This work presents some basic results on a theory of translations between logics and a short revision about Łukasiewicz's logics. Then, it is shown, using facts about algebraic semantics, that there is a conservative translation from every finite Łukasiewicz's logic into classical logic. However, this is not a constructive result.

In this paper we present a new hierarchy of analytical tableaux systems TNDC n, 1≤n<ω, for da Costa's hierarchy of propositional paraconsistent logics Cn, 1≤n<ω. In our tableaux formulation, we introduce da Costa's “ball” operator “o”, the generalized operators “k” and “(k)”, for 1≤k, and the negations “~k”, for k≥1, as primitive operators, differently to what has been done in the literature, where these operators are usually defined operators. We prove a version of Cut Rule for the TNDC n, 1≤n<ω, (...) and also prove that these systems are logically equivalent to the corresponding systems Cn, 1≤n<ω. The systems TNDC n constitute completely automated theorem proving systems for the systems of da Costa's hierarchy Cn, 1≤n<ω. (shrink)

This work presents the concepts of translation and conservative translation between logics. By using algebraic semantics we introduce several conservative translations involving the classical propositional calculus and the many-valued calculi of Post and Lukasiewicz.

In this paper we introduce the concept of conservative translation between logics. We present some necessary and sufficient conditions for a translation to be conservative and study some general properties of logical systems, these properties being characterized by the existence of conservative translations between the systems. We prove that the class constituted by logics and conservative translations between them determines a co-complete subcategory of the bi-complete category constituted by logics and translations.

In 1999, da Silva, D'Ottaviano and Sette proposed a general definition for the term translation between logics and presented an initial segment of its theory. Logics are characterized, in the most general sense, as sets with consequence relations and translations between logics as consequence-relation preserving maps. In a previous paper the authors introduced the concept of conservative translation between logics and studied some general properties of the co-complete category constituted by logics and conservative translations between them. In this paper we (...) present some conservative translations involving classical logic, Lukasiewicz three-valued system L3, the intuitionistic system I1 and several paraconsistent logics, as for instance Sette's system P1, the D'Ottaviano and da Costa system J3 and da Costa's systems Cn, 1≤ n≤ω. (shrink)

In 1999, da Silva, D'Ottaviano and Sette proposed a general definition for the term translation between logics and presented an initial segment of its theory. Logics are characterized, in the most general sense, as sets with consequence relations and translations between logics as consequence-relation preserving maps. In a previous paper the authors introduced the concept of conservative translation between logics and studied some general properties of the co-complete category constituted by logics and conservative translations between them. In this paper we (...) present some conservative translations involving classical logic, Lukasiewicz three-valued system L₃, the intuitionistic system Iⁱ and several para-consistent logics, as for instance Sette's system Pⁱ, the D'Ottaviano and da Costa system J₃ and da Costa's systems $\text{C}_{n}$ , 1 ≤ n ≤ ω. (shrink)

In this paper we present a new hierarchy of analytical tableaux systems TNDC n, 1≤n (...) and also prove that these systems are logically equivalent to the corresponding systems Cn, 1≤nshrink)

In the Organon Aristotle describes some deductive schemata in which inconsistencies do not entail the trivialization of the logical theory involved. This thesis is corroborated by three different theoretical topics by him discussed, which are presented in this paper. We analyse inference schema used by Aristotle in the Protrepticus and the method of indirect demonstration for categorical syllogisms. Both methods exemplify as Aristotle employs classical reductio ad absurdum strategies. Following, we discuss valid syllogisms from opposite premises (contrary and contradictory) studied (...) by the Stagerian in the Analytica Priora (B15). According to him, the following syllogisms are valid from opposite premises, in which small Latin letters stand for terms such as subject and predicate, and capital Latin letters stand for the categorical propositions such as in the traditional notation: (i) in the second figure, Eba,Aba ` Eaa (Cesare), Aba, Eba ` Eaa (Camestres), Eba, I ba ` Oaa (Festino), and Aba,Oba ` Oaa (Baroco); (ii) in the third one, Eab,Aab ` Oaa (Felapton), Oab,Aab ` Oaa (Bocardo) and Eab, Iab ` Oaa (Ferison). Finally, we discuss the passage from the Analytica Posteriora (A11) in which Aristotle states that the Principle of Non-Contradiction is not generally presupposed in all demonstrations (scientific syllogisms), but only in those in which the conclusion must be proved from the Principle; the Stagerian states that if a syllogism of the first figure has the major term consistent, the other terms of the demonstration can be each one separately inconsistent. These results allow us to propose an interpretation of his deductive theory as a broad sense paraconsistent theory. Firstly, we proceed to a hermeneutical analysis, evaluating its logical significance and the interplay of the results with some other points of Aristotle’s philosophy. Secondly, we point to a logical interpretation of the Aristotelian syllogisms from opposite premises in the antilogisms method proposed by Christine Ladd-Franklin in 1883, and we also present a logical treatment of the Aristotelian demonstration with inconsistent material in the paraconsistent logics Cn, 1 _ n _!, introduced by da Costa in 1963. These two issues seem having not yet been analysed in detail in the literature. (shrink)

