Paraconsistent Research Articles

PARACONSISTENT AND PARACOMPLETE ZERMELO–FRAENKEL SET THEORY

Abstract We present a novel treatment of set theory in a four-valued paraconsistent and paracomplete logic, i.e., a logic in which propositions can be both true and false, and neither true nor false. Our approach is a significant departure from previous research in paraconsistent set theory, which has almost exclusively been motivated by a desire to avoid Russell’s paradox and fulfil naive comprehension. Instead, we prioritise setting up a system with a clear ontology of non-classical sets, which can be used to reason informally about incomplete and inconsistent phenomena, and is sufficiently similar to ${\mathrm {ZFC}}$ to enable the development of interesting mathematics. We propose an axiomatic system ${\mathrm {BZFC}}$ , obtained by analysing the ${\mathrm {ZFC}}$ -axioms and translating them to a four-valued setting in a careful manner, avoiding many of the obstacles encountered by other attempted formalizations. We introduce the anti-classicality axiom postulating the existence of non-classical sets, and prove a surprising results stating that the existence of a single non-classical set is sufficient to produce any other type of non-classical set. Our theory is naturally bi-interpretable with ${\mathrm {ZFC}}$ , and provides a philosophically satisfying view in which non-classical sets can be seen as a natural extension of classical ones, in a similar way to the non-well-founded sets of Peter Aczel [1]. Finally, we provide an interesting application concerning Tarski semantics, showing that the classical definition of the satisfaction relation yields a logic precisely reflecting the non-classicality in the meta-theory.

Intelligent Farming based on Uncertainty Expert System with Butterfly Optimization Algorithm for Crop Recommendation

Meeting the current population's food demands has become challenging, given the rising population, frequent climate fluctuations, and limited resources. Smart farming, also known as precision agriculture, has emerged as an advanced approach to tackle modern challenges in crop production. At the heart of this cutting-edge technology is machine learning, serving as the driving force behind its implementation. Though, there are many algorithms are available in crop prediction process, the problem of predicting vague information is still a challenging issue. Unfortunately, existing algorithms mostly avoids the complicated instances in crop recommendation dataset by not handling them effectively, due to imbalance class distribution. Hence in this research work to conduct an intelligent farming, two different uncertain theories are adopted to handle the issue of vagueness in appropriate recommendation of crop by considering soil fertility and climatic condition. The proposed is developed based on uncertainty expert system with both neutrosophicalparaconsistent inference model. The neutrosophic inference model is integrated with the paraconsistent logic to overcome the problem of uncertainty in prediction of appropriate crop by representing the factors in terms of certainty degree and contradiction degree. The rule generated by paraconsistent model is validated to improve the accuracy of crop prediction by fusing the knowledge of butterfly optimization algorithm. The nectar searching behavior of the butterflies are used for searching potential rules as a validation process. With the pruned rules generated by uncertainty expert model, the suitable crop is predicted more accurately compared to the other existing prediction models.

Semantic Closure and Classicality

The semantic paradoxes show that semantic theories that internalize their semantic concepts, such as truth and validity, cannot validate all classical logic. That is, it is necessary to weaken some connective of the object language, taken as the guilty of the paradoxes, or give up some property of the consequence relation of the logical theory. Both strategies may distance us from classical logic, the logic commonly used in our current mathematical theories. So, a desirable solution to semantic paradoxes cannot distance us from classical logic. This paper analyzes two interesting proposals that aim to maintain classical logic as most as possible. The first strategy, the Barrio & Pailos & Szmuc-approach (2017) (BPS-approach), proposes the paraconsistent logic MSC that contains in its object language a connective capable of recovering classical inference whenever the sentences at issue are consistent. So, they show that it is possible to build a semantic theory over this logic that is immune to the semantic paradoxes. The second approach is based on the hierarchy STω of non-transitive systems STn, proposed by Pailos (2020a). This hierarchy recovers classical metainferences as many as possible in higher levels of the hierarchy. We argue in favor of the second approach by arguing that the first strategy must adopt weak self-referential procedures to avoid the paradoxes.

