Paraconsistent Research Articles

Navigating the tensions in environmental innovation: a paradox perspective

PurposeThis study aims to investigate the hybrid nature and scope of environmental innovation (EI) by assuming a paradox perspective and developing it empirically. Specifically, the authors raise the questions of how the opposite elements of EI characteristics can be arranged and combined to generate benefits for companies and markets.Design/methodology/approachA fuzzy-set qualitative comparative analysis (fsQCA) is conducted to analyse European companies operating in telecommunications and in information and communication technology (ICT). This method helps us interpret the complexity occurring in the real world, in which the contribution of a specific attribute to the outcome might change according to other interacting and concurring aspects.FindingsBy recognising the conflicting aspects inherent to the complexity of EI, this study addresses how these tensions can be embraced. Specifically, the paradox logic is proposed to open EI strategy to a “both-and” perspective, with the purpose of making EI goals concretely feasible and integrated into a holistic view.Practical implicationsParadoxical resolution denotes purposeful iterations between alternatives to ensure simultaneous attention to them over time. A paradox logic can support managers in making the EI strategy more workable and reconciling the extremes as well as possible.Originality/valueThis study unpacks the multiple enactments of EI by exploring the factors enabling integrated EI benefits. By adopting a paradox approach, the EI strategy may be interpreted in a “both-and” perspective, allowing firms to concretely achieve integrated EI benefits.

Leibnizian Identity and Paraconsistent Logic

The standard Leibnizian view of identity allows for substitutivity of identicals and validates transitivity of identity within classical semantics. However, in a series of works, Graham Priest argues that Leibnizian identity invalidates both principles when formalized in paraconsistent semantics. This paper aims to show the Leibnizian view of identity validates substitutivity of identicals and transitivity of identity whether the logic is classical or paraconsistent. After presenting Priest's semantics of identity, I show what a semantic expression of Leibnizian identity does amount to. Then, I argue that Priest's semantic definition of identity is not Leibnizian. Finally, I offer a semantics characterization of identity in paraconsistent logic that is truly Leibnizian. I demonstrate that the correct formalization of Leibnizian identity in paraconsistent logic also validates substitutivity of identicals and transitivity of identity.

Chris Kraus’ Auto-Fictional Strategies of Failure

La production écrite de Chris Kraus, notamment son ouvrage de 1997 désormais devenu culte I Love Dick , est marqué par une fascination pour la figure de l’artiste ratée. Cet article interroge les modalités d’écriture mises en place pour témoigner de cette fascination qui s’écrit sur un mode mineur, le journal, tout en s’insérant dans une tradition intellectuelle et artistique de la marge. L’artiste se pense en termes de rivalité avec ses propres ambitions tout autant qu’avec les institutions artistiques qu’elle tente d’intégrer. En célébrant la figure de l’artiste ratée, Chris Kraus revient sur la tradition de la culture de la subversion pour penser l’échec comme une position éthique radicale.

First-order swap structures semantics for some logics of formal inconsistency

Abstract The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (i.e. logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous approaches to quantified LFIs presented in the literature. The case of QmbC, the simpler quantified LFI expanding classical logic, will be analyzed in detail. An axiomatic extension of QmbC called $\textbf{QLFI1}_\circ $ is also studied, which is equivalent to the quantified version of da Costa and D’Ottaviano 3-valued logic J3. The semantical structures for this logic turn out to be Tarkian structures based on twist structures. The expansion of QmbC and $\textbf{QLFI1}_\circ $ with a standard equality predicate is also considered.

Adoption of an indicator panel in educational management to decision-making support

The use of technology to assist in the performance of daily activities and to carry out communication between individuals has become a necessary task in the face of technological advances. In the context of public institutions, the insertion of technology is also based on the possibilities of making the activities of this sector more efficient and better quality, in addition to allowing greater transparency and accessibility of information for society. For public managers, the information and communication technology tools allow for a more accurate assessment of the variables and possibilities involved in a decision-making process and, thus, to make better decisions in a sector whose main customer is society (users). Therefore, this paper aimed to analyze the use and acceptance of a decision support tool in a public educational institution called the Indicators Panel. For this, the Unified Theory of Acceptance and Use of Technology (UTAUT) was used, and the results were measured using the paraconsistent logic. The results indicate that it is possible to consider the use and acceptance of the decision support system in the public educational institution by reducing the propositions of the UTAUT Model in three factors: Usability, Performance, and Relationship. Regarding the UTAUT Model, it was found that the moderating variables of gender, age, and experience do not significantly influence the adoption of the decision support system. It is important to note that managers point the tool as very important for the development of their activities and emphasize that ease of use is one of the main points for the adoption of technology.

