We propose the notion of partial recursiveness and strong partial recursiveness for fuzzy maps. We prove that a fuzzy map f is partial recursive if and only if it is computable by a Turing fuzzy machine and that f is strongly partial recursive and deterministic if and only if it is computable via a deterministic Turing fuzzy machine. This gives a simple and manageable tool to investigate about the properties of the fuzzy machines.

We propose the notion of partial recursiveness and strong partial recursiveness for fuzzy maps. We prove that a fuzzy map f is partial recursive if and only if it is computable by a Turing fuzzy machine and that f is strongly partial recursive and deterministic if and only if it is computable via a deterministic Turing fuzzy machine. This gives a simple and manageable tool to investigate about the properties of the fuzzy machines.

Musonius problématise la politique stoïcienne de manière originale. Sous la direction du maître, l'individu assimile les principes de la vertu et renoue, dans l'ascèse, avec l'impulsion fondamentale de l'oikeiôsis. Le mariage, modèle de toute relation, fonde la petite comme la grande cité qu'il préfigure.

This note is motivated by Whitehead’s researches in inclusion-based point-free geometry as exposed in An Inquiry Concerning the Principles of Natural Knowledge and in The concept of Nature. More precisely, we observe that Whitehead’s definition of point, based on the notions of abstractive class and covering, is not adequate. Indeed, if we admit such a definition it is also questionable that a point exists. On the contrary our approach, in which the diameter is a further primitive, enables us to avoid (...) such a drawback. Moreover, since such a notion enables us to define a metric in the set of points, our proposal looks to be a good starting point for a foundation of the geometry metrical in nature (as proposed, for example, by L.M. Blumenthal). (shrink)

Whitehead, in his famous book "Process and Reality", proposed a definition of point assuming the concepts of “region” and “connection relation” as primitive. Several years after and independently Grzegorczyk, in a brief but very interesting paper proposed another definition of point in a system in which the inclusion relation and the relation of being separated were assumed as primitive. In this paper we compare their definitions and we show that, under rather natural assumptions, they coincide.

Contextualizar os processos oriundos de um período pandêmico é reconhecer que, para a nossa sociedade, o que vivemos com a pandemia da Covid-19 foi, de fato, inédito e histórico. Além de apresentar um cenário de acúmulo de emoções, mudança de rotina e sentimentos de medo e angústias, uma nova forma de interação social e trabalho precisou ser vivenciada. Assim, verificamos a importância de levantar reflexões acerca da maternidade vivenciada no contexto de isolamento social pelas mulheres que são mães discentes e (...) que precisaram conciliar suas atividades de cuidados diários com os estudos acadêmicos. É fundamental refletir sobre como funcionou o ambiente universitário no formato virtual e como tem sido o processo de retorno às aulas presenciais. Desse modo, neste artigo, o objetivo é apresentar reflexões acerca dos efeitos que o isolamento social no contexto da Covid-19 pode ter gerado à saúde mental de mulheres que são mães e universitárias. Tal texto compõe o levantamento bibliográfico do projeto de pesquisa “Atenção à saúde mental de mães universitárias no contexto da Covid-19”, realizado no curso de Psicologia da Universidade Federal do Pará. Acreditamos ser possível vivenciar no ambiente acadêmico aquilo que consideramos uma clínica da situação contemporânea e que colabora para a criação de espaços de acolhimento dentro da Universidade. No caso específico desta pesquisa, buscamos um acolhimento voltado para as mães universitárias que buscam permanecer nesses espaços, mesmo diante de tantos desafios. (shrink)

Effective domain theory is applied to fuzzy logic. The aim is to give suitable notions of semi-decidable and decidable L-subset and to investigate about the effectiveness of the fuzzy deduction apparatus.

ENTREVISTA COM PROFESSORAS(ES) DE FILOSOFIA DO ENSINO FUNDAMENTAL DO CEARÁCom: Jocilaine Moreira Batista do Vale, Mario Jonny de Castro Cunha, Syssa AdleyRodrigues Monteiro, Fabiana Martins TôrresPor: Antônio Alex Pereira de Sousa, Paulo Willame Araújo de Lim.

Whitehead, in his famous book Process and Reality, proposed a definition of point assuming the concepts of "region" and "connection relation" as primitive. Several years after and independently Grzegorczyk, in a brief but very interesting paper, proposed another definition of point in a system in which the inclusion relation and the relation of being separated were assumed as primitive. In this paper we compare their definitions and we show that, under rather natural assumptions, they coincide.

This paper attempts to answer, as well as give metaphysical specificity to, a question within the philosophy and theology of gender which strikes the heart of the Christian confession of the gospel. Against critics who say that the masculinity of Christ’s human nature renders him unable to save women as well as men, it draws on the recent literature on feminist metaphysics and analytic Christology to develop a model of the Incarnation able to avoid such criticisms.

