Since the late 1980’s Kim has presented some major reasons to abandon SC. In MIAPW at least four of these reasons are offered: under SC we lose mental causation, mental realism and psychological explanations. Moreover, supervenience cannot do the job as the cementing relation in SC.

Quantum mechanics, and the micro level indeterminacy it implies, is generally accepted by philosophers. So too naturalism on which macro states are held to supervene on micro states is now orthodox in the philosophy of mind and science. Still, in both fields it is frequently assumed that macro systems evolve deterministically. This assumption is commonly implicit and undefended, though at times it is made explicit and given minimal defense. In neither case is the incompatability of quantum indeterminacy, macro-micro dependence, and (...) macro level determinism fully acknowledged. Even when incompatability is recognized, it is held that there is hope that quantum indeterminacy might be confined to micro levels. We argue that this is a vain hope. For certain standard quantum mechanical systems, micro indeterminism entails macro indeterminism unless macro states are effectively independent from micro states. This result obtains whether the relationship between supervenient and subvenient states is deterministic or indeterministic. (shrink)

How does mind fit into nature? Philosophy has long been concerned with this question. No contemporary philosopher has done more to clarify it than Jaegwon Kim, a distinguished analytic philosopher specializing in metaphysics and philosophy of mind. With new contributions from an outstanding line-up of eminent scholars, this volume focuses on issues raised in Kim's work. The chapters cluster around two themes: first, exclusion, supervenience, and reduction, with attention to the causal exclusion argument for which Kim is widely celebrated; and (...) second, phenomenal consciousness and qualia, with attention to the prospects for a functionalist account of the mental. This volume is sure to become a major focus of attention and research in the disciplines of metaphysics and philosophy of mind. (shrink)

Since the late 1980’s Kim has presented some major reasons to abandon SC. In MIAPW at least four of these reasons are offered: under SC we lose mental causation, mental realism and psychological explanations. Moreover, supervenience cannot do the job as the cementing relation in SC.

In 1986, Mikenberg et al. introduced the semantic notion of quasi-truth defined by means of partial structures. In such structures, the predicates are seen as triples of pairwise disjoint sets: the set of tuples which satisfies, does not satisfy and can satisfy or not the predicate, respectively. The syntactical counterpart of the logic of partial truth is a rather complicated first-order modal logic. In the present article, the notion of predicates as triples is recursively extended, in a natural way, to (...) any complex formula of the first-order object language. From this, a new definition of quasi-truth is obtained. The proof-theoretic counterpart of the new semantics is a first-order paraconsistent logic whose propositional base is a 3-valued logic belonging to hierarchy of paraconsistent logics known as Logics of Formal Inconsistency, which was proposed by Carnielli and Marcos in 2002. (shrink)

In this paper we propose an approach to multi-source belief revision where the trust or credibility assigned to informant agents can be revised. In our proposal, the credibility of each informant represented as a strict partial order among informant agents, will be maintained in a repository called credibility base. Upon arrival of new information concerning the credibility of its peers, an agent will be capable of revising this strict partial order, changing the trust assigned to its peers accordingly. Our goal (...) is to formalize a set of change operators over the credibility base: expansion, contraction, prioritized, and non-prioritized revision. These operators will provide the capability of dynamically modifying the credibility of informants considering the reliability of the information. This dynamics will reflect a new perception of trust assigned to the informant, or extend the set of informants by admitting the addition of new informant agents. (shrink)

In this paper we introduce a formalism for single-agent decision making that is based on Dynamic Argumentation Frameworks. The formalism can be used to justify a choice, which is based on the current situation the agent is involved. Taking advantage of the inference mechanism of the argumentation formalism, it is possible to consider preference relations, and conflicts among the available alternatives for that reasoning. With this formalization, given a particular set of evidence, the justified conclusions supported by warranted arguments will (...) be used by the agent’s decision rules to determine which alternatives will be selected. We also present an algorithm that implements a choice function based on our formalization. Finally, we complete our presentation by introducing formal results that relate the proposed framework with approaches of classical decision theory. (shrink)

The essays in Fanon and the Decolonization of Philosophy all trace different aspects of the mutually supporting histories of philosophical thought and colonial politics in order to suggest ways that we might decolonize our thinking. From psychology to education, to economic and legal structures, the contributors interrogate the interrelation of colonization and philosophy in order to articulate a Fanon-inspired vision of social justice. This project is endorsed by his daughter, Mireille Fanon-Mendès France, in the book's preface.