The Normal and Self-extensional Extension of Dunn–Belnap Logic

A logic $$\mathbf{L}$$ is called self-extensional if it allows to replace occurrences of a formula by occurrences of an $$\mathbf{L}$$ -equivalent one in the context of claims about logical consequence and logical validity. It is known that no three-valued paraconsistent logic which has an implication can be self-extensional. In this paper we show that in contrast, the famous Dunn–Belnap four-valued logic has (up to the choice of the primitive connectives) exactly one self-extensional four-valued extension which has an implication. We also investigate the main properties of this logic, determine the expressive power of its language (in the four-valued context), and provide a cut-free Gentzen-type proof system for it.

Need anything follow from a contradiction?

ABSTRACT Classical and intuitionistic logic both validate Ex Contradictione Quodlibet (ECQ), according to which any proposition whatsoever follows from a contradiction. Many philosophers have found ECQ counter-intuitive, but criticisms of the principle have almost universally been directed from a position of support for relevance or other orthodox paraconsistent logics, according to which some, but not necessarily all, propositions follow from a contradiction. This paper draws attention to the historically significant view that nothing whatsoever follows from a contradiction – Ex Contradictione Nihil (ECN). It addresses the key arguments – model-theoretic, proof-theoretic, meaning theoretic and holist – deployed by proponents of ECQ against their standard opponents, and shows that each can be defeated from a position of support for ECN. In the course of answering these arguments, some understanding is developed of possible motivations for ECN and a solid case is built that ECN deserves further investigation.

Paraconsistent logic approach for active noise reduction

The Active Noise Reduction (ANR) is widely used in aircraft, headsets, telecommunications and medicine systems, to reduce or eliminate noise, while maintaining the characteristics of the desired signal. In this article a network of paraconsistent artificial neural cells (PANC) will be presented, based on the paraconsistent annotated logic by 2 values annotations (PAL2v) that allows to operate as ANR. Simulations indicate that the results presented by ANRPAL are better than those obtained by classic filters.

Obtaining infinitely many degrees of inconsistency by adding a strictly paraconsistent negation to classical logic

This paper is devoted to a consequence relation combining the negation of Classical Logic ($$\mathbf {CL}$$) and a paraconsistent negation based on Graham Priest’s Logic of Paradox ($$\mathbf {LP}$$). We give a number of natural desiderata for a logic $$\mathbf {L}$$ that combines both negations. They are motivated by a particular property-theoretic perspective on paraconsistency and are all about warranting that the combining logic has the same characteristics as the combined logics, without giving up on the radically paraconsistent nature of the paraconsistent negation. We devise the logic $$\mathbf {CLP}$$ by means of an axiomatization and three equivalent semantical characterizations (a non-deterministic semantics, an infinite-valued set-theoretic semantics and an infinite-valued semantics with integer numbers as values). By showing that this logic is maximally paraconsistent, we prove that $$\mathbf {CLP}$$ is the only logic satisfying all postulated desiderata. Finally we show how the logic’s infinite-valued semantics permits defining different types of entailment relations.