RESUMO Hans Jonas na obra O Princípio Responsabilidade: ensaio de uma ética para a civilização tecnológica (2006 [1979]) apresenta o diagnóstico de uma civilização debilitada e perecível, constantemente ameaçada pelos poderes do homem tecnológico. De posse desta análise, constrói uma proposta no sentido de novas fundações para o edifício ético a partir de uma responsabilidade. Jonas constata o caráter antropocêntrico de uma ética que não abrangia as consequências dos impactos oriundas da ação humana sobre o homem e a vida na (...) biosfera. Em seu ideário filosófico sobre a civilização tecnológica, estende as atitudes dos homens para além do agir próximo, reconhecendo um direito próprio da natureza. A recolocação conceitual da natureza, dotada de finalidade própria, expressa que o poder tecnológico promove os desafios morais da contemporaneidade, visto que há a possibilidade certa (causas) e incerta (consequências) de os efeitos acumulativos desta mesma tecnologia pôr em perigo a continuidade futura da vida sobre o planeta. O imperativo da responsabilidade resulta do poder do homem contemporâneo sobre si e sobre o planeta. Caracteriza-se por ser uma responsabilidade perante a natureza e perante o próprio homem. A concepção de responsabilidade em Jonas está em conformidade com uma nova exigência axiológica. É uma responsabilidade que se firma com a preservação da vida em um futuro distante e com a continuidade da vida tal como conhecemos. O que justifica um pretenso biocentrismo no princípio responsabilidade é o fato de que a continuidade da existência gera uma obrigação com a vida, porque dizer sim a ela é ser. O grande objetivo de uma nova abordagem biocêntrica, como o imperativo de Jonas, é de manter a existência da humanidade futura, em um futuro que existam candidatos a um universo moral em um mundo concreto – o autêntico objetivo da responsabilidade.: Hans Jonas in the book The imperative of the responsibility: in search of an ethics for the technological age (2006 [1979]) presents a diagnosis of a civilization weakened and perish, constantly threatened by the powers of technological man. Armed with this analysis, a proposal to build new foundations for the building from an ethical responsibility. Jonas notes the character of an anthropocentric ethic that did not cover the consequences of impacts arising from human action on man and life in the biosphere. In his philosophical ideas on the technological civilization extends men's attitudes beyond the next act, recognizing an inherent right of nature. The replacement of the conceptual nature, with its own purpose, expressed that technological power promote the moral challenges of contemporary times, since there is a certain possibility (causes) and uncertain (consequences) of the cumulative effects of this same technology to jeopardize the continued future life on the planet. The imperative of responsibility results from the power of modern man about himself and the planet. It is characterized by being a responsibility to nature and to the man himself. The conception of responsibility in Jonas is in accordance with a new demand axiological. It is a responsibility that is established with the preservation of life in the distant future and the continuity of life as we know. What justifies a purported biocentrism the principle responsibility is the fact that the continued existence creates a bond with life, because she is saying yes to be. The ultimate goal of a new approach biocentric, as the imperative of Jonas, is to maintain the existence of mankind in the future, a future in which there are candidates for a moral universe in a concrete world - the real goal of the responsibility. Keywords : the imperative of responsibility, demand axiological, nature, biocentrism. (shrink)

Dissertação de Mestrado. VALE, Rose Silvania Figueiredo do. A ideia de Deus em Kant: da ilusão da razão pura ao postulado de agente moral. 2012. 132 folhas. Dissertação (Mestrado) – Pontifícia Universidade Católica de Minas Gerais, Programa de Pós-graduação em Ciências da Religião, Belo Horizonte. Palavras-chave : Ideias transcendentais. Ilusão. Razão. Moral. Deus. Homem. Key works : Transcendental ideas, Illusion, Reason, Moral, God, Man.

If X is set and L a lattice, then an L-subset or fuzzy subset of X is any map from X to L, [11]. In this paper we extend some notions of recursivity theory to fuzzy set theory, in particular we define and examine the concept of almost decidability for L-subsets. Moreover, we examine the relationship between imprecision and decidability. Namely, we prove that there exist infinitely indeterminate L-subsets with no more precise decidable versions and classical subsets whose unique shaded (...) decidable versions are the L-subsets almost-everywhere indeterminate. (shrink)

Let S be a set, P the class of all subsets of S and F the class of all fuzzy subsets of S. In this paper an “extension principle” for closure operators and, in particular, for deduction systems is proposed and examined. Namely we propose a way to extend any closure operator J defined in P into a fuzzy closure operator J* defined in F. This enables us to give the notion of canonical extension of a deduction system and to (...) give interesting examples of fuzzy logics. In particular, the canonical extension of the classical propositional calculus is defined and it is showed its connection with possibility and necessity measures. Also, the canonical extension of first order logic enables us to extend some basic notions of programming logic, namely to define the fuzzy Herbrand models of a fuzzy program. Finally, we show that the extension principle enables us to obtain fuzzy logics related to fuzzy subalgebra theory and graded consequence relation theory. (shrink)

