Non-classical Logics Research Articles

Notes on the Force of Black Domesticity

Abstract Drawing on histories of black domesticity, Simone de Beauvoir’s writings about woman’s situation in housework, and Angela Y. Davis’s refutation of the myth of the black matriarch, this article argues that the force of the black domestic is elusive because it cannot be understood through immanence and transcendence. Through an alternative logic based on black female presence that exceeds the confines of the human, the force of black domesticity emerges as a proliferation of objects that endure the test of time.

Insight into soft binary piecewise lambda operation: a new operation for soft sets

AbstractThe notion of soft set operations is one of the key concept for soft set theory as the theory has been progressing, both theoretically and practically, based on this notion. As proposing new soft set operations, deriving their algebraic properties, and studying the algebraic structure of soft sets from the perspective of soft set operations offer a comprehensive understanding of their applications as well as the appreciation of how soft set algebra can be applied to classical and nonclassical logic, in this study, a new soft set operation, called the “soft binary piecewise lambda operation" is proposed. Since one of the the main objective of abstract algebra is to analyze the properties of the operations defined on a set to classify the algebraic structures, the operation’s full properties and its distributions over other soft set operations are investigated to reveal which algebraic structures the operation forms individually, and together with other soft set operations in the collection of soft sets over the universe. It is showed that the operation forms a noncommutative semigroup and a right-left system, besides semi-rings and near-semi-rings together with certain types of soft set operations under certain conditions in the collection of soft sets over the universe. Since such in-depth analyses advance our knowledge of the applications of soft sets over a range of field, this novel operation may serve as an inspiration to create new perspectives for addressing issues related to parametric data, soft set-based cryptography, or decision-making techniques in practical settings, business, and technology.

Communicated Resilience in Mothers’ Narratives about the Diagnosis and Birth of Their Child with Down Syndrome

ABSTRACT Down syndrome (DS) is the most prevalent chromosomal condition, affecting one in every 733 babies born annually in the United States . Grounded in the communication theory of resilience (CTR;), the present analysis was conducted to evaluate mothers’ communicated resilience in narratives about the birth and diagnosis of their child with DS. In so doing, we sought to refine the theory by clarifying the conceptualization of CTR resilience processes (i.e. putting alternative logics to work, foregrounding productive action, maintaining and using communication networks, crafting normalcy, and affirming identity anchors). Qualitative analyses revealed all five CTR resilience processes along with novel nuances that expand existing perspectives and refine CTR concepts. Our findings suggest that foregrounding productive action should be analyzed separately from backgrounding negative feelings, and we revisit crafting normalcy with respect to disability. Opportunities for practical application to support families are provided.

Communicatively constructing resilience: Exploring family resilience in the experience of hereditary cancer

AbstractObjectiveThe goal was to explore how families communicate to cope with hereditary cancer conditions and identify factors that may enhance resilience and recommended decision‐making.BackgroundFamilies with Hereditary Breast and Ovarian Cancer syndrome (HBOC), Lynch syndrome (LS), and Li‐Fraumeni syndrome (LFS) have an increased lifetime risk of developing cancer. We use the communication theory of resilience (CTR) to examine how families engage in resilience and make health decisions about hereditary cancer risks over time.MethodWe conducted 42 dyadic interviews with families with HBOC, LS, and LFS. Themes emerged through qualitative analysis for each of the resilience processes outlined by CTR (crafting normalcy, communication networks, identity anchors, alternative logics, and foregrounding productive action while legitimizing negative feelings), illustrating how family members manage stressors associated with hereditary cancer over time.ResultsParticipants described enacting each of the five CTR processes to manage the acute and chronic stressors associated with hereditary cancer. We described themes that emerged within each of the five resilience processes.ConclusionFindings demonstrate the ways in which families managing hereditary cancer risks enact resilience processes and how these processes may have a complex relationship to coping and medical decision‐making.ImplicationsFindings demonstrate areas for intervention to support familial resilience.