Exactly true and non-falsity logics meeting infectious ones

In this paper, we study logical systems which represent entailment relations of two kinds. We extend the approach of finding ‘exactly true’ and ‘non-falsity’ versions of four-valued logics that emerged in series of recent works [Pietz & Rivieccio (2013). Nothing but the truth. Journal of Philosophical Logic, 42(1), 125–135; Shramko (2019). Dual-Belnap logic and anything but falsehood. Journal of Logics and their Applications, 6, 413–433; Shramko et al. (2017). First-degree entailment and its relatives. Studia Logica, 105(6), 1291–1317] to the case of infectious logics, namely to the case of Deutsch's logic introduced in Deutsch [Relevant analytic entailment. The Relevance Logic Newsletter, 2(1), 26–44; The completeness of S. Studia Logica, 38(2), 137–147]. The particular systems obtained in this way are and . We present them in the form of sequent calculi and prove corresponding soundness and completeness theorems. We illuminate the connection between , and two well-known systems, strong Kleene three-valued logic and Priest's Logic of Paradox . This connection allows us to investigate the characterisation of the entailment relations associated with and as well as to introduce the notion of ‘infectious analogue’ of a certain logic. We also study implicative extensions of and and prove soundness and completeness theorems for them as well.

Classifying material implications over minimal logic

The so-called paradoxes of material implication have motivated the development of many non-classical logics over the years, such as relevance logics, paraconsistent logics, fuzzy logics and so on. In this note, we investigate some of these paradoxes and classify them, over minimal logic. We provide proofs of equivalence and semantic models separating the paradoxes where appropriate. A number of equivalent groups arise, all of which collapse with unrestricted use of double negation elimination. Interestingly, the principle ex falso quodlibet, and several weaker principles, turn out to be distinguishable, giving perhaps supporting motivation for adopting minimal logic as the ambient logic for reasoning in the possible presence of inconsistency.

On the Historical Transformations of the Square of Opposition as Semiotic Object

In this paper, we would show how the logical object “square of opposition”, viewed as semiotic object (articulated in textual or/and diagrammatic code), has been historically transformed since its appearance in Aristotle’s texts until the works of Vasiliev. These transformations were accompanied each time with a new understanding and interpretation of Aristotle’s original text and, in the last case, with a transformation of its geometric configuration. The initial textual codification of the theory of opposition in Aristotle’s works is transformed into a diagrammatic one, based on a new “reading” of the Aristotelian text by the medieval scholars that altered the semantics of the O form. Further, based on the medieval “Neo-Aristotelian” reading, the logicians of the nineteenth century suggest new diagrammatic representations, based on new interpretations of quantification of judgements within the algebraic and the functional logical traditions. In all these interpretations, the original square configuration remains invariant. However, Nikolai A. Vasiliev marks a turning point in history. He explicitly attacks the established logical tradition and suggests a new alternation of semantics of the O form, based on Aristotelian concepts that were neglected in the Aristotelian tradition of logic, notably the concept of indefinite judgement. This leads to a configurational transformation of the “square” of opposition into a “triangle”, where the points standing for the O and I forms are contracted into one point, the M(I, O) form that now stands for particular judgement with altered semantics. The new transformation goes beyond the Aristotelian logic paradigm to a new “Non-Aristotelian” logic (and associated ontology), i.e. to paraconsistent logic, although the argumentation used in support of it is phrased in (Neo-)Aristotelian style and the context of discovery is foundational (analogical to Lobachevsky’s research on the axiomatics of geometry). It establishes a bifurcation (proliferation) point in the development of logic. No unique logic is recognized, but different logics concerning different domains (ontologies, respectively). One branch of logic remains to be the “Neo-Aristotelian” one, while the new logic is “Non-Aristotelian”.

On Paraconsistent Beauty: A Variety of Perspectives and Movements

This work deals with the nature and merits of judgments of value in paraconsistent aesthetics, discussing the concept of “paraconsistent beauty” that is flexible and varied. The possibility of the existence of a negative paraconsistent aesthetics is considered, because the discussion on paradoxes includes the problem of negation. There are comments on aspects of paraconsistent aesthetics in the absurd, in literature, in tragedy and in comedy. In paraconsistent aesthetics we take profit of the main ideas of a new kind of logic, the so-called paraconsistent logic.

What is Paradoxical About ‘Fermi’s Paradox’?

In this review of Milan Ćirković's The Great Silence: Science and Philosophy of Fermi's Paradox, we attempt to reconstruct the logic of Fermi's paradox as understood by the author, and we critically examine the reasoning that leads to the paradox. We show that there is no plausible solution to Fermi's paradox that can satisfy all of Ćirković's proposed desiderata, which in turn suggests that the author's standards for hypothesis adjudication need to be revised.