ABSTRACT In this work the connections between the fuzzy closure operators and the graded consequence relations are examined Namely, as it is well known, in the crisp case there is a complete equivalence between the notion of closure operator and the one of consequence relation. We extend this result by proving that the graded consequence relations are related to a particular class of fuzzy closure operators, namely the class of fuzzy closure operators that can be obtained by a chain of (...) classical closure operators. (shrink)

In the framework of fuzzy logic a definition of vague object is proposed based on the notion of fuzzy equivalence. Indeed, while a crisp object is defined as a “concrete thing” together with an equivalence, I propose to define a vague object as a “concrete thing” together with a fuzzy equivalence.

We propose a first order modal logic, theQS4E-logic, obtained by adding to the well-known first order modal logicQS4 arigidity axiom schemas:A → □A, whereA denotes a basic formula. In this logic, thepossibility entails the possibility of extending a given classical first order model. This allows us to express some important concepts of classical model theory, such as existential completeness and the state of being infinitely generic, that are not expressibile in classical first order logic. Since they can be expressed in (...) -logic, we are also induced to compare the expressive powers ofQS4E and . Some questions concerning the power of rigidity axiom are also examined. (shrink)

We define the notion of “potential existence” by starting from the fact that in multi-valued logic the existential quantifier is interpreted by the least upper bound operator. Besides, we try to define in a general way how to pass from potential into actual existence.

De Cock and Kerre, in considering Poincaré paradox, observed that the intuitive notion of "approximate similarity" cannot be adequately represented by the fuzzy equivalence relations. In this note we argue that the deduction apparatus of fuzzy logic gives adequate tools with which to face the question. Indeed, a first-order theory is proposed whose fuzzy models are plausible candidates for the notion of approximate similarity. A connection between these structures and the point-free metric spaces is also established.

This volume addresses how spatialized identities, belongingness and hospitality are interrogated in British and Irish contemporary art (painting, installation, video, photography, new public art) at a time when economic and political crises tend to encourage individual or exclusive usages of space. It sketches a cartography of encounters encompassing the home, the neighbourhood, the village or city, and the nation. Artists interrogate how intimacy is both facilitated and threatened by spatial devices, how space fashions our perception of gender, social or ethnic (...) identity and activates power relations. They explore the need for a home or a homeland and the various forms exile or placelessness can take. They may also take part in the restoration of the Commons and the constitution of alternative communities. Whether the analyses focus on the private sphere (in urban, suburban or rural contexts), or on shared communal spaces, they ponder the mechanisms of inclusion and exclusion at work in human encounters and shed light on how artistic apparatuses make the tensions between openness to the other and rejection or withdrawal perceptible. The approach, borrowing from art history as well as anthropology lays emphasis on context, situationality and field work; it proposes to repoliticize relational art and concludes on the dialogical positionality which lies at the core of art. (shrink)

We face with the question of a suitable measure theory in Euclidean point-free geometry and we sketch out some possible solutions. The proposed measures, which are positive and invariant with respect to movements, are based on the notion of infinitesimal masses, i.e. masses whose associated supports form a sequence of finer and finer partitions.

We explore the notion of a measure in a mereological structure and we deal with the difficulties arising. We show that measure theory on connection spaces is closely related to measure theory on the class of ortholattices and we present an approach akin to Dempster’s and Shafer’s. Finally, the paper contains some suggestions for further research.

We show that it is possible to base fuzzy control on fuzzy logic programming. Indeed, we observe that the class of fuzzy Herbrand interpretations gives a semantics for fuzzy programs and we show that the fuzzy function associated with a fuzzy system of IF-THEN rules is the fuzzy Herbrand interpretation associated with a suitable fuzzy program.

We show that the existence of an infinite set can be reduced to the existence of finite sets “as big as we will”, provided that a multivalued extension of the relation of equipotence is admitted. In accordance, we modelize the notion of infinite set by a fuzzy subset representing the class of wide sets.

A metric approach to Popper's verisimilitude question is proposed which is related to point-free geometry. Indeed, we define the theory of approximate metric spaces whose primitive notions are regions, inclusion relation, minimum distance, and maximum distance between regions. Then, we show that the class of possible scientific theories has the structure of an approximate metric space. So, we can define the verisimilitude of a theory as a function of its (approximate) distance from the truth. This avoids some of the difficulties (...) arising from the known definitions of verisimilitude. (shrink)