Paraconsistent Research Articles

Raven paradox: problem and solution given on the basis of Aristotle’s logic

The paper is devoted to the solution of two well-known paradoxes of inductive logic: Hempel’s and Goodman’s, which the science has not solved unambiguously yet. The results of this research can be used in any natural science, but they are especially relevant for areas where there is an emphasis placed on environmental friendliness and sustainable development. The central problem of this research is the problem of limits of applying classical logic laws. The problem is solved by method of reduction of logical laws to those cases where they, according to Aristotle, act faultlessly, and refusal of their recognition in the cases where their action is questionable. The aim of the paper is to demonstrate the solution of both problems within Aristotle’s logic. In that regard, the following results are received: common faults of previous solutions of Hempel’s paradox, consisting in ignoring any of its parties, are revealed; the original nature of Goodman’s paradox, consisting in wrong interpreting “inductive confirmation” criteria is opened; two methods of forming and assessing the subject volumes of statements are revealed: analytical and synthetical ones; it is proved that the theses treated in Hempel’s paradox as equivalent ones are not always so, but only on condition of their subjects’ reality and of their subject volumes’ identity; it is established that the conditions of the statement equivalence correspond to the limits of applying logic laws in Aristotle’s interpretation.

Strengthening preference ranking organisation method for enrichment evaluation with features of paraconsistent Pavelka style fuzzy logic

Strengthening preference ranking organisation method for enrichment evaluation with features of paraconsistent Pavelka style fuzzy logic

PANN Component for Use in Pattern Recognition in medical diagnostics decision-making

In the most varied specialties in the health hospital field, health professionals constantly need the main activity to make decisions in a timely manner and usually do so only in view of the data collected in clinical examinations. This has been the main source to define in an assertive way even in increasingly complex scenarios, notably in pathologies resulting from cancer cells. In this article, there is the possibility to present medical specialists with new aid to complement with inputs that add to their final decision-making. For this, the objective is to use the concepts of artificial intelligence applied in artificial neural networks and propose the use of paraconsistent logic architected in components of paraconsistent artificial neural networks (PANN) to support specialists in decision-making.

Application of architecture using AI in the training of a set of pixels of the image at aid decision-making diagnostic cancer

Medical Medicine specialists are using images more and more as support in decision making in the identification of pathologies with greater complexity and severity in the specific case. Predictive and diagnostic models in images with neoplasia (collagen V) associated with exposure to asbestos fibers were studied. In this article we intend to initially assess machine learning on the basis containing 100 images classified by specialists with characteristics of normality and abnormality to aid diagnosis. Therefore, the objective is to analyze and use the concepts of learning by the technique of artificial intelligence with neural networks that culminated in significant advances of 81% of correct answers in the image diagnostics and to propose the application of the Paraconsistent Standard Analyser Unit of Artificial Neural Networks in order to categorize the degree of abnormality (normal, almost normal, almost abnormal, abnormal) with the use of the extreme and non-extreme states of Paraconsistent Logic and thus support specialists in decision making in the diagnosis of cancer.

Software optimization for LGPD compliance using Paraconsistent Evidential Annotated Logic Eτ

Every country in the world was concern about personal privacy data and protection models in Brazil Act promulgated late because LGPD Act (Protection Data Brazilian Law) came into force only in September 2020, otherwise elaborated in August 2018. With this advent the need to raise the awareness of people and companies about the information importance. The population still stays apart from the risk in personal data privacy, which grows every day a lot of companies are not in compliance with this LGPD Act. The study objective first part is a bibliographic review that points to the LGPD Act, activities, and function of the DPO – Data Protection Officer. Second, the application survey with the software of data protection and its approval used Paraconsistent Logic Evidential Annotated Eτ. Then, we detail the methodology used and compare the results with the discussions. Within these discussions, the information from the statistics collected by the ANPPD - National Association of Data Privacy Professionals at the CNPPD National Congress of Data Privacy Professionals in March / 2021 compared with the points of the analysis carried out using the Paraconsistent Logic Evidential Annotated Eτ.

Introduction

As a descriptive philosophy, it might seem that the ethical nowhere has its place in phenomenology. And yet, phenomenology is every-where shot through with normative concerns. This section includes articles from the 2018 conference Toward a Phenomenological Ethics, where two themes emerged regarding the elusive place of the ethical in phenomenology: first, research demonstrates that early phenomenology was indeed oriented by the ethical; second, Critical Phenomenology examines ethical questions in terms of intersubjectivity and oppression. In this introduction, I suggest that the place of the ethical in phenomenology implies a certain paradoxical logic of expression, and I consider the relationship between expression and encroachment. This points to a double responsibility for the cultivation of our own virtual and the virtual that we collectively sustain. I conclude with a brief re􀏔lection on how these ideas might help us to rethink our responsibilities in the age of COVID-19.