Trata-se de uma reflexão sobre as ameaças aos direitos humanos, sobretudo à dignidade e à liberdade, e à essência humana geradas pelo avanço da biotecnologia. O foco de alerta e resgate da noção de cuidado de si perpassa a perspectiva de futuro de M. Foucault e usa como complemento e desfecho a noção de responsabilidade de H. Jonas para a manutenção da vida e para a realização do sentido do humano e das novas gerações – papel ético por excelência. O (...) texto divide-se em duas partes: a primeira é inspirada em Foucault e a segunda, em Jonas. O leitor é convidado a refletir dentro de uma dupla consideração do tema. PALAVRAS-CHAVE – Dignidade. Direitos humanos. Cuidado de si. Responsabilidade. Futuro. M. Foucault. H. Jonas. (shrink)

We analyze the prestige of 1,500 scholars in economics, sociology, and management who have Spanish and French institutional affiliations operationalized by their h-index in Scopus and Google Scholar. We use a negative binomial count model to examine how some individual factors affect the h-index from both databases. The results show a non-monotonic relationship between the researchers’ career length and their h-index. There is a positive and statistically significant relationship between total research output and the h-index. The share of publications in (...) English over total publications has also a positive and statistically significant effect on the h-index, except in a single case, while the share of publications in other foreign languages does not have such effect. Finally, we found that the effects of the number of citations received by documents in English and by those in the vernacular language on the h-index vary according to the database, the country, and the discipline in question. (shrink)

Resumo:Este artigo discute a leitura que faz o estudo introdutório de Luiz Henrique Lopes dos Santos (1992) dos aforismos iniciais do Tractatus. Tal leitura vê, nesses aforismos iniciais, as consequências ontológicas de um argumento transcendental cuja premissa é a concepção de figuração desenvolvida nos aforismos subsequentes. Em contraste com essa leitura, aqui é defendido que se possa entender esses aforismos iniciais como uma investigação de toda normatividade, explicitando o vínculo entre necessidade e totalidade. Assim se aponta para uma nova perspectiva (...) de interpretação do Tractatus e de seus vínculos com a tradição crítica. Abstract:This article discusses the reading made in the introductory study by Luiz Henrique Lopes dos Santos (1992) of the initial aphorisms of the Tractatus. Such a reading holds, in these initial aphorisms, the ontological consequences of a transcendental argument whose premise is the conception of picturing developed in the subsequent aphorisms. In contrast to this reading, it is argued here that these initial aphorisms can be understood as an investigation of all normativity, making explicit the link between necessity and totality. Thus, the present paper points out to a new perspective of interpretation of the Tractatus and its links with the critical tradition. (shrink)

In this note, an error in the axiomatization of Ivlev’s modal system Sa+ which we inadvertedly reproduced in our paper “Finite non-deterministic semantics for some modal systems”, is fixed. Additionally, some axioms proposed in were slightly modified. All the technical results in which depend on the previous axiomatization were also fixed. Finally, the discussion about decidability of the level valuation semantics initiated in is taken up. The error in Ivlev’s axiomatization was originally pointed out by H. Omori and D. Skurt (...) in the paper “More modal semantics without possible worlds”, where an alternative solution was proposed. (shrink)

In The American Evasion of Philosophy Cornell West makes a comparison between the developments of European and classical American philosophies. Within West's analogy, however, two important American figures are missing: Josiah Royce and George H. Mead. In the context of this framework, this article ..

