This paper contains a joint study of two sentential logics that combine a many-valued character, namely tetravalence, with a modal character; one of them is normal and the other one quasinormal. The method is to study their algebraic counterparts and their abstract models with the tools of Abstract Algebraic Logic, and particularly with those of Brown and Suszko's theory of abstract logics as recently developed by Font and Jansana in their "A General Algebraic Semantics for Sentential Logics". The logics studied (...) here arise from the algebraic and lattice-theoretical properties we review of Tetravalent Modal Algebras, a class of algebras studied mainly by Loureiro, and also by Figallo, Landini and Ziliani, at the suggestion of the late Antonio Monteiro. (shrink)

In this paper two deductive systems associated with relevance logic are studied from an algebraic point of view. One is defined by the familiar, Hilbert-style, formalization of R; the other one is a weak version of it, called WR, which appears as the semantic entailment of the Meyer-Routley-Fine semantics, and which has already been suggested by Wójcicki for other reasons. This weaker consequence is first defined indirectly, using R, but we prove that the first one turns out to be an (...) axiomatic extension of WR. Moreover we provide WR with a natural Gentzen calculus. It is proved that both deductive systems have the same associated class of algebras but different classes of models on these algebras. The notion of model used here is an abstract logic, that is, a closure operator on an abstract algebra; the abstract logics obtained in the case of WR are also the models, in a natural sense, of the given Gentzen calculus. (shrink)

In this paper we study the relations between the fragment L of classical logic having just conjunction and disjunction and the variety D of distributive lattices, within the context of Algebraic Logic. We prove that these relations cannot be fully expressed either with the tools of Blok and Pigozzi's theory of algebraizable logics or with the use of reduced matrices for L. However, these relations can be naturally formulated when we introduce a new notion of model of a sequent calculus. (...) When applied to a certain natural calculus for L, the resulting models are equivalent to a class of abstract logics (in the sense of Brown and Suszko) which we call distributive. Among other results, we prove that D is exactly the class of the algebraic reducts of the reduced models of L, that there is an embedding of the theories of L into the theories of the equational consequence (in the sense of Blok and Pigozzi) relative to D, and that for any algebra A of type (2,2) there is an isomorphism between the D-congruences of A and the models of L over A. In the second part of this paper (which will be published separately) we will also apply some results to give proofs with a logical flavour for several new or well-known lattice-theoretical properties. (shrink)

ukasiewicz''s four-valued modal logic is surveyed and analyzed, together with ukasiewicz''s motivations to develop it. A faithful interpretation of it in classical (non-modal) two-valued logic is presented, and some consequences are drawn concerning its classification and its algebraic behaviour. Some counter-intuitive aspects of this logic are discussed in the light of the presented results, ukasiewicz''s own texts, and related literature.

In this paper we study the relations between the fragment L of classical logic having just conjunction and disjunction and the variety D of distributive lattices, within the context of Algebraic Logic. We prove that these relations cannot be fully expressed either with the tools of Blok and Pigozzi's theory of algebraizable logics or with the use of reduced matrices for L. However, these relations can be naturally formulated when we introduce a new notion of model of a sequent calculus. (...) When applied to a certain natural calculus for L, the resulting models are equivalent to a class of abstract logics (in the sense of Brown and Suszko) which we call distributive. Among other results, we prove that D is exactly the class of the algebraic reducts of the reduced models of L, that there is an embedding of the theories of L into the theories of the equational consequence (in the sense of Blok and Pigozzi) relative to D, and that for any algebra A of type (2,2) there is an isomorphism between the D-congruences of A and the models of L over A. In the second part of this paper (which will be published separately) we will also apply some results to give proofs with a logical flavour for several new or well-known lattice-theoretical properties. (shrink)

The object of this paper is to make a study of four systems of modal logic (S4, S5, and their intuitionistic analogues IM4 and IM5) with the techniques of the theory of abstract logics set up by Suszko, Bloom, Brown, Verdú and others. The abstract concepts corresponding to such systems are defined as generalizations of the logics naturally associated to their algebraic models (topological Boolean or Heyting algebras, general or semisimple). By considering new suitably defined connectives and by distinguishing between (...) having the rule of necessitation only for theorems or as a full inference rule (which amounts to dealing with all filters or with open filters of the algebras) we are able to reduce the study of a modal (abstract) logic L to that of two nonmodal logics L - and L + associated with L. We find that L is "of IM4 type" if and only if L - and L + are both intuitionistic and have the same theorems, and logics of type S4, IM5 or S5 are obtained from those of type IM4 simply by making classical L -, L + or both. We compare this situation with that found in recent approaches to intuitionistic modal logic using birelational models or using higher-level sequent-systems. The treatment of modal systems with abstract logics is rather new, and in our way to it we find several general constructions and results which can also be applied to other modal systems weaker than those we study in detail. (shrink)