Towards a Metatheoretical Postmodern Approach to Legal Reasoning

This paper focuses on legal reasoning, arguing that although methodological theories are important, they are not enough to explain how to reason in law. In fact, because the different philosophical perspectives vary so significantly in their ability to resolve legal conflicts, when a less “adapted” perspective decides a legal question, the results can be disastrous. Thus, this paper inaugurates a new attitude, stating that a general philosophical perspective is the only way out. Relying on a metatheoretical postmodern approach, it argues that logic, analysis, argumentation and hermeneutics are complementary theories that offer a unique perception of law. It concludes that the approach proposed makes possible not only a comprehensive view of the way legal reasoning behaves, but more than this, a proportionate flexibility to both civil and common law systems. Keywords: Paraconsistent Logic; Metatheoretical Postmodern Approach; Metatheoretical Perspective; Paraconsistent Deontic Logic; Ontological Hermeneutics

The Construction of Negative Theology in Pesantren and Madrasa in Malang, East Java

This article discusses the metaphysical construction of divinity in the Indonesian Islamic education institutions, namely madrasa and pesantren. The research has been held in Malang, East Java. It focuses on constructing the negative concept of theology that grows and develops in these Islamic education institutions. In doing so, this study employs a qualitative approach coupled with Miles’ and Hubermann’s data analysis. The study finds that negative theological discourse is an arena of “prophetization” of the divine values ​​whose style of expression is apophatic. Therefore, it constructs its theological knowledge based on the logic of negation and paradox. It also “rejects” the knowledge construction for the same reason. This view affects the system of Islamic education and the framework of its educational objectives to be more oriented to the aspects of humanity and divinity or the profane and transcendental dimension. In other words, negative theology has implications for the axiology of Islamic education.

On the strongest three-valued paraconsistent logic contained in classical logic and its dual

Abstract $\textrm{LP}^{\mathbin{\supset },{\mathsf{F}}}$ is a three-valued paraconsistent propositional logic that is essentially the same as J3. It has the most properties that have been proposed as desirable properties of a reasonable paraconsistent propositional logic. However, it follows easily from already published results that there are exactly 8192 different three-valued paraconsistent propositional logics that have the properties concerned. In this paper, properties concerning the logical equivalence relation of a logic are used to distinguish $\textrm{LP}^{\mathbin{\supset },{\mathsf{F}}}$ from the others. As one of the bonuses of focusing on the logical equivalence relation, it is found that only 32 of the 8192 logics have a logical equivalence relation that satisfies the identity, annihilation, idempotent and commutative laws for conjunction and disjunction. For most properties of $\textrm{LP}^{\mathbin{\supset },{\mathsf{F}}}$ that have been proposed as desirable properties of a reasonable paraconsistent propositional logic, its paracomplete analogue has a comparable property. In this paper, properties concerning the logical equivalence relation of a logic are also used to distinguish the paracomplete analogue of $\textrm{LP}^{\mathbin{\supset },{\mathsf{F}}}$ from the other three-valued paracomplete propositional logics with those comparable properties.

Negative Theology Construction in Islamic Education System: An Analytical Study

This study focuses on the construction of the negative concept of divinity (theology) developed in the educational system such as madrasas or pesantren. Therefore, the aim of this study is to analyze the construction of negative theology in the Islamic education system developed in madrasas or pesantren in Malang, East Java, Indonesia. To critically discuss the issue, this study used a qualitative approach with phenomenological research design and Miles and Huberman’s framework in analyzing the data. Study findings expose that negative theological discourse denoted an arena for the prophetization of divine values ​​whose style of expression was apophatic. Apparently, it constructs its theological knowledge as well as “rejects” the knowledge construction with the logic of negation and paradox. The implications for the Islamic education system are the framework of educational objectives is oriented to aspects of humanity and divinity; or the profane and transcendental dimension. It indicates that negative theology contributes to novel insights into the axiology of Islamic education.

Social Entrepreneurship: The Logic of Paradox

Social entrepreneurship is a paradoxical phenomenon wherein seemingly incompatible elements such as business and social logics coexist. Previous research has been insufficient to systematically describe how social entrepreneurship organizations (SEO) try to balance these logics and why these same paradoxical elements make social entrepreneurship what it is. Using the systematic literature review method, this paper examines six major paradoxes and how they affect both the theory and practice of social entrepreneurship by furthering the nascent discussion about the role of paradoxes in SEOs. Viewed through the lens of organizational logics, this paper argues that the dynamic interplay between these paradoxes initiates and drives the innovations and changes necessary for the very existence of SEOs.