Inspired by the early Wittgenstein’s concept of nonsense (meaning that which lies beyond the limits of language), we define two different, yet complementary, types of nonsense: formal nonsense and pragmatic nonsense. The simpler notion of formal nonsense is initially defined within Tarski’s semantic theory of truth; the notion of pragmatic nonsense, by its turn, is formulated within the context of the theory of pragmatic truth, also known as quasi-truth, as formalized by da Costa and his collaborators. While an expression will (...) be considered formally nonsensical if the formal criteria required for the assignment of any truth-value (whether true, false, pragmatically true, or pragmatically false) to such sentence are not met, a (well-formed) formula will be considered pragmatically nonsensical if the pragmatic criteria (inscribed within the context of scientific practice) required for the assignment of any truth-value to such sentence are not met. Thus, in the context of the theory of pragmatic truth, any (well-formed) formula of a formal language interpreted on a simple pragmatic structure will be considered pragmatically nonsensical if the set of primary sentences of such structure is not well-built, that is, if it does not include the relevant observational data and/or theoretical results, or if it does include sentences that are inconsistent with such data. (shrink)

O principal objetivo deste artigo é apresentar uma identidade possível entre os conceitos de forma e de qualidade na filosofia de Charles Sanders Peirce, por meio de seus argumentos em sua Semiótica e em sua Cosmologia. Em outras palavras, nosso objetivo é mostrar que a primeiridade consiste em uma forma, parte constitutiva da natureza da terceiridade, na medida em que a tendência à generalização ou à aquisição de hábitos estava prefigurada na origem do cosmos. De natureza indutiva, o passo do (...) nada absoluto para uma unidade de qualidades prefigura um universo inteligível de natureza formal. Esta unidade já pode ser considerada uma restrição de uma potencialidade de força maior presente naquele nada germinal: a primeira categoria é configurada, então, como sendo de natureza potencial qualitativa. O adjetivo “qualitativa” apresenta uma espécie de restrição da potencialidade para a qual nos referimos: tal potencial é desta ou daquela espécie. A segunda categoria, por sua vez, surge de um caos de sentimentos: não é a interação entre tais sentimentos que traz a segunda categoria à realidade, mas a mera manifestação do sentimento que é, por sua vez, caracterizado como a aparência momentânea da qualidade. Esta aparência não é potencial, mas atual. Ela já é um fato; ela já é uma restrição da potencialidade qualitativa. Sentimento enquanto atualidade e qualidade em seu estado potencial prefiguram a origem do outro que se apresenta: este outro está, portanto, inscrito na natureza da qualidade e já apresenta a dualidade objeto e objeto representado. Por fim, a tendência à generalização é reconhecida por meio das relações que as qualidades estabelecem entre si: na medida em que o aparecimento de uma ou mais qualidades se manteve insistente, tais qualidades começaram a estabelecer relações entre si, permitindo a formação indutiva de leis e objetos mais complexos, mas sempre devedores do material disponível prefigurado na origem: qualidades. (shrink)