SummaryIn this synthetic exposition, devoted to the relations which exist between psľchic functions and anatomic structures, Dr Pontes first insists on the difficulties of the subject and of its scientific analysis. Soma, Psyche, and social Milieu form a kind of continuum which is artificiallľ dissociated by our one‐sided approaches. Experimentation cannot be fullľ practised on man, nor can its results on animal be extended to man without serious risks of error. Similar limitations appear if, resorting to the pathological method, we (...) try to apply to the normal conclusions arrived at through the Study of the abnormal. Special reference is made here to psychosurgery, a topic quite familiar to Dr Fontes, who is Dr Egas Moniz’ countryman.The author then summarises our present knowledge concerning the structure, connections and functions of encephalic centers, especially; the thalamus, the hypothalamus and the frontal lobes.Finally, he subscribes, though not without serious reservations, to the hierarchical conception of the Nervous Sľstem as well as of the human mind, first suggested by Jouffroy, after him developed by Baillarger, Janet, Wallon in France, by Hughlings Jackson in Great Britain, and recentlľ revived in Europe by von Mona‐kow and Mourgue, Eľ, and Delaľ. This view enables one to consider nervous or psľchic illnesses as various dissolutions, resulting on the one hand from the suppression of higher centers or powers, on the other hand from the liberation of lower ones. It agrees rather well with the informations gathered by the anatomy and the physiology of the nervous sľstem, and with the conclusions suggested by psychosurgical opérations. To the thalamus and hypothalamus correspond the lower and older manifestations of mind: emotion and instinct, to the cortex the higher and more recent adaptive and intellectual processes. The hypothalamus plays a most important role in the nervous machinery as a regulator of vegetative and instinctive life, of wake and sleep, of consciousness, and of the basic biological rhythms. At the cortical level the frontal lobe appears as the structural basis for such psychical functions as Ego‐control, Will, Personality, and succèssfull action on the milieu. (shrink)

This is a contribution to the discussion on the role of truth degrees in manyvalued logics from the perspective of abstract algebraic logic. It starts with some thoughts on the so-called Suszko’s Thesis (that every logic is two-valued) and on the conception of semantics that underlies it, which includes the truth-preserving notion of consequence. The alternative usage of truth values in order to define logics that preserve degrees of truth is presented and discussed. Some recent works studying these in the (...) particular cases of Łukasiewicz’s many-valued logics and of logics associated with varieties of residuated lattices are also presented. Finally the extension of this paradigm to other, more general situations is discussed, highlighting the need for philosophical or applied motivations in the selection of the truth degrees, due both to the interpretation of the idea of truth degree and to some mathematical difficulties. (shrink)

In our previous paper Algebraic Logic for Classical Conjunction and Disjunction we studied some relations between the fragmentL of classical logic having just conjunction and disjunction and the varietyD of distributive lattices, within the context of Algebraic Logic. The central tool in that study was a class of closure operators which we calleddistributive, and one of its main results was that for any algebraA of type (2,2) there is an isomorphism between the lattices of allD-congruences ofA and of all distributive (...) closure operators overA. In the present paper we study the lattice structure of this last set, give a description of its finite and infinite operations, and obtain a topological representation. We also apply the mentioned isomorphism and other results to obtain proofs with a logical flavour for several new or well-known lattice-theoretical properties, like Hashimoto's characterization of distributive lattices, and Priestley's topological representation of the congruence lattice of a bounded distributive lattice. (shrink)

A filter of a sentential logic ? is Leibniz when it is the smallest one among all the ?-filters on the same algebra having the same Leibniz congruence. This paper studies these filters and the sentential logic ?+ defined by the class of all ?-matrices whose filter is Leibniz, which is called the strong version of ?, in the context of protoalgebraic logics with theorems. Topics studied include an enhanced Correspondence Theorem, characterizations of the weak algebraizability of ?+ and of (...) the explicit definability of Leibniz filters, and several theorems of transfer of metalogical properties from ? to ?+. For finitely equivalential logics stronger results are obtained. Besides the general theory, the paper examines the examples of modal logics, quantum logics and Łukasiewicz's finitely-valued logics. One finds that in some cases the existence of a weak and a strong version of a logic corresponds to well-known situations in the literature, such as the local and the global consequences for normal modal logics; while in others these constructions give an independent interest to the study of other lesser-known logics, such as the lattice-based many-valued logics. (shrink)