In this paper we explore a generalization of traditional abduction which can simultaneously perform two different tasks: given an unprovable sequent Γ ⊢ G, find a sentence H such that Γ, H ⊢ G is provable ; given a provable sequent Γ ⊢ G, find a sentence H such that Γ ⊢ H and the proof of Γ, H ⊢ G is simpler than the proof of Γ ⊢ G . We argue that the two tasks should not be distinguished, (...) and present a general procedure for finding suitable hypotheses or lemmas. When the original sequent is provable, the abduced formula can be seen as a cut formula with respect to Gentzen's sequent calculus, so the abduction method is cut-based. Our method is based on the tableau-like system KE and we argue for its advantages over existing abduction methods based on traditional Smullyan-style Tableaux. (shrink)

Open peer commentary on the article “The Autopoiesis of Social Systems and its Criticisms” by Hugo Cadenas & Marcelo Arnold. Upshot: I discuss the foundations of what I have said in my work as a biologist on autopoiesis, molecular autopoietic systems and social systems. I argue that the theme of sociology should be to understand how is it that we come out of the social manner of living that is the foundation of our origin as languaging and reflecting human (...) beings. (shrink)

This article gives a conceptual review of the e-value, ev(H|X) – the epistemic value of hypothesis H given observations X. This statistical significance measure was developed in order to allow logically coherent and consistent tests of hypotheses, including sharp or precise hypotheses, via the Full Bayesian Significance Test (FBST). Arguments of analysis allow a full characterization of this statistical test by its logical or compositional properties, showing a mutual complementarity between results of mathematical statistics and the logical desiderata lying at (...) the foundations of this theory. (shrink)

Open peer commentary on the article “The Autopoiesis of Social Systems and its Criticisms” by Hugo Cadenas & Marcelo Arnold. Upshot: Cadenas and Arnold contribute towards a better understanding of what is at stake in the long debate concerning the applicability of Maturana’s autopoiesis concept to social systems. However, their target article has two shortcomings: it does not provide a deeper understanding of the reasons why Luhmann’s adoption of the autopoiesis concept has proved to be sterile after decades of (...) debate; and their historic account does not integrate recent developments that need to be highlighted to improve interdisciplinary research. (shrink)

Physiological responses in futsal have not been studied together with temporal information about the players’ stay on the court. The aim of this study was to compare heart rate and blood lactate concentration responses between 1-H and 2-H considering the time of permanency of the players on the court at each substitution in a futsal match. HR was recorded during entire match and [La−] was analyzed after each substitution of seven players. %HRmean and [La−] mean did not differ between 1-H (...) and 2-H. Time in intensity zones of 50–100 %HRmax differed only in 60–70 %HRmax. HR coefficient of variation throughout the match was low and among the four outfield players on the court. Substitutions, time of permanence on the court, ratio between time in- and out-ratio on the court also were similar between 1-H and 2-H. Balancing the number of substitutions, and the In:Outcourt ratio of players in both halves of the match, playing lower time at 1-H, ~8 min for each participation in the match, made it possible to maintain intensity of the match in 2-H similar to the 1H. These results are a good guidance to coaches and for application in future studies. (shrink)

Review of Horgan, Sabatés, and Sosa's (eds.) *Qualia and Mental Causation in a Physical World: Themes from the Philosophy of Jaegwon Kim*.