The ``Many Sides of Logic'' is a volume containing a selection of the papers delivered at three simultaneous events held between 11-17 May 2008 in Paraty, RJ, Brazil, continuing a tradition of three decades of Brazilian and Latin-American meetings and celebrating the 30th anniversary of an institution congenital with the mature interest for logic, epistemology and history of sciences in Brazil: CLE 30 - 30th Anniversary of the Centre for Logic, Epistemology and the History of Science at the State University (...) of Campinas (UNICAMP) XV EBL -15th Brazilian Logic Conference XIV SLALM - 14th Latin-American Symposium on Mathematical Logic Several renowned logicians, philosophers and mathematicians gathered in colonial Paraty, a historic village on the Brazilian coast founded in the 17th Century and surrounded by the luscious Atlantic rain forest to deliver lectures and talks celebrating the many sides of logic: the philosophical, the mathematical, the computational, the historical, and the multiple facets therein. The topics of the joint conferences, well represented here, included philosophical and mathematical Logic and applications with emphasis on model theory and proof theory, set theory, non-classical logics and applications, history and philosophy of logic, philosophy of the formal sciences and issues on the foundations of mathematics. The events have been preceded by a Logic School planned for students and young researchers held at the UNICAMP campus in Campinas, SP. (shrink)

This impressive compilation of the material presented at the Second World Congress on Paraconsistency held in Juquehy-Sao Sebastião, São Paulo, Brazil, represents an integrated discussion of all major topics in the area of paraconsistent logic---highlighting philosophical and historical aspects, major developments and real-world applications.

This research aims to identify the ethical issues perceived by intensive care nurses in their everyday practice. It also aims to understand why these situations were considered an ethical issue and what interventions/strategies have been or are expected to be developed so as to minimize them. Data were collected using a semi-structured interview with 15 nurses working at polyvalent intensive care units in 4 Portuguese hospitals, who were selected by the homogenization of multiple samples. The qualitative content analysis identified end-of-life (...) decisions, privacy, interaction, team work, and health-care access as emerging ethical issues. Personal, team, and institutional aspects emerge as reasons behind the experience of these issues. Personal and team resources are used in and for solving these issues. Moral development and training are the most significant strategies. (shrink)

Faculty resistance to Writing Across the Curriculum (WAC) is an issue that has been recognized by WAC program directors and practitioners for decades, yet it remains unresolved. Perhaps the problem is not resistance per se, but how we interpret and react to it. Faculty resistance is typically viewed as an impediment to the pedagogical change WAC programs hope to achieve. Moreover, the label of "resistance" is often used without further examination of the underlying causes. Based on research and experience as (...) doctoral Writing Fellows in the Borough of Manhattan Community College WAC Program, we argue that so-called resistances are often justified concerns in regard to implementing WAC under given institutional, disciplinary, departmental, and personal constraints. We also suggest that if we listen and respond to these concerns, they become means to facilitate faculty engagement with WAC. By working through their concerns and adapting WAC to their context, faculty can take ownership of WAC and further develop the practice. Thus, what at first appears to be an impediment to deep-rooted pedagogical change ”resistance” can be used to encourage faculty to make WAC their own. (shrink)

Proceedings of the II World Congress on Paraconsistency held in Juquey, SP, Brazil, from May 12-19, 2000.

One of the most profound insights of the dynamic systems perspective is that new structures resulting from the developmental process do not need to be planned in advance, nor is it necessary to have these structures represented in genetic or neurological templates prior to their emergence. Rather, new structures can emerge as components of the individual and the environment self-organize; that is, as they mutually constrain each other's actions, new patterns and structures may arise. This theoretical possibility brings into developmental (...) theory the important concept of indeterminism--the possibility that developmental outcomes may not be predictable in any simple linear causal way from their antecedents. This is the first book to take a critical and serious look at the role of indeterminism in psychological and behavioral development. * What is the source of this indeterminism? * What is its role in developmental change? * Is it merely the result of incomplete observational data or error in measurement? It reviews the concepts of indeterminism and determinism in their historical, philosophical, and theoretical perspectives--particularly in relation to dynamic systems thinking--and applies these general ideas to systems of nonverbal communication. Stressing the indeterminacy inherent to symbols and meaning making in social systems, several chapters address the issue of indeterminism from metaphorical, modeling, and narrative perspectives. Others discuss those indeterministic processes within the individual related to emotional, social, and cognitive development. (shrink)