Esticando a verdade sem alcançar a contradição: o caso do dialeteísmo

Dialeteias são contradições verdadeiras. Dialeteísmo é a visão de que há dialeteias e dialeteístas são aqueles que defendem tal visão. Uma das principais motivações para o dialeteísmo encontra-se nos paradoxos semânticos, como o paradoxo do Mentiroso. A sentença do mentiroso, na abordagem dialeteísta, instancia uma dialeteia. O problema é: como aceitar contradições verdadeiras? Como dialeteísmo é a visão que algumas, mas não todas, contradições são verdadeiras, o dialeteísmo demanda um tratamento paraconsistente. Porém, não é qualquer sistema paraconsistente que pode ser aplicado ao dialeteísmo. A interpretação do símbolo de negação deve ser um operador formador de contradição (ofc) com o sentido relevante para a aplicação dialeteísta. Especificamente, na versão de dialeteísmo que discutiremos nesse artigo, defendida por Graham Priest, temos que, para que o dialeteísmo faça sentido, a negação da lógica subjacente deve atender a dois requisitos: (i) ser um ofc e (ii) não ser explosiva. A Lógica do Paradoxo (LP) tem sido apontada como a lógica adequada ao dialeteísmo. Veremos que, a fim de lidar com contradições sem trivialidade, dialeteístas “esticam” a verdade de modo que a verdade possa incluir, em alguns casos, a falsidade também. Nesse caso, haveria sentenças verdadeiras e falsas, chamadas de aglutinações de valores de verdade (truth-value gluts). Em LP, aglutinações de valores de verdade são fundamentais para garantir os requisitos (i) e (ii). Todavia, vamos argumentar que tal procedimento de esticar a verdade, permitindo aglutinações, garante a paraconsistência ao custo de distorcer a interpretação da noção de contradição envolvida no dialeteísmo. Especificamente, tal distorção enfraquece a interpretação da negação comprometendo o sentido de contradição relevante para o dialeteísmo. Vamos argumentar que as próprias restrições dialeteístas a uma compreensão adequada do Mentiroso mostram que as condições (i) e (ii) são incompatíveis e que, com isso, o projeto dialeteísta enfrenta consideráveis obstáculos.

Evidências e dependência ontológica: sobre interpretações de lógicas paraconsistentes

Neste texto, apresentamos duas abordagens distintas, mas não necessariamente excludentes, da paraconsistência. A primeira trata das lógicas da evidência e verdade (logics of evidence and truth), nas quais contradições são interpretadas como evidência não conclusiva, simultânea e conflitante para um par de proposições A e ¬A. A segunda abordagem propõe que as diferenças entre a lógica clássica e alguns sistemas de lógica paraconsistente correspondem à distinção entre objetos ontologicamente independentes e ontologicamente dependentes, sendo esses últimos caracterizados como objetos cuja existência depende de nossos processos psicológicos e práticas linguísticas. Em ambas as alternativas, ilustramos como justificar a legitimidade das lógicas paraconsistentes sem endossar a tese de que a realidade, para ser descrita corretamente, requer proposições contraditórias.

Paracomplete Logics Dual to the Genuine Paraconsistent Logics: The Three-valued Case

In 2016 Béziau, introduce a restricted notion of paraconsistency, the so-called genuine paraconsistency. A logic is genuine paraconsistent if it rejects the laws φ,¬φ ⊢ ψ and ⊢ ¬(φ ∧ ¬φ). In that paper the author analyzes, among the three-valued logics, which of them satisfy this property. If we consider multiple-conclusion consequence relations, the dual properties of those above mentioned are ⊢ φ,¬φ and ¬(ψ∨¬ψ) ⊢. We call genuine paracomplete logics those rejecting the mentioned properties. We present here an analysis of the three-valued genuine paracomplete logics.

An Extension of the Stable Semantics via Lukasiewicz Logic

Logic Programming and fuzzy logic are active areas of research, and their scopes in terms of applications are growing fast. Fuzzy logic is a branch of many-valued logic based on the paradigm of inference under vagueness. In this work we recall some of the interplay between three 3-valued logics that are relevant in these areas: The Lukasiewicz logic, the intermediate logic G3 and the paraconsistent logic G3′, and we present a contribution to the area of answer sets that consists in extending a definition of stable model based on proof theory in logic G3, to a more general definition that can be based on any of the more expressive logics G3′ or Lukasiewicz. Finally we present and explore a new 4-valued logic that bears relation to G3 and to Lukasiewicz 4-valued logic.