In lieu of an abstract, here is a brief excerpt of the content:Husserlian Phenomenology and the Treatment of DepressionCommentary and CritiqueMarilyn Nissim-Sabat (bio)KeywordsHusserl, phenomenology, psychotherapy, drug therapyProfessor Hadreas begins his interesting and challenging essay by saying that, "This paper is concerned with a model of self-awareness which fits the testimony of subjects' reactions to selective serotonin reuptake inhibitors (SSRIs), of which fluoxetine (Prozac, Lilly, Indianapolis, IN) is probably the best known" (2010, 43). Several important features of Dr. Hadreas' approach can (...) be inferred from this statement. Most important, the verbatim testimony of subjects regarding their states of self-awareness is analyzed and interpreted for its compatibility with three philosophical models of self-awareness: Empiricism, rationalism, and Husserlian phenomenology. This is the methodology through which the author aims to show that one of the three models is more adequate than the others as a model of the self-awareness of the subjects, and that model is that of Husserlian phenomenology (hereinafter, phenomenology, with the understanding that only phenomenology according to Husserl is intended by both Dr. Hadreas and myself). In formulating this as the aim of his paper and his research, Dr. Hadreas has taken on an extremely difficult task.In general, attempts to show that any philosophical stance bears directly and immediately on the understanding of patients' symptoms, as well as on both theoretical and therapeutic work with people with mental disorders, is, owing to the ostensible gap in levels of conceptualization and systematicity, that is, the theory/praxis divide ostensibly separating the two realms, extraordinarily difficult. The task is rendered even more difficult in work like that of Prof. Hadreas,' in which, I believe, the researcher does not want to "apply" philosophy parasitically, as if research into psychiatric phenomena in relation to philosophy is just a matter of cannibalizing philosophy for self-justification, or vice versa; rather, Hadreas wants to preserve the integrity of both research into the phenomenology of psychiatric disorders and of [End Page 53] the philosophical perspective that may improve understanding of those disorders. In undertaking an effort along these lines, Hadreas breaks new ground.In particular, for this commentator, bringing Husserlian phenomenology to bear on these issues is particularly gratifying. Moreover, and most important, Hadreas bases his critique of classical empiricist and rationalist models of self-awareness on bringing to the fore Husserl's views on pre-reflective consciousness. This is extremely important for, as Dan Zahavi, noted Husserlian phenomenologist and philosopher of the phenomenology–psychiatry interface, points out, not only in the book cited by Hadreas but in a more recent article (Zahavi 2003), Husserl's notion of self-awareness has been critiqued by many who claim that he lacked a notion of pre-reflective consciousness. Indeed, Zahavi's (2003) work in this area quite effectively refutes these claims, and he does so by drawing on a large body of evidence from Husserl's posthumous writings. Thus, Hadreas is to be congratulated for using Husserl's long-neglected notion of pre-reflective consciousness as a means of approaching phenomenologically the testimony of patients who discussed changes in their self-awareness owing to their experiences with SSRI medications, chiefly fluoxetine. However, it is just because I share with Hadreas the conviction that Husserlian phenomenology is the best philosophical approach to understanding, and indeed, possibly improving the treatment of mental disorders, that I think it is vital to raise some questions regarding Hadreas' approach.My first critical comment is this: Hadreas' aim in writing his paper is unclear in a way that calls his project into question. In the conclusion of his paper, he indicates that his findings can enable psychiatrists to determine which patients are more likely to experience "SSRI cures." Given this, it would seem that his purpose in introducing Husserlian phenomenology is to facilitate this goal. Those subjects, he finds (based on his phenomenological analysis of the subjects' own testimony), who "have lived enough of life to have formed, for better or worse, an abiding empirical ego" are more likely to be "good responders" to SSRIs. It would seem, then, that this finding would aid psychiatrists in evaluating patients who have been treated, or who might be treated, with SSRIs. This, then, if correct, would be a considerable... (shrink)