Over the past decade, research has revealed biomolecular condensates' relevance in diverse cellular functions. Through a phase separation process, they concentrate macromolecules in subcompartments shaping the cellular organization and physiology. In the nucleus, biomolecular condensates assemble relevant biomolecules that orchestrate gene expression. We here hypothesize that chromatin condensates can also modulate the nongenetic functions of the genome, including the nuclear mechanical properties. The importance of chromatin condensates is supported by the genetic evidence indicating that mutations in their members are causative (...) of a group of rare Mendelian diseases named chromatinopathies (CPs). Despite a broad spectrum of clinical features and the perturbations of the epigenetic machinery characterizing the CPs, recent findings highlighted negligible changes in gene expression. These data argue in favor of possible noncanonical functions of chromatin condensates in regulating the genome's spatial organization and, consequently, the nuclear mechanics. In this review, we discuss how condensates may impact nuclear mechanical properties, thus affecting the cellular response to mechanical cues and, eventually, cell fate and identity.Chromatin condensates organize macromolecules in the nucleus orchestrating the transcription regulation and mutations in their members are responsible for rare diseases named chromatinopathies. We argue that chromatin condensates, in concert with the nuclear lamina, may also govern the nuclear mechanical properties affecting the cellular response to external cues. (shrink)

Este trabajo presenta seis ponencias en torno a los problemas que atraviesan distintos sectores de la población en situación de vulnerabilidad social en el goce de sus derechos humanos en el contexto de la pandemia global de COVID-19. Las exposiciones reflexionan sobre los prejuicios y vulnerabilidades que atraviesan las personas adultas mayores; las violencias de género en contextos de aislamiento; las personas en contextos de movilidad excluidas de las medidas de protección; el tratamiento y priorización de las personas con discapacidad (...) en los centros de derivación de COVID-19; la protección de las garantías penales en la administración de justicia durante los juicios de lesa humanidad llevados en forma remota; y el avance de las causas por crímenes de lesa humanidad durante la pandemia. (shrink)

The Joint Non-Trivialization Theorem, two Definability Theorems and the generalized Quantifier Elimination Theorem are proved for J 3-theories. These theories are three-valued with more than one distinguished truth-value, reflect certain aspects of model type logics and can. be paraconsistent. J 3-theories were introduced in the author's doctoral dissertation.

The main objective o f this descriptive paper is to present the general notion of translation between logical systems as studied by the GTAL research group, as well as its main results, questions, problems and indagations. Logical systems here are defined in the most general sense, as sets endowed with consequence relations; translations between logical systems are characterized as maps which preserve consequence relations (that is, as continuous functions between those sets). In this sense, logics together with translations form a (...) bicomplete category of which topological spaces with topological continuous functions constitute a full subcategory. We also describe other uses of translations in providing new semantics for non-classical logics and in investigating duality between them. An important subclass of translations, the conservative translations, which strongly preserve consequence relations, is introduced and studied. Some specific new examples of translations involving modal logics, many-valued logics, para- consistent logics, intuitionistic and classical logics are also described. (shrink)

