both realists and antirealists. More precisely, in this paper we address the following issues: 1) whether Mitchell’s proposal can be classified as a genuine form of scientific realism; 2) whether the fact that in Mitchell’s proposal figure some variants of the no miracle argument is in tension with some other of its features. (shrink)

O que proponho nesse artigo é demonstrar interpretativamente alguns pontos de conexão entre os termos pensamento da identidade e o fetichismo na filosofia de T. W. Adorno (1903-1969). Essa conexão é parte de uma elaboração, ou uma ampliação, do conceito de fetichismo na filosofia adorniana cuja evidência surge a partir de duas perspectivas interpretativas: [i] por uma interpretação externa à filosofia de Adorno, tal como uma história filosófica do conceito; e [i.i.] por uma interpretação interna à sua filosofia, considerando o (...) fetichismo como elemento de constelação de seu pensamento e, consequentemente, demonstrando sua conexão com o pensamento da identidade. Enfim, nesse artigo me aterei a essa interpretação interna à filosofia de Adorno, usando a obra Dialética Negativa (1966), bem como a obra Dialética do Esclarecimento (1947), escrita em parceria com M. Horkheimer (1895-1973), a fim de atingir o objetivo proposto. (shrink)

The passage has been an object of scholarly debate: the lack of independent sources on the mathematical construction described by Aristotle, the terseness of the formulation and the resulting syntactical ambiguities make the exact interpretation of the text quite difficult, as already noted by Philoponus. What does it mean that the gnomons are ‘placed round the one and without’ (περὶ τὸ ἓν καὶ χωρίς)? And in what sense is this an indication of the even being ‘cut off, enclosed (ἐναπολαμβανόμενον), and (...) limited (περαινόμενον) by the odd’? The aim of the present paper is to discuss the available interpretations of the passage and to propose a new one. (shrink)

Hoje se lê a parte final do Contrato Social (1762) à luz do movimento contínuo - que perpassa toda a obra do genebrino - entre o geral e o particular, entre a norma e o fato, as leis como podem/devem ser e os homens como são. A república ideal já fora toda esboçada em cada um dos parágrafos da Dedicatória à Genebra escrita por Rousseau para compor a introdução ao Discurso Sobre a Origem e o Fundamento da Desigualdade entre os (...) Homens (o Segundo Discurso publicado em 1755). Mas é no Contrato Social que as diretrizes ganham fundamento e se apresentam enquanto tratado de direito político. (shrink)

L'époque, selon certains, serait celle de l'espace, après l'effondrement des grandes eschatologies historiques. L'espace a, on l'oublie, une histoire. Quant à l'histoire, elle trouverait dans sa mise en relation avec les discours de la spatialité (architecture, écologie, géographie), les moyens de s'inscrire dans l'effectivité.

Synapsins I and II are a family of synaptic vesicle‐associated phosphoproteins involved in the short‐term regulation of neurotransmitter release. In this review, we discuss a working model for the molecular mechanisms by which the synapsins act. We propose that synapsin I links synaptic vesicles to actin filaments in the presynaptic nerve terminal and that these interactions are modulated by the reversible phosphorylation of synapsin I through various signal transduction pathways. The high degree of homology between the synapsins suggests that some (...) of the functional properties of synapsin I are also shared by synapsin II. (shrink)

Neste artigo, pretendo explicitar o papel da lógica formal no projeto crítico kantiano. No tratamento dessa questão, abordarei a relação entre a lógica formal, frequentemente chamada por Kant de lógica geral, e a lógica transcendental. Assumirei a tese de que a lógica formal e a lógica transcendental são duas ciências racionais puras, distintas, independentes, porém, com conexões entre si, a despeito das leituras que sugerem que a lógica transcendental substitua a lógica formal ou que a lógica formal mantenha a sua (...) existência, devendo, no entanto, ser subordinada à lógica transcendental. Na caracterização da lógica formal, utilizarei, sobretudo, a Jäsche-Logik. Quanto à lógica transcendental, exposta na Kritik der reinen Vernunft, irei me servir da leitura semântica de Loparic para tratar do conhecimento metafísico da natureza. Inicio o artigo apontando a proximidade de Kant com a lógica formal e o seu emprego na elaboração do projeto crítico. (shrink)

The concentration of high-frequency controls in a limited period of time constitutes an important feature of many law-enforcement policies around the world. In this paper, we offer a comprehensive investigation on the relative efficiency and effectiveness of various crackdown policies using a lab-in-the-field experiment with real passengers of a public transport service. We introduce a novel game, the daily public transportation game, where subjects have to decide, over many periods, whether to buy or not a ticket knowing that there might (...) be a control. Our results show that concentrated crackdowns are less effective and efficient than random controls; prolonged crackdowns reduce fare-dodging during the period of intense monitoring but induce a burst of fraud as soon as they are withdrawn; pre-announced controls induce more fraud in the periods without control. Overall, we also observe that real fare-dodgers fraud more in the experiment than non-fare-dodgers. (shrink)

Com este artigo se pretende passar pelas leituras feitas sobre o texto do profeta Zacarias. Não há a intenção de se fazer uma abordagem exegética, mas antes, apenas um histórico da pesquisa do profeta - tão pouco lido no Brasil e na América Latina. Sua relevância conduz ao conhecimento das posições e propostas mais clássicas e as mais inovadoras da interpretação deste texto profético. Como também reconhecendo as últimas dificuldades encontradas na sua interpretação.

O objetivo do artigo é compreender como as metamorfoses econômicas e sociais vivenciadas e experienciadas nas comunidades quilombolas do território Terra da Liberdade, situadas no Baixo Tocantins, estado do Pará, produzem dizeres e linguagem, e, assim, formas de uma comunicação de resistência. Parte-se da reflexão de Heidegger (2001) sobre a relação entre existência e lugar para compreender o processo de construção dialogada do Protocolo de Consultas do território. A metodologia utilizada foi a observação participante com entrevistas abertas e semiestruturadas, num (...) diálogo entre etnografia e fenomenologia. Observamos que o direito de "se dizer" é um conjunto de lutas comunicacionais. Compreendendo comunicação como dizer coletivo e social, o artigo reflete sobre lutas por reconhecimento da identidade, dos direitos, do território. (shrink)

In this paper we analyze the resilience to decoherence of the Macroscopic Quantum Superpositions (MQS) generated by optimal phase-covariant quantum cloning according to two coherence criteria, both based on the concept of Bures distance in Hilbert spaces. We show that all MQS generated by this system are characterized by a high resilience to decoherence processes. This analysis is supported by the results of recent MQS experiments of N=3.5×104 particles.

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. (shrink)