Traditional disciplinary guidelines are inadequate to address some of the ethical dilemmas that emerge when conducting research on violence against women and girls. This article is organized according to the ethical principles of respect for persons, privacy and confidentiality, justice, beneficence, and nonmaleficence. In the article, I describe dilemmas involved in cross-cultural research, research on children, informed consent, voluntariness, coercion, deception, safety, mandated reporting, and dissemination. In the article, I include examples from qualitative and quantitative studies in many nations. I (...) also offer suggestions for researchers and institutional review boards. (shrink)

Łukasiewicz’s infinite-valued logic is commonly defined as the set of formulas that take the value 1 under all evaluations in the Łukasiewicz algebra on the unit real interval. In the literature a deductive system axiomatized in a Hilbert style was associated to it, and was later shown to be semantically defined from Łukasiewicz algebra by using a “truth-preserving” scheme. This deductive system is algebraizable, non-selfextensional and does not satisfy the deduction theorem. In addition, there exists no Gentzen calculus fully adequate (...) for it. Another presentation of the same deductive system can be obtained from a substructural Gentzen calculus. In this paper we use the framework of abstract algebraic logic to study a different deductive system which uses the aforementioned algebra under a scheme of “preservation of degrees of truth”. We characterize the resulting deductive system in a natural way by using the lattice filters of Wajsberg algebras, and also by using a structural Gentzen calculus, which is shown to be fully adequate for it. This logic is an interesting example for the general theory: it is selfextensional, non-protoalgebraic, and satisfies a “graded” deduction theorem. Moreover, the Gentzen system is algebraizable. The first deductive system mentioned turns out to be the extension of the second by the rule of Modus Ponens. (shrink)

This paper is concerned with the particular problems raised by observations of phenomena outside the common course of nature for their validation as knowledge. It examines to what extent the content of the reports and, in particular, their lack of intrinsic plausibility affected the methods used in their authentication and the assessment of testimony at the Royal Society in the first half of the eighteenth century. I show that literary strategies were usually necessary but not sufficient for the validation of (...) these kinds of observations. Next, I discuss why visual representations were especially useful in establishing the singularity of the observations, but I point out that their high costs and other restrictions meant that they were not so widespread. In contrast I show that, for a long period of time, testimony was used in the majority of the reports as the true stamp of authenticity. I note, however, that the Royal Society accepted reports by authors of varied social status, level of education and occupation, and I discuss some of the factors responsible for the complexity of the handling of testimony at the Society. I argue against Shapin that in the case of reports of extraordinary phenomena, the competence of the reporter and witnesses was often more important than their social status. The increasing role of expertise in the assessment of observations at the Society become especially apparent by the middle of the eighteenth century.Author Keywords: Authentication; Competence; Monstrous births; Singular; Testimony; Royal Society of London. (shrink)

In this paper we consider the structure of the class FGModS of full generalized models of a deductive system S from a universal-algebraic point of view, and the structure of the set of all the full generalized models of S on a fixed algebra A from the lattice-theoretical point of view; this set is represented by the lattice FACSs A of all algebraic closed-set systems C on A such that (A, C) ε FGModS. We relate some properties of these structures (...) with tipically logical properties of the sentential logic S. The main algebraic properties we consider are the closure of FGModS under substructures and under reduced products, and the property that for any A the lattice FACSs A is a complete sublattice of the lattice of all algebraic closed-set systems over A. The logical properties are the existence of a fully adequate Gentzen system for S, the Local Deduction Theorem and the Deduction Theorem for S. Some of the results are established for arbitrary deductive systems, while some are found to hold only for deductive systems in more restricted classes like the protoalgebraic or the weakly algebraizable ones. The paper ends with a section on examples and counterexamples. (shrink)

Traditional disciplinary guidelines are inadequate to address some of the ethical dilemmas that emerge when conducting research on violence against women and girls. This article is organized according to the ethical principles of respect for persons, privacy and confidentiality, justice, beneficence, and nonmaleficence. In the article, I describe dilemmas involved in cross-cultural research, research on children, informed consent, voluntariness, coercion, deception, safety, mandated reporting, and dissemination. In the article, I include examples from qualitative and quantitative studies in many nations. I (...) also offer suggestions for researchers and institutional review boards. (shrink)