“No lo hicieron extraterrestres; fueron personas como nosotros[1]” comentaban en el programa especial del InfoK[2] sobre el Holocausto. Kitson, Steward y Husbands lo justifican: una de las mayores dificultades del alumnado que aprende contenidos históricos es entender por qué las personas de un contexto hicieron lo que hicieron. Desde la enseñanza de la historia se ha reflexionado ampliamente sobre las causalidades relacionadas con ciertos hechos históricos, pero se ha dado menos peso a analizar las interpretaciones sobre la agencia histórica. En (...) este artículo nos proponemos repasar y concretar la conceptualización que desde la didáctica de las ciencias sociales se ha dado a la agencia histórica en la comprensión de las causalidades para entender las decisiones y las responsabilidades de las personas en contextos como el del Holocausto para entender que todas las personas somos agentes sociales, de cambio y continuidad y, por tanto, agentes históricas. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Mild Cognitive Impairment:What's in a Name?Steven R. Sabat (bio)Keywordslabeling, mild cognitive impairment, recall memory, selfhood, stereotype threatCorner and Bond (2006) raise a number of important conceptual issues related to the problems involved in defining mild cognitive impairment (MCI), differentiating it from normal aging, the definition of normal aging itself, and ethical issues surrounding the possible adverse effects of a diagnosis of MCI on the individuals thus described. It would (...) seem that portentous ramifications are involved and that clarifying the conceptual issues would be of great value, not only to researchers but also to the ever-growing population of elderly people. In what follows, I address some of these issues further.Problems of Definition and MeasurementOne of the problems that the authors discuss at the outset of their article concerns what methods are appropriate for detecting those with MCI: "Neuropsychological tests alone do not discriminate between normal aged-related memory loss and MCI or dementia and clinical judgment remains central to diagnosis" (Corner and Bond 2006, 5). Of course, to be able to discriminate between normal aged-related memory problems and MCI, we must first be able to define the former. What exactly is normal? As the authors correctly point out, the term has different meanings, one being normative (usual), another being nonpathologic. Is it normal (usual) for some sort of breakdown to occur in brain systems as a function of increased age? If so, is there a threshold age below which the very same physiologic breakdown is unusual? Would such a threshold age, if one existed, be the same for everyone, regardless of genotype and the cumulative interactive effects of nutrition, health, and stress-related factors over a period of decades? In effect, is some sort of memory impairment part of the natural (usual) process of aging for some people at particular ages rather than for others? And exactly what does it mean to be mildly impaired in the cognitive domain?Hogan and McKeith (2001) presented a working group's definition characterizing MCI such that people who complain about memory problems and who also provide objective evidence of such problems, yet who simultaneously display "normal general cognitive function and intact activities of daily living" (Hogan and McKeith 2001, 1131), should be identified and followed. Here again, however, we confront the problem of defining "normal general cognitive function" as well as "normal activities of daily living." Can one have normal general cognitive function without normal memory function? If so, what exactly constitutes [End Page 13] general cognitive function and on what conceptual or theoretical basis is such a definition valid? Furthermore, what sort of memory function are we talking about? Memory can be said to involve a number of stages: encoding, storage, and retrieval. Retrieval can be of the explicit type (conscious recall or recognition of specific information) with which people with Alzheimer's disease (AD) often reveal deficits or of the implicit type (a change in behavior as a result of previous experience of which the person may have no conscious recollection) as demonstrated in people with AD (Knopman and Nissen 1987). That is, people with AD can display deficits in explicit memory functions without similar deficits simultaneously in implicit memory functions.A partial answer to the question about memory loss in MCI may be found in the use of the Mini-Mental State Examination (MMSE; Folstein, Folstein, and McHugh 1975), originally intended to be used as a screening device, but employed more and more frequently as an outcome measure to assess cognitive decline as well as the efficacy of drug treatments. Although the examination purports to test orientation, registration, attention, calculation, recall, language (naming, repeating, reading, writing, three-stage command), and construction, a task analysis reveals that the test is not quite as "global" in the cognitive domain as it is purported to be. For example, ten of the maximum thirty points on the examination are earned for "orientation" in time and place. Yet, all of the questions in this section of the test require intact recall of the relevant information. For example, if a person is asked, "What day of the week is this?" and replies "I don't know," the... (shrink)

No cinema brasileiro recente, o diálogo entre o documentário e a ficção tem merecido destaque, com produções de baixo orçamento e ideias originais. É o caso de Santiago (João Moreira Salles, 2007) e Viajo Porque Preciso, Volto Porque Te Amo (Marcelo Gomes, Karim Aïnouz, 2009), filmes que trabalham esse diálogo de forma sutil e diegética, ressignificando imagens de um arquivo próprio, pessoal.

This paper describes the characteristics of people who return to learning to achieve at least a level 2 qualification, drawing on the 1958 National Child Development Cohort Study. Results show that adults who gained level 2 were more likely than those who did not to have been engaged in a range of learning activities at earlier ages, including learning during childhood, staying in education during adolescence and undertaking courses leading and not leading to qualifications during adulthood. The factor that has (...) the highest impact on progression by age 33 and by age 42 is early school attainment. This means that for individuals who do well at school there is a greater chance of achievement of qualifications during adulthood, even when this qualification is not achieved by age 23. We further find that socioeconomic constraints in adulthood may be less of a barrier to progression than is often believed. Taking together, these findings suggest that the main focus should be on paying particular attention to attitudinal barriers to learning, rather than just being concerned with removing economic and social constraints. (shrink)