‘나다움’을 찾아가는 과정에서 겪는 의복행동의 교육적 경험에 관한 연구

Objectives The purpose of this study is to explore the experience process of learners who complete ‘myself’ and to reveal that the aesthetic experience sensed by learners in the process is an educational experience that helps the individual’s qualitative growth. Methods First, we explore clothing behavior as a process of finding ‘myself’ through theoretical consideration of John Dewey’s experiential philosophy of ‘an experience’ and educational experience. Second, by describing, analyzing, and interpreting clothing behavior based on ‘one experience,’ it helps understand the aesthetic experience for true clothing behavior that reveals ‘myself.’ Third, by revealing that the aesthetic experience of clothing behavior is what Dewey calls ‘an experience,’ we explore how the learner’s experiential process of completing his or her self through clothing behavior, which is interpreted as ‘an experience,’ is reborn as an educational experience. Results Educational experience as a clothing behavior is ‘an experience’ that promotes the overall and continuous growth and development of humans by not only promoting the process of understanding one’s identity but also immersing oneself in the process of discovering ‘myself.’ Conclusions By revealing that clothing behavior interpreted in light of Dewey's ‘an experience’ is an educational experience for discovering ‘myeself’, it differs from the conventional view that interprets clothing behavior as pursuing external beauty by focusing only on physical appearance. Provides an alternative logic for approach. It is meaningful in attempting to establish a basis for an educational approach to clothing behavior as self-discovery in pursuit of a happy experience of change.

Uniform Cut-Free Bisequent Calculi for Three-Valued Logics

We present a uniform characterisation of three-valued logics by means of a bisequent calculus (BSC). It is a generalised form of a sequent calculus (SC) where rules operate on the ordered pairs of ordinary sequents. BSC may be treated as the weakest kind of system in the rich family of generalised SC operating on items being some collections of ordinary sequents, like hypersequent and nested sequent calculi. It seems that for many non-classical logics, including some many-valued, paraconsistent and modal logics, the reasonably modest generalisation of standard SC offered by BSC is sufficient. In this paper, we examine a variety of three-valued logics and show how they can be formalised in the framework of BSC. We present a constructive syntactic proof that these systems are cut-free, satisfy the subformula property, and allow one to prove the interpolation theorem in many cases.

Healthcare Providers’ Resilience Communication: A New Type of Patient-Centered Communication

Patient-centered communication (PCC) is considered a key component of quality healthcare, with reported levels of PCC rising over the last decade. However, engagement with patient emotions and uncertainty have been slower to rise, and healthcare providers at times use PCC behaviors to manipulate patients. Healthcare providers’ use of the communication theory of resilience’s (CTR) processes could benefit patients. A cross-sectional survey in the United States (N = 486) tested associations between CTR processes and patient satisfaction and perceived physical and mental health. All five core CTR processes were positively correlated with patient outcomes. When controlling for traditional PCC behaviors: (a) crafting normalcy, identity anchors, and alternative logics were positively related to patient satisfaction, (b) no processes were related to perceived mental health, and (c) communication networks, alternative logics, and productive action were positively related to perceived physical health. Condition severity moderated three associations. At moderate-high severity, crafting normalcy and communication networks were positively related to perceived mental health, and crafting normalcy was positively related to perceived physical health. Findings extend CTR into the patient-provider relationship and demonstrate the practical potential of CTR processes for improving patient outcomes. The study also forwards a measure of healthcare provider resilience communication (HPRC).

Challenges for Non-Classical Reasoning in Contemporary AI Applications

In knowledge representation and reasoning, a key area in artificial intelligence research, non-classical logics play a prominent double role: firstly, non-classical logic languages allow for a precise and transparent encoding of domain specific knowledge. Secondly, as the logical languages are equipped with custom-tailored rules of logical inference, they make available a principled approach to derive new knowledge from previous information. In practice, the first aspect addresses data storage and retrieval, the second aspect the utilization of available information. This article briefly surveys contemporary challenges of NCL research in AI.

It Takes Two to Tango: The Technocracy-populism Nexus in Italy and the EU from a Critical-realist Perspective

ABSTRACT The nexus between technocracy and populism in Italy can be better understood from a long-term perspective. Adopting a critical-realist approach to the explanation of political change, it is possible to identify the main contextual factors that favoured, from the early 1990s, the rise of these two alternative yet compatible logics of politics, which can be conceived as both causes and symptoms of the fatigue of representative democracy. This also allows (i) a better understanding of the entanglement of populism and technocracy after the global crisis of 2008, and (ii) the conceptualisation of the position of the European Union (EU) as a catalyst of these processes within a multi-level spatial nexus.

A NEW SOFT SET OPERATION: COMPLEMENTARY EXTENDED STAR OPERATION

Soft set theory has established itself as a valuable mathematical framework for tackling issues marked by uncertainty, demonstrating its applicability across a range of theoretical and practical fields since its inception. Central of this theory is the operations of soft sets. To enhance the theory and to make a theoretical contribution to the theory, a new type of soft set operation, called “complementary extended star operation” for soft set, is proposed. An exhaustive examination of the properties of this operation has been undertaken, including its distributions over other soft set operations, with the goal of clarifying the relationship between the complementary extended star operation and other soft set operations. This paper also attempts to make a contribution to the literature of soft sets in the sense that studying the algebraic structure of soft sets from the standpoint of soft set operations offers a comprehensive understanding of their application as well as an appreciation of how soft set can be applied to classical and nonclassical logic.