Swyneshed, Aristotle and the Rule of Contradictory Pairs

Roger Swyneshed, in his treatise on insolubles (logical paradoxes), dating from the early 1330s, drew three notorious corollaries from his solution. The third states that there is a contradictory pair of propositions both of which are false. This appears to contradict what Whitaker, in his iconoclastic reading of Aristotle’s De Interpretatione, dubbed “The Rule of Contradictory Pairs” (RCP), which requires that in every such pair, one must be true and the other false. Whitaker argued that, immediately after defining the notion of a contradictory pair, in which one statement affirms what the other denies of the same thing, Aristotle himself gave counterexamples to the rule. This gives some credence to Swyneshed’s claim that his solution to the logical paradoxes is not contrary to Aristotle’s teaching, as many of Swyneshed’s contemporaries claimed. Insolubles are false, he said, because they falsify themselves; and their contradictories are false because they falsely deny that the insoluble itself is false. Swyneshed’s solution depends crucially on the revision he makes to the acount of truth and falsehood, brought out in his first thesis: that a false proposition can signify as it is, or as Paul of Venice, who took up and developed Swyneshed’s solution some sixty years later, puts it, a false proposition can have a true significate. Swyneshed gave a further counterexample to (RCP) when he claimed that some insolubles, like future contingents, are neither true nor false. Dialetheism, the contemporary claim that some propositions are both true and false, is wedded to the Rule, and in consequence divorces denial from the assertion of the contradictory negation. Consequently, Swyneshed’s logical heresy is very different from that found in dialetheism.

The Genetic Power of Paradox: From Dark Precursor to Quasi-Causality

In this article, I conduct a selective reading of Difference and Repetition that intertwines with The Logic of Sense, specifically in relation to the concept of paradox, underscoring how Deleuze's work itself is a performance of the necessity of paradoxical thinking and the insistence on an image of thought which incorporates paradox as its central feature. I argue that para-sense anticipates the centrality of paradox in Logic of Sense, just as the obscure, unilluminated element of Ideas anticipates the significance of non-sense for the proliferation of sense therein. Likewise, the dark precursor as that which enables communication between different kinds bears a resemblance to the idea of the quasi-cause that we find in The Logic of Sense. Paradox, the paradoxical instant and para-sense, as figures which help us to cultivate and maintain the discordant relations of passion to thought, the corporeal and incorporeal, and word and thing, unfix our thinking so that we can allow ourselves to be more thoroughly immersed in the multiplicities and intensities that surround us. This is the possibility of a kind of doubling that is not based on the sterility of representation, but rather the genitality of learning and proliferation of (non)sense.

Fatores críticos de sucesso que melhoram a gestão escolar

Destaques: As instituições de ensino precisam cada vez mais lidar com a responsabilidade de transmitir conhecimento ao promover o desenvolvimento do estudante e qualificá-lo para o mercado de trabalho. Para se manterem competitivas neste mercado necessitam satisfazer as necessidades dos seus clientes (pais e alunos). Portanto, os gestores educacionais devem utilizar estratégias para melhorar e desenvolver o ambiente organizacional da escola.Objetivo: Analisar, por meio da identificação, descrição e avaliação, os Fatores Críticos de Sucesso (FSC) que influenciam a melhoria da gestão escolar. Estes fatores envolvem aspectos como: treinamento, projeto político pedagógico, ferramentas de ensino e qualidade percebida. Além disso, contribuir com dados que corroborem com o desenvolvimento da gestão escolar.Metodologia: O referencial teórico utilizado para tratar os FCS de Rockart (1979) é o komolgorov-Smirnov (1979). Como o método Kolmogorov-Smirnov tem aplicação simplificada, a Lógica Paraconsistente será também empregada, pois permite o tratamento com naturalidade de divergências, inconsistências e contradições, além de permitir a obtenção de resultados mais precisos e próximos da realidade (Casarin, 2007).Resultados: Foi constatado que o uso e a priorização dos FCS podem influenciar positivamente o desempenho do gestor escolar. É importante esclarecer que as escolas não deixam de ser empresas que prestam serviços e como tal devem considerar o emprego de estratégias que melhorem sua competitividade, produtividade, rentabilidade e excelência. Conclui-se que a gestão escolar pôde melhorar seu desempenho utilizando a priorização dos FCS na seguinte ordem crescente de importância: ferramentas de ensino, treinamento, projeto político pedagógico e qualidade percebida.Limitações: Este trabalho se restringe às dez melhores escolas da cidade de Niterói, de acordo com conceito no Exame Nacional do Ensino Médio (ENEM). Essa delimitação faz com que os resultados obtidos estejam sujeitos a padrões, como comportamento e exigências do mercado.Implicações práticas: Espera-se, além de agregar valor à literatura vigente, estimular os estudos em torno do tema proposto, visando cada vez mais auxiliar os gestores escolares na eficácia das ações.Valor e originalidade: Foram encontrados poucos estudos na literatura propondo a utilização dos FCS para tratar a melhoria de gestão em instituições de ensino. Sendo assim, este trabalho pretende descrever propostas inovadoras para este segmento; dar ao gestor educacional um papel de destaque ao identificar e priorizar os FCS; e, finalmente, contribuir com outros trabalhos que avaliam o impacto da capacitação de educadores no avanço da gestão escolar e na qualidade do atendimento aos estudantes.