No Órganon Aristóteles descreve alguns esquemas dedutivos nos quais a presença de inconsistências não acarreta a trivialização da teoria lógica envolvida. Esta tese é corroborada por três diferentes situações teóricas estudadas por ele, as quais são apresentadas neste trabalho. Analizamos o esquema de inferência utilizado por Aristóteles no Protrepticus e o método de demonstração indireta para os silogismos categóricos. Ambos os métodos exemplificam como Aristóteles emprega estratégias de redução ao absurdo logicamente clássicas. Na sequência, discutimos os silogismos válidos a partir (...) de premissas opostas (contrárias e contraditórias) estudadas pelo Estagirita no Analytica Priora (B15). De acordo com o autor, os seguintes silogismos são válidos a partir de premissas opostas, nos quais letras latinas minúsculas denotam termos como sujeito e predicado, enquanto que letras latinas maiúsculas denotam proposições categóricas tal como na notação tradicional: (i) na segunda figura, Eba,Aba ` Eaa (Cesare), Aba, Eba ` Eaa (Camestres), Eba, I ba ` Oaa (Festino), e Aba,Oba ` Oaa (Baroco); (ii) na terceira, Eab,Aab ` Oaa (Felapton), Oab,Aab ` Oaa (Bocardo) e Eab, Iab ` Oaa (Ferison). Por fim, discutimos a passagem do Analytica Posteriora (A11) no qual Aristóteles enuncia que o Princípio de Não-Contradição não é, em geral, pressuposto de toda demonstração (silogismo científico), mas apenas daquelas nas quais a conclusão deve ser provada a partir do Princípio; o Estagirita enuncia que se um silogismo da primeira figura tiver o termo maior consistente, os outros termos da demonstração podem ser separadamente inconsistentes. Estes resultados permitem-nos propor uma interpretação de sua teoria dedutiva como uma teoria paraconsistente lato sensu. Primeiramente, efetuamos uma análise hermenêutica, avaliando seu significado lógico e a correlação desses resultados com outros aspectos da filosofia de Aristóteles. Em segundo lugar, consignamos uma interpretação dos silogismos aristotélicos a partir de premissas opostas à luz dos antilogismos propostos por Christine Ladd-Franklin em 1883, e da demonstração aristotélica com termos inconsistentes nas lógicas paraconsistentes Cn, 1 n !, introduzidas por da Costa em 1963. Esses dois aspectos não parecem ter sido ainda detalhadamente analisados na literatura. DOI:10.5007/1808-1711.2010v14n1p71. (shrink)

This paper discusses some problems related to the practical experience of social research in university institutions. It describes the process of access to field work and the relationship with university managers as key informants during a qualitative research about the present politics of economic..

Recent literature have underlined the connections between children’s reading skills and capacity to create and use mental representations or mental images; furthermore data highlighted the involvement of visuospatial abilities both during math learning and during subsequent developmental phases in performing math tasks. The present research adopted a longitudinal design to assess whether the processes of mental imagery in preschoolers (ages 4–5 years) are predictive of mathematics skills, writing and reading, in the early years of primary school (ages 6–7 years). The (...) research lasted for two school years; in the first phase, the general group of participants consisted of 100 children, and although all participants agreed to be part of the research, in the second phase, there was a mortality rate of 30%. In order to measure school learning and mental imagery processes four batteries of tests were used. The mental imagery battery evaluated mental generation, inspection and transformation processes. Data underlined that the different aspects in which mental imagery processes are articulated are differently implied in some skills that constitute school learning. These findings emphasise the potential usefulness of a screening for mental imagery ability for schoolchildren to adopt effective measures to increase their mental imagery abilities. (shrink)

Three experiments examined contributions of study phase awareness of word identity to subsequent word-identification priming by manipulating visual attention to words at study. In Experiment 1, word-identification priming was reduced for ignored relative to attended words, even though ignored words were identified sufficiently to produce negative priming in the study phase. Word-identification priming was also reduced after color naming relative to emotional valence rating (Experiment 2) or word reading (Experiment 3), even though an effect of emotional valence upon color naming (...) (Experiment 2) indicated that words were identified at study. Thus, word-identification priming was reduced even when word identification occurred at study. Word-identification priming may depend on awareness of word identity at the time of study. (shrink)

In this article, I show how resources for an education for non-dichotomous thinking can be drawn from the two Daoist texts, the Daodejing and the Zhuangzi. Dichotomous thinking can be defined as thinking that considers things in terms of strict and even irreconcilable dichotomous oppositions. The authors of the Daodejing and the Zhuangzi are known for their criticism of such dichotomous thinking. At the same time however, these authors seem to fall into this very kind of thinking which they criticize. (...) That is to say, the Daodejing and the Zhuangzi often promote adherence to conventionally ‘lower’ values over ‘higher’ ones. I believe though that this tension can be resolved if viewed through a pedagogical framework. Specifically, the adherence to ‘lower values’ can be seen as the initial step in the process of Daoist self-cultivation where one reduces the artificial distinctions one adheres to in order to prepare one’s disposition for union with Dao, which in turn entails non-dichotomous thinking. (shrink)

This volume corresponds to the Proceedings of the XIII Brazilian Logic Conference held at the CLE - Centre for Logic, Epistemology and the History of Science in Campinas, SP, Brazil from May 26-30, 2003 under the auspices of the SBL - Brazilian Logic Society and the ASL - Association for Symbolic Logic.