Three New Genuine Five-valued Logics Intended to Model Non-trivial Concepts

We introduce three 5-valued paraconsistent logics that we name FiveASP1, FiveASP2 and FiveASP3. Each of these logics is genuine and paracomplete. The new value is called e attempting to model the notion of ineffability. If one drops e from any of these logics one obtains a well known 4-valued logic introduced by Avron. If, on the other hand one drops the “implication” connective from any of these logics, one obtains Priest logic FDEe. We present some properties of these logics.

A Basic Dual Intuitionistic Logic and Some of its Extensions Included in G3$$_{\text {DH}}$$

The logic DHb is the result of extending Sylvan and Plumwood’s minimal De Morgan logic B $$_{\text {M}}$$ with a dual intuitionistic negation of the type Sylvan defined for the extension CC $$\omega $$ of da Costa’s paraconsistent logic C $$\omega $$ . We provide Routley–Meyer ternary relational semantics with a set of designated points for DHb and a wealth of its extensions included in G3 $$_{\text {DH}}$$ , the expansion of G3 $$_{+}$$ with a dual intuitionistic negation of the kind considered by Sylvan (G3 $$_{+}$$ is the positive fragment of Godelian 3-valued logic G3). All logics in the paper are paraconsistent.

To the question on philosophical-methodological foundations of English legal positivism of the XIX century (legal teachings of J. Bentham and J. Austin)

The subject of this research is the  aggregate of philosophical ideas and methodological paradigms that underlie the concepts of the “first” legal (statist) positivism in England of the XIX century. The author traces the impact of certain philosophical trends and legal concepts of the XVIII – early XIX centuries upon the philosophical and methodological foundations of the positivist concepts of J. Bentham and J. Austin. The article describes the influence of social atomism, and exploratory rationality of Modern Age upon the “first” legal positivism of philosophical rationalism of the XVIII century. The impact of such philosophical and legal concepts as nominalism, the historical school of lawyers, and philosophical positivism of A. Comte upon the “first” legal positivism was reconstructed. The scientific novelty consists in reconstruction of the influence of an entire number of philosophical and legal ideas and concepts upon the development of “first” legal positivism. Correlation between the legal doctrine of J. Bentham, philosophical concepts of the XVIII century, and the legal teaching of T. Hobbes is underlined. The author draws the ideological parallels between the philosophical nominalism, logical paradox of D. Hume, and legal doctrines of J. Bentham and J. Austin. The author reveals the key “channels” of the impact of German Historical School upon legal positivism, describes the similarities and differences between the scientific positivism of A. Comte and the concepts of legal positivism of J. Bentham and J. Austin. The philosophical-methodological framework of the concepts of “first” legal positivism were subjected to a significant influence of the methodological paradigm of philosophical rationalism, social atomism, exploratory scientific rationality of Modern Age, and nominalism.

O cárcere brasileiro e o perfil social do sistema prisional do Maranhão

O Brasil elevou sua taxa de aprisionamento em aproximadamente 200% nos últimos 20 anos. O presente trabalho tem dois objetivos: primeiro, o de caracterizar o sistema carcerário do Brasil por estado, a partir da análise de indicadores fornecidos pelo Ministério da Justiça e Departamento Penitenciário Nacional – DEPEN. Segundo traçar o perfil socioespacial das unidades prisionais do Estado do Maranhão com base nos dados do Tribunal de Justiça e Secretaria Estadual de Administração Penitenciária - SEAP. Em consonância com outros estudos, nossos resultados apontam para o “buraco negro” que se tornou o sistema prisional brasileiro. Já no Maranhão, o aumento progressivo da população carcerária deve-se mais a uma política de repressão e criminalização à pobreza, do que a uma política capaz de reduzir as ocorrências criminais letais ou não letais.

Application of Shannon Entropy in the Construction of a Paraconsistent Model of the Atom

In this paper, we present a model of the atom that is based on a nonclassical logic called paraconsistent logic (PL), which has the main property of accepting the contradiction in logical interpretations without the conclusions being annulled. The proposed model is constructed with an extension of PL called paraconsistent annotated logic with annotation of two values (PAL2v), which is associated with an interlaced lattice of four vertices. We use the logarithmic function of the Shannon entropy H(s) to construct the paraconsistent equations and thus adopt a probabilistic model for representations in quantum physics. Through analyses of the interlaced lattice, comparative values are obtained for some of the phenomena and effects of quantum mechanics, such as superposition of states, wave functions, and equations that determine the energy levels of the atomic shells of an atom. At the end of this article, we use the hydrogen atom as a basis for the representation of the PAL2v model, where the values of the energy levels in six orbital shells are obtained. As an example, we present a possible method of applying the PAL2v model to the use of Raman spectroscopy signals in the detection of lubricating mineral oil quality.