This paper describes the characteristics of people who return to learning to achieve at least a level 2 qualification, drawing on the 1958 National Child Development Cohort Study. Results show that adults who gained level 2 were more likely than those who did not to have been engaged in a range of learning activities at earlier ages, including learning during childhood, staying in education during adolescence and undertaking courses leading and not leading to qualifications during adulthood. The factor that has (...) the highest impact on progression by age 33 and by age 42 is early school attainment. This means that for individuals who do well at school there is a greater chance of achievement of qualifications during adulthood, even when this qualification is not achieved by age 23. We further find that socioeconomic constraints in adulthood may be less of a barrier to progression than is often believed. Taking together, these findings suggest that the main focus should be on paying particular attention to attitudinal barriers to learning, rather than just being concerned with removing economic and social constraints. (shrink)

This paper reports results from a longitudinal study on the impact of the lockdown on daily self-reported life satisfaction levels during the first wave of the COVID-19 pandemic in Spain. A stable panel (N= 1,131) of adult subjects were surveyed during 84 consecutive days (March 29–June 20, 2020). They were asked to report daily life satisfaction and health state levels. Interestingly, daily life satisfaction increased during the lockdown. At the beginning of the experiment, subjects were asked to guess the end-week (...) of the lockdown, against a possible monetary reward for accurate forecasts. Subjects predicting a longer lockdown period reported a higher average level of daily life satisfaction. Females reported on average lower levels of daily life satisfaction, but exhibited a stronger tendency to report higher levels of life satisfaction, the longer their lockdown forecast. Individual heterogeneity in life satisfaction levels can be partly attributed to personality traits, with neuroticism having a negative effect, while extraversion and agreeableness having a positive effect on daily life satisfaction. (shrink)

We provide a model in which students must choose whether or not to cheat on a course exam. By assuming that the moral cost of acting dishonestly decreases as the number of other people who behave in the same way increases, our model explains one important channel by which unethical behavior of other individuals can influence observers’ behavior. Through the use of the Global Games approach of equilibrium selection, we build a framework that provides the micro-foundations of peer effects on (...) academic dishonesty and shows how better student technology of cheating and higher disutility of effort make the cheating equilibrium more likely to be selected. By extending the model, we find that the peer effect strength is not affected by the level of homogeneity of the cohort, but decreases in the size of the class. Our approach may be seen as an important step towards reduced-form models of peer effects on dishonest behavior. (shrink)

But never let it be doubted that depression, in its extreme form, is madness. (Styron, 1990, p. 62)There is nothing wrong with our biology or our intelligence; sometimes we are just stuck. (Cvetkov...

The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (that is, 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 aproaches 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 QLFI1o 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 QLFI1o with a standard equality predicate is also considered. (shrink)

From the early to mid-1970s, Michel Foucault posited that power consists of a relation rather than a substance and that this relation is comprised of unequal forces engaged in a warlike struggle against each other, resulting invariably in the domination of some forces over others. This understanding of power, which he retrospectively dubbed `Nietzsche's hypothesis' and `the model of war', underpinned his well-known analyses of disciplinary power. Yet, Foucault in his Collège de France course from the academic year 1975-6, `Society (...) Must Be Defended', suddenly began to call into question this understanding and his doubts about it did not abate well into the late 1970s. In this article, we suggest that his militant politics in the early 1970s sustained his adherence to the war model and that his more cautious political attitude later in the decade underpinned his suspicions about this model. Key Words: biopolitics • Henri de Boulainvilliers • Michel Foucault • Thomas Hobbes • militancy • F. W. Nietzsche • politics • power • race • war. (shrink)

In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap structure induces naturally a (...) non-deterministic matrix. The aim of this paper is to obtain a swap structures semantics for some Ivlev-like modal systems proposed in 2015 by M. Coniglio, L. Fariñas del Cerro and N. Peron. Completeness results will be stated by means of the notion of Lindenbaum–Tarski swap structures, which constitute a natural generalization to multialgebras of the concept of Lindenbaum–Tarski algebras. (shrink)

Multialgebras have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are given. Specifically, (...) a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multialgebras in a suitable way. A decomposition theorem similar to Birkhoff’s representation theorem is obtained for each class of swap structures. Moreover, when applied to the 3-valued algebraizable logics J3 and Ciore, their classes of algebraic models are retrieved, and the swap structures semantics become twist structures semantics. This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI, suggests that swap structures can be seen as non-deterministic twist structures. This opens new avenues for dealing with non-algebraizable logics by the more general methodology of multialgebraic semantics. (shrink)