Computer-Aided Searching for a Tabular Many-Valued Discussive Logic—Matrices

Abstract In the paper, we tackle the matter of non-classical logics, in particular, paraconsistent ones, for which not every formula follows in general from inconsistent premisses. Our benchmark is Jaśkowski’s logic, modeled with the help of discussion. The second key origin of this paper is the matter of being tabular, i.e. being adequately expressible by finitely many finite matrices. We analyse Jaśkowski’s non-tabular discussive (discursive) logic $ \textbf {D}_{2}$, one of the first paraconsistent logics, from the perspective of a trivalent tabular logic. We are motivated to step down from the ongoing modal $ \textbf {S5}$-perspective of developing $ \textbf {D}_{2}$ both by certain mysteries that have been surrounding it and by gaps in Jaśkowski’s arguments contra the multivalent tabular perspective. Although Jaśkowski’s idea to use $ \textbf {S5}$ in order to define $ \textbf {D}_{2}$ is very attractive since it allows one to benefit from the tools and results of modal logic, it also gives a ‘non-direct’ formulation and, as it appeared later, is superfluous with respect to what is meant to be achieved since one can define the very same logic but using modal logics weaker than S5. It is also known, due to Kotas, that discussive logic is not finite-valued. So, in light of Kotas’s result that $ \textbf {D}_{2}$ is non-tabular, we propose to associate it with a few dozen discussive formulae that Jaśkowski unequivocally and illustratively suggests to be its theorems or non-theorems rather than with axioms of its modern axiomatizations (one of which Kotas employs) in order to be capable of performing a computer-aided brute-force search for suitable trivalent matrices in the cases of one and two designated values. As a result, we find trivalent matrices with two designated values that might be dubbed ‘discussive’ because they meet Jaśkowski’s suggestion to validate and invalidate the litmus theorems and non-theorems, respectively, despite the fact that none of them validates all the negation axioms in the modern axiomatizations of $ \textbf {D}_{2}$. The matrices found are then analysed along with highlighting the ones that were previously mentioned in the literature. We conclude the paper with a comparative analysis of Omori’s results and a test of Karpenko’s hypothesis.

Saving logic from paradox via nonclassical recapture

The Liar paradox arguably shows that a coherent and self-applicable notion of truth is governed by nonclassical logic. It then seems natural to conclude that classical logic is inadequate for defining a truth theory. In this article, we argue that this is not the case. In the spirit of Reinhardt (Math Logic Formal Syst 94:227, 1985; J Philos Logic 15:219–251, 1986), and in analogy with Hilbert’s program for the foundation of classical mathematics, we will articulate an instrumentalist justification for the use classical logic: it will be argued that classical reasoning is a useful but dispensable instrument, which can yield philosophically adequate truth theories.

Non-lethal weapons and the sensory repression of dissent in democracies

This article examines the use of ‘non-lethal’ weapons (NLWs) by liberal democracies to govern dissent in non-war contexts. We argue that NLWs can enable sensorial governance, specifically through sensory repression of dissent. Although accented as non-lethal, NLWs are better conceived of as what we term ‘Weapons of Sensory Repression’ (WSRs). From tear gas to sound cannons to skunk bombs and more, WSRs target the human senses – visual, auditory, olfactory, proprioceptive – and impose debility not death, thus enabling the use of technologies of repression against dissenting collective assemblies at lower threat thresholds than conventional weapons, arguably disincentivizing alternatives to repression. Since law enforcement in liberal democracies is not explicitly linked to political control and such democracies derive legitimacy from responsiveness to public opinion, it is worth highlighting what WSRs make im/possible in this regard. Empirically, WSRs create and confirm subordinate citizenship in liberal democracies for those who are already de facto lacking in certain rights. Emphasizing that liberal democracies renew themselves through challenges involving mass mobilization, we suggest that the employment of these weapons transforms problems of political change into problems of technological crowd management by dehumanizing those that propose alternative logics for dominant economic, nationalist or racial orders.

Low Power CMOS Full Adder Cells based on Alternative Logic for High-Speed Arithmetic Applications

Low Power CMOS Full Adder Cells based on Alternative Logic for High-Speed Arithmetic Applications

META-CLASSICAL NON-CLASSICAL LOGICS

Abstract Recently, it has been proposed to understand a logic as containing not only a validity canon for inferences but also a validity canon for metainferences of any finite level. Then, it has been shown that it is possible to construct infinite hierarchies of ‘increasingly classical’ logics—that is, logics that are classical at the level of inferences and of increasingly higher metainferences—all of which admit a transparent truth predicate. In this paper, we extend this line of investigation by taking a somehow different route. We explore logics that are different from classical logic at the level of inferences, but recover some important aspects of classical logic at every metainferential level. We dub such systems meta-classical non-classical logics. We argue that the systems presented deserve to be regarded as logics in their own right and, moreover, are potentially useful for the non-classical logician.