Paradoxes in scientific cognition and nonclassical logics

The subject of this research is the scientific paradoxes and such means for its resolution as nonclassical logics. The author defends a thesis that paradoxes often stimulate the scientific development. It is demonstrated that most vividly the problem of paradoxes manifested in crises in the fundamentals of mathematics; the attempts for its resolution in many ways contributes to the emergence of nonclassical logics. It is substantiated that nonclassical logics helped to resolve and explain the paraded occurring in scientific cognition. Comparative analysis is conducted on the capabilities of  three-valued “quantum logics” of Garrett Birkhoff and John von Neumann and “logics of complementarity” of Hans Reichenbach. Potential of the three-valued logics of D. Bochvar and nonclassical systems of A. Zinoviev in resolution and explanation of logical paradoxes, as well as importance of temporary logics of G. H. Wright for the philosophy of science is revealed. Special attention is paid  to the paraconsistent logics. The author determines two points of view in understanding of their essence and value for science and philosophy, which juxtaposition shows that none of them fully complies with the actual state of affairs. The main conclusion consists in the statement that paradoxes of scientific cognition should not be assessed just negatively; they also carry a positive meaning: detection of paradoxes in the theory testifies to the need for their elimination, more detailed research and stricter approach towards development of the theory, which in solution of this task can be accomplished by nonclassical logics.

On epistemic and ontological interpretations of intuitionistic and paraconsistent paradigms

Abstract From the technical point of view, philosophically neutral, the duality between a paraconsistent and a paracomplete logic (for example intuitionistic logic) lies in the fact that explosion does not hold in the former and excluded middle does not hold in the latter. From the point of view of the motivations for rejecting explosion and excluded middle, this duality can be interpreted either ontologically or epistemically. An ontological interpretation of intuitionistic logic is Brouwer’s idealism; of paraconsistency is dialetheism. The epistemic interpretation of intuitionistic logic is in terms of preservation of constructive proof; of paraconsistency is in terms of preservation of evidence. In this paper, we explain and defend the epistemic approach to paraconsistency. We argue that it is more plausible than dialetheism and allows a peaceful and fruitful coexistence with classical logic.

Método Paraconsistente de Avaliação em Finanças Comportamentais

This study aims to analyze the behavior of a group in relation to finance, through the paraconsistent annotated evidential logic (LPA). Among the authors searched for the constitution of this conceptual work, stressed-If Abe, J.M (2011), Da Silva Filho, J.I. & ABE, J.M (2001), De Carvalho, F.R.; Abe, J.M.( 2011), Kahneman, D; Tversky (2012), Kimura, K (2003), Lima, M.V (2003) , Reis, N.F (2007). The methodology used was the exploratory research. The most important conclusion about the topic researched is that people are influenced by anchoring in its decision-making financial and paraconsistent logic (LPA) used in this study allows us to take into consideration the contradiction between these decisions.