The Logic of Imagination and Gender Paradox:On the Adaptation Research of Red Rose White Rose

Eileen Chang's novels are deeply loved by the big screen for their cinematic imaginative literary style, highly informative and intellectual literary charm, and desolate and colorful literary temperament. However, these characteristics also bring controversy to her adaptation of movies. This article does not focus on exploring the inevitable changes brought about by media transformation, but directly points to the narrative core of the text. Taking the adaptation film Red Rose White Rose directed by Stanley Kwan as an example, by comparing the core narrative themes of the novel and the film, this study explores the narrative adaptation strategies and underlying logic of the film.

Semantic Incompleteness of Hilbert system for a Combination of Classical and Intuitionistic Propositional Logic

This paper shows Hilbert system (C+J)-, given by del Cerro and Herzig (1996) is semantically incomplete. This system is proposed as a proof theory for Kripke semantics for a combination of intuitionistic and classical propositional logic, which is obtained by adding the natural semantic clause of classical implication into intuitionistic Kripke semantics. Although Hilbert system (C+J)- contains intuitionistic modus ponens as a rule, it does not contain classical modus ponens. This paper gives an argument ensuring that the system (C+J)- is semantically incomplete because of the absence of classical modus ponens. Our method is based on the logic of paradox, which is a paraconsistent logic proposed by Priest (1979).

Sequent-type rejection systems for finite-valued non-deterministic logics

A rejection system, also referred to as a complementary calculus, is a proof system axiomatising the invalid formulas of a logic, in contrast to traditional calculi which axiomatise the valid ones. Rejection systems therefore introduce a purely syntactic way of determining non-validity without having to consider countermodels, which can be useful in procedures for automated deduction and proof search. Rejection calculi have first been formally introduced by Łukasiewicz in the context of Aristotelian syllogistic and subsequently rejection systems for many well-known logics have been proposed. In this paper, we deal with rejection systems for so-called non-deterministic finite-valued logics, a special case of non-deterministic many-valued logics which were introduced by Avron and Lev as a generalisation of traditional many-valued logics. More specifically, we introduce a systematic method for constructing sequent-style rejection systems for any given non-deterministic finite-valued logic. Furthermore, as special instances of our method, we provide concrete calculi for specific paraconsistent logics which can be characterised in terms of non-deterministic two- and three-valued semantics, respectively.

The New Clarity: Awakening in the Post-Truth Era

In the wake of Trump and Brexit, the late 2010s gave rise to an ambient sense of a post-truth crisis. It signals the social media fuelled breakdown of liberal democracy and its 'fourth estate' into fragmented and mutually antagonising epistemic media bubbles. Yet at the same time, the new online political movements driving this crisis became enthralled with the radical sense of waking up from a false reality to absolute Truth, ranging from new (con)spiritual fascinations with mystical clarity to far-right ideas about a Great Awakening and red-pilling. This article tries to make sense of this strange resurgence of 'awakening' and the experience of radical epistemic clarity from within post-truth culture. We argue that what we refer to as the New Clarity represents the bleeding edge of our current post-truth predicament, which at once intensifies 'postmodern' sentiments of cynicism, irony and play and breaks with them in the form of new political-epistemic radicalisms. To draw out this paradoxical relationship between post-truth and the New Clarity, we survey three historical dimensions of postmodernism as theorised by Lyotard and others at the closing of the 20th century, namely: cynicism and the crisis of critique, new spiritualities and authoritarian conspiracism, and the spiralling dialectic between neoliberalism and populism. Breaking down these dimensions to understand the New Clarity, we take the QAnon conspiracy movement as embodying its paradoxical logic. Doing so we offer a critical heuristic for charting the rise of new conspiratorial and spiritual Awakenings today.

Risk management in civil construction: the contractor's perceptions

Purpose: This study seeks to understand how the managers of the civil construction industry perceive risk management in their projects and businesses based on a case study in the region of Volta Redonda-RJ. Design/methodology/approach: Primary data was collected through questionnaires and interviews. The primary quantitative data were analyzed using Paraconsistent Logic and presented with descriptive statistics. Findings: It was found that 87% of the sample did not go through any steps of the risk management process. For those that did, the steps were essentially intuitive and informal. Further, a distortion was observed on behalf of the managers regarding the understanding of what risk management is, what it is helpful for, and the difference between their projects and the business itself. Practical implications: Although not generalizable, the research results show a high appetite for risk on the part of contractors but a low willingness to absorb its effects. Originality/value: Studies that apply paraconsistent logic to understand builders' perceptions of the importance of risk management are scarce in the literature. Also, there is little literature about the management aspects of this industry.