In between impossible worlds

ABSTRACT The common view has it that there are two families of approaches towards the logical structure of impossible worlds – Australasian and North American. According to the first, impossible worlds are closed under the relation of logical consequence of one of the non-classical logics. The North American approach is more liberal, allowing for impossible worlds where no logic holds. After pointing out the questionable consequences of each view, I propose a third one. While this new perspective allows for worlds where no logical consequence holds, it also imposes some constraints on what worlds are built upon. This renders the proposed view not as restrictive as the Australasian approach and not as liberal as the North American approach. Due to its intermediary nature, I have named this perspective ‘the Pacific’ approach.

Toward Opportunity-Centered Institutional Logics: Evidence from Hispanic-Serving Institutions and Science Equity Efforts

ABSTRACT In U.S. 4-year postsecondary institutions, predominant institutional logics — the embedded assumptions that guide organizational action — have traditionally focused on prestige seeking via acquisition of resources, reputation, and research capabilities. This focus can hinder the design and implementation of teaching approaches and structures that support equitable student experiences and outcomes, particularly for minoritized students. This study examined the institutional logics guiding the organizational behavior of four broadly accessible Hispanic-Serving Institution (HSI) computer science departments. All were participating in a multi-institutional network of HSIs designed to advance science equity efforts and postsecondary attainment for Latinx students in the discipline. A multiple case study of these four departments included 63 interviews with faculty and administrators, 69 observations of departmental activities, and extensive participant-observations of the network before, during, and after site visits. Data analysis revealed three themes — inclusivity, talent development, and cultural responsiveness — that indicate how departmental personnel employ institutional logics alternative to prestige-seeking institutional logics. The paper discusses the implications of these alternative institutional logics, characterized as opportunity-centered logics, to effect equity-focused institutional transformation, strengthening of HSIs’ capacities to serve Latinx and minoritized students, and inclusive efforts in science.

Every loaf of bread is political – Reflections on collective care responses to Covid-19 in Cape Town

Feminist perspectives on care have demonstrated how capitalism undervalues care work. The Covid-19 pandemic highlighted this further, as systems of production and social reproduction became destabilized globally. In many countries, the formal pandemic response fell short of attending to the daily, fundamental care needs of people living through the crisis, especially those compromised by the socio-economic effects of the pandemic. These needs were often attended to at the community level. This article explores a community-led network of care, known as CANs, that emerged in response to the pandemic in Cape Town. It makes three overarching observations. The first is that community-led responses were characterised by a push towards the collectivisation of care work. The second is that this enabled emergent strategies and relational practices of care, centring notions of solidarity, inter-dependence and horizontal exchange of resources and knowledge. Finally, we observed that, although the devaluation of care work limited the recognition and material support extended to CANs, opportunities to re-politicise care work as resistance work emerged. These represent a prefigurative moment in which alternative logics and strategies can transform the vision of our health and care systems, and the notion of community participation in and ownership of those systems.

Attack principles in sequent-based argumentation theory

Abstract Attack principles have been introduced in semi-abstract argumentation frameworks and, in the present work, we interpret them in sequent-based argumentation frameworks. Thus, we investigate the role of minimality and consistency of the support set of an argument. Through the notion of preservation of strength, we introduce a formal criterion to sort out the attack principles; isolate the more “acceptable” ones, i.e. those easier to justify; and recover a new argumentative semantics for the non-classical logic that arises from dropping the rules $(\neg , r)$, $(\land , r)$ and $(\supset , l)$ from Gentzen’s classical sequent calculus for classical logic $\textsf{LK}$.

Critical Math Kinds: A Framework for the Philosophy of Alternative Mathematics

AbstractMathematics, even more than the other sciences, is often presented as essentially unique, as if it could not be any other way. And yet, prima facie alternative mathematics are all over the place, from non-Western mathematics to mathematics based on nonclassical logics. Taking inspiration from Robin Dembroff’s analysis of critical gender kinds, and from Andrew Aberdein and Stephen Read’s analysis of alternative logics, in this paper I will introduce a practice-centered framework for the study of alternative mathematics based on the notion of critical math kind. After sketching a model of mainstream mathematics, I will provide examples of how deviation along several distinct dimensions can occur, and how deviations can vary in their gravity. I will then discuss how the framework can be used to think of questions concerning the alternativeness status and philosophical implications of alleged alternative mathematics, and help us in identifying alternatives that suit our purposes.