This paper reviews the impact of Rasiowa's well-known book on the evolution of algebraic logic during the last thirty or forty years. It starts with some comments on the importance and influence of this book, highlighting some of the reasons for this influence, and some of its key points, mathematically speaking, concerning the general theory of algebraic logic, a theory nowadays called Abstract Algebraic Logic. Then, a consideration of the diverse ways in which these key points can be generalized allows (...) us to survey some issues in the development of the field in the last twenty to thirty years. The last part of the paper reviews some recent lines of research that in some way transcend Rasiowa's approach. I hope in this way to give the reader a general view of Rasiowa's key position in the evolution of Algebraic Logic during the twentieth century. (shrink)

Axel Honneth desenvolve o conceito de reconhecimento, encarado como uma necessidade fundamental do ser-humano, de forma a constituir-se no núcleo de uma teoria da justiça que procura especificar as condições intersubjetivas de autorrealização individual. Apresenta-se uma teoria da justiça assente na reconstrução das práticas e condições de reconhecimento já institucionalizadas, analisando as instituições sociais em um sentido amplo. Pretende-se aproximar a concepção normativa da justiça da análise sociológica das sociedades modernas, através da reconstrução normativa e ao colocar a ênfase na (...) liberdade social, baseada na dimensão intersubjetiva das instituições de reconhecimento. A liberdade social prevê o acesso às instituições de reconhecimento. Um dos objetivos é esboçar os problemas desse avanço interpretativo da teoria crítica do reconhecimento, pelo que iremos convocar a teoria da luta pelo reconhecimento de Honneth, incluir a sua reactualização mais recente do Direito de Hegel e explorar a sua proposta normativa para as condições de uma vida ética. (shrink)

A definition and some inaccurate cross-references in the paper A Survey of Abstract Algebraic Logic, which might confuse some readers, are clarified and corrected; a short discussion of the main one is included. We also update a dozen of bibliographic references.

The “representation problem” in abstract algebraic logic is that of finding necessary and sufficient conditions for a structure, on a well defined abstract framework, to have the following property: that for every structural closure operator on it, every structural embedding of the expanded lattice of its closed sets into that of the closed sets of another structural closure operator on another similar structure is induced by a structural transformer between the base structures. This question arose from Blok and Jónsson abstract (...) analysis of one of Blok and Pigozzis’s characterizations of algebraizable logics. The problem, which was later on reformulated independently by Gil-Férez and by Galatos and Tsinakis, was solved by Galatos and Tsinakis in the more abstract framework of the category of modules over a complete residuated lattice, and by Galatos and Gil-Férez in the even more abstract setting of modules over a quantaloid. We solve the representation problem in Blok and Jónsson’s original context of M-sets, where M is a monoid, and characterise the corresponding M-sets both in categorical terms and in terms of their inner structure, using the notions of a graded M-set and a generalized variable introduced by Gil-Férez. (shrink)

A pair of deductive systems (S,S’) is Leibniz-linked when S’ is an extension of S and on every algebra there is a map sending each filter of S to a filter of S’ with the same Leibniz congruence. We study this generalization to arbitrary deductive systems of the notion of the strong version of a protoalgebraic deductive system, studied in earlier papers, and of some results recently found for particular non-protoalgebraic deductive systems. The necessary examples and counterexamples found in the (...) literature are described. (shrink)

Este artigo tem por objetivo ampliar a compreensão daquilo que Michel Foucault definiu como a “função-psi” e suas influências na instauração do poder. Esse poder se refere ao desenvolvimento de um saber sobre o comportamento humano, cujo conhecimento foi e vem sendo utilizado pelo que Foucault chamou de “normalização” da sociedade. É também objeto deste trabalho buscar o entendimento do “poder disciplinar”, surgido a partir dos estudos do comportamento humano pela Psicologia, para entender como esses estudos promoveram a patologização das (...) experiências individuais. Assim, nasce o que Foucault denominou biopoder: um poder concentrado na figura do Estado e voltado para o gerenciamento da vida e do corpo da população. Um poder disciplinador e normalizador, exercido por meio de tecnologias políticas destinadas a inserir os indivíduos no aparelho de produção. (shrink)

Esta proposta de comunicação visa apresentar brevemente as relações institucionais entre as comunidades indígenas que ocupam o território nacional e as figuras jurídicas que historicamente lhes foram aplicadas pelos poderes atribuídos ao Direito Positivo, vigente em cada um dos momentos mais relevantes dessa história. Faremos essa genealogia da figura do índio no ordenamento jurídico nacional tendocomo base, sobretudo, os trabalhos de Manuela Carneiro da Cunha (1987, 1992, 2012) Perrone-Moisés (1992), José Afonso da Silva (2016) e Carlos Marés (2010). No entanto, (...) pretendemos centrar nossa análise no contexto contemporâneo. (shrink)

Jürgen Habermas é um pensador moderno que nos apresenta uma racionalidade capaz de