Semantical investigations on non-classical logics with recovery operators: negation

Abstract We investigate mathematical structures that provide natural semantics for families of (quantified) non-classical logics featuring special unary connectives, known as recovery operators, that allow us to ‘recover’ the properties of classical logic in a controlled manner. These structures are known as topological Boolean algebras, which are Boolean algebras extended with additional operations subject to specific conditions of a topological nature. In this study, we focus on the paradigmatic case of negation. We demonstrate how these algebras are well-suited to provide a semantics for some families of paraconsistent Logics of Formal Inconsistency and paracomplete Logics of Formal Undeterminedness. These logics feature recovery operators used to earmark propositions that behave ‘classically’ when interacting with non-classical negations. Unlike traditional semantical investigations, which are carried out in natural language (extended with mathematical shorthand), our formal meta-language is a system of higher-order logic (HOL) for which automated reasoning tools exist. In our approach, topological Boolean algebras are encoded as algebras of sets via their Stone-type representation. We use our higher-order meta-logic to define and interrelate several transformations on unary set operations, which naturally give rise to a topological cube of opposition. Additionally, our approach enables a uniform characterization of propositional, first-order and higher-order quantification, including restrictions to constant and varying domains. With this work, we aim to make a case for the utilization of automated theorem proving technology for conducting computer-supported research in non-classical logics. All the results presented in this paper have been formally verified, and in many cases obtained, using the Isabelle/HOL proof assistant.

The White gaze: epistemological imposition and paradoxical logic in educational research

This article critically examines the constraints associated with mainstream ethnographic research, including methodologies, analyses, epistemologies, and logic, herein referred to as the White gaze, a reinforcement of White supremacy. The focus is on how the White gaze infringes upon Black epistemologies and BIPOC epistemologies more broadly. The study highlights the pioneering work of Du Bois’ “The Philadelphia Negro” a notable ethnographic study that transcends the limitations of the White gaze. It emphasizes the importance of incorporating concepts, perspectives, and language that stem from intimacy and rapport, allowing for a comprehensive representation of the diversity and nuances within Black communities. Furthermore, the article addresses the detrimental impact of mainstream research on Black communities resulting from the White gaze. It exposes the historical absence, denial, and discrediting of decades worth of BIPOC-centric research and resources to advance their communities’ well-being. Drawing on various scholarly sources (Fenwick, 2022; Foster, 1994; Horsford, 2021; Morris, 2015; Smith, 1999; Stanfield & Dennis, 1993; Walker, 2013; Wright, 2019; Zuberi & Bonilla-Silva, 2008), it highlights the systemic barriers hindering the dissemination and recognition of BIPOC knowledge. This article highlights the omnipresence of the White gaze in academic research—specifically, its effect on educational research and practices shaping school culture—that prevents, for example, Black epistemologies from informing research on Black students. And lastly, offers implications for educational research and practice.

Quantum reality with negative-mass particles

Physical interpretations of the time-symmetric formulation of quantum mechanics, due to Aharonov, Bergmann, and Lebowitz are discussed in terms of weak values. The most direct, yet somewhat naive, interpretation uses the time-symmetric formulation to assign eigenvalues to unmeasured observables of a system, which results in logical paradoxes, and no clear physical picture. A top-down ontological model is introduced that treats the weak values of observables as physically real during the time between pre- and post-selection (PPS), which avoids these paradoxes. The generally delocalized rank-1 projectors of a quantum system describe its fundamental ontological elements, and the highest-rank projectors corresponding to individual localized objects describe an emergent particle model, with unusual particles, whose masses and energies may be negative or imaginary. This retrocausal top-down model leads to an intuitive particle-based ontological picture, wherein weak measurements directly probe the properties of these exotic particles, which exist whether or not they are actually measured.

IS CANTOR’S THEOREM A DIALETHEIA? VARIATIONS ON A PARACONSISTENT APPROACH TO CANTOR’S THEOREM

AbstractThe present note was prompted by Weber’s approach to proving Cantor’s theorem, i.e., the claim that the cardinality of the power set of a set is always greater than that of the set itself. While I do not contest that his proof succeeds, my point is that he neglects the possibility that by similar methods it can be shown also that no non-empty set satisfies Cantor’s theorem. In this paper unrestricted abstraction based on a cut free Gentzen type sequential calculus will be employed to prove both results. In view of the connection between Priest’s three-valued logic of paradox and cut free Gentzen calculi this, a fortiori, has an impact on any paraconsistent set theory built on Priest’s logic of paradox.

The effect of placentation type, litter size, lactation and gestation length on cancer risk in mammals.

Reproduction is a central activity for all living organisms but is also associated with a diversity of costs that are detrimental for survival. Until recently, the cost of cancer as a selective force has been poorly considered. Considering 191 mammal species, we found cancer mortality was more likely to be detected in species having large, rather than low, litter sizes and long lactation lengths regardless of the placentation types. However, increasing litter size and gestation length are not per se associated with an enhanced cancer mortality risk. Contrary to basic theoretical expectations, the species with the highest cancer mortality were not those with the most invasive (i.e. haemochorial) placentation, but those with a moderately invasive (i.e. endotheliochorial) one. Overall, these results suggest that (i) high reproductive efforts favour oncogenic processes' dynamics, presumably because of trade-offs between allocation in reproduction effort and anti-cancer defences, (ii) cancer defence mechanisms in animals are most often adjusted to align reproductive lifespan, and (iii) malignant cells co-opt existing molecular and physiological pathways for placentation, but species with the most invasive placentation have also selected for potent barriers against lethal cancers. This work suggests that the logic of Peto's paradox seems to be applicable to other traits that promote tumorigenesis.

TIME TRAVEL AND PARALLEL WORLDS IN CINEMATOGRAPHY

Time travel is one of the biggest themes of science fiction, to the point of being considered a genre in itself. The idea of going to relive the past, or to discover the future in advance, is an old human dream caused by the fact that the human being progresses through time in a constant but irreversible way. One of the earliest mentions of time travel is the character of Merlin the Wizard in the Arthurian cycle of the Knights of the Round Table, who visited past times. The Celts believed in the possibility of time travel and parallel worlds, from tombs, mounds to other mythological places. The theme of time travel is partly related to the world of prophecies, which was also widespread among ancient peoples. Physicists and philosophers, as well as today’s science fiction thinkers and writers, have always been interested in time travel, the theoretical and surrealistic effects of light-speed travel, and the logical paradoxes that would arise from time travel.

Cubic Paraconsistent Analysers with Evidence Filter and Temporal Analysis

Ambiguous or inconsistent information is frequently present in the input of any real-world system that relies on multiple data sources. In the presence of inconsistencies, an expert system based on classical logic is trivialised due to the principle of explosion, that forces any proposition (and its negation) to be inferred. Instead, a family of non-classical logics, called Paraconsistent Logics, formalises the idea that even from inconsistent premises, useful conclusions can be drawn. Within this context, the Paraconsistent Annotated Logics with Annotation of Two Values (PAL2v), which use a pair of favourable and unfavourable evidences as annotations, have been particularly successful in engineering applications. Structures called Para-Analysers can be built with these logics that provide the appropriate means to analyse the truth value of a proposition under conflicting/contradictory evidences. The work reported in this paper extends the traditional Para-Analysers with an evidence filter. This new model can be represented as a cubic structure representing various Para-Analyser lattices, each of which is selected according to the quality of the evidence, that is updated with respect to measurements executed at run time. The resulting three-dimensional paraconsistent analysis structure is encapsulated as an expert-system cell called Cubic Paraconsistent Analyser with Evidence Filter and Temporal Analysis (CPAet). Sets of CPAet nodes are combined constituting distinct network topologies that are used to infer the operating conditions of equipment in data networks of electrical systems control and supervision, resulting in a fault detection and classification system. Tests on simulated systems show that the CPAet networks were effective to deal with inconsistencies without trivialising the inferences, while also providing a more informed (finer grained) decision on the data network equipment state, when compared to the traditional paraconsistent analysers.

Mythical systems: sign and symbol

PurposeThe process of elaboration of the symbolic universe leads to important insights into the role of symbols in understanding human reasoning. Symbols become explanatory axes of universal global realities. Myths were constructed on these explanatory paths forming a superstructure of all belief systems with paraconsistent logic for the symbolism and a symbolic syntax. Myths and symbols are to be found in all cultures. Some of the most powerful and influential ones occur in popular culture since these often have the greatest immediate social impact.Design/methodology/approachSemiotic and logical development of the symbols is in mythical systems. The dissolution of the myth and the degradation of the myth's symbols constitute a long-drawn-out process in modern Western society and wherever s influence reaches. Myth is a story that may contain symbolic elements, but compared to the symbols or images of the exceptional, myth is characterized by a “story.”FindingsStarting from a minimal definition to define myths and propose the following definition: Myth is a traditional tale that relates memorable and exemplary actions of extraordinary personages in prestigious and distant times, and myths have various forms and functions, perhaps some more clearly defined with a signifier than others, and different approaches can be combined for a better understanding of the myths. Dispensing with such simplistic assertions, and starting from a minimal definition to define myth, myth is a traditional tale that relates memorable and exemplary actions of extraordinary personages in prestigious and distant times.Originality/valueAny symbol F originates in a unit that has two aspects and functions when the unit is restored. Thus, the symbol is rather “for something” than “of something” and the symbolic objects express the objects' correspondence in one unit or hendiadys. One semantic characteristic of symbols is “recognition”. The symbol F reveals a reality by means of the homogenous association of the signifier and significance in the symbol's constitution; although reality is separate, there is a homogeneous relation between the symbolizing and symbolized in symbolization.

The Logic of Posthuman Inquiry: Affirmative Politics, Validity, and Futurities

Empirical research informed by posthumanist philosophy is proliferating in the social sciences. This research takes many forms and is willfully pluralistic and creative in the analytic approaches it takes. The innovation, however, is not entirely free form. Posthumanist scholarship both employs familiar forms of inference and is also forwarding a distinctive array of inferential practices that until now have not been commonly present in mainstream/whitestream social sciences. Attending to the logic of emerging posthumanist empiricism can help clarify the affirmative ethics and politics of posthumanist inquiry. This essay offers that a modal, dialethic, paraconsistent logic of action is more suited to posthumanist inquiry than a classical logic of representation. This logic of action locates validity not with the accuracy of representations, but in the specific character of the futurities enabled and disabled by the ontologically generative action of inquiry. Implications for an axiology of posthumanist empiricism are explored.

Alkaline gases emission estimation and paraconsistent logic techniques application to label bagasse combustion conditions

When some renewable energy sources are used, such as biomass solid waste, it is necessary to measure and control pollutant emissions. Since raw sugarcane comes from a wide variety of supply sources, it is necessary to monitor the behavior of the biomass residues during the burning process to control flame stability, emissions, and combustion efficiency. The variation in the combustion temperature of biomass affects the combustion efficiency and also the emission of alkaline metals, such as potassium (K) and sodium (Na), which can cause corrosion in boilers. The objective of the present work is to estimate the content of alkali gases in the flames during the burning of solid biomass residues, specifically sugarcane bagasse in this case. The flame emission spectroscopy (FES) spectrometry technique is used and flame emission spectra is captured during the combustion of bagasse in a pilot furnace. The flame temperature is calculated using the two-color method together with the inverse Levenberg-Marquard method. Models and correlations from literature are used to obtain a database of emission content of sodium and potassium. Using paraconsistent logic techniques, a predictor algorithm is implemented and bagasse samples were labeled to identify similar physical combustion conditions. The results of the emission of sodium and potassium estimated for groups labeled using the algorithm of paraconsistent logic are compared and show good agreement between them. A good and reasonable agreement was found in the estimation of the emission content of potassium and sodium.

Complement-Topoi and Dual Intuitionistic Logic

Mortensen studies dual intuitionistic logic by dualizing topos internal logic, but he did not study a sequent calculus. In this paper I present a sequent calculus for complement-topos logic, which throws some light on the problem of giving a dualization for LJ.

The Logical Structure of Dialectic

I give a formal model of dialectical progression, as found in Hegel and Marx. The model is outlined in the first half of the paper, and deploys the tools of a formal paraconsistent logic. In the second half, I discuss a number of examples of dialectical progressions to be found in Hegel and Marx, showing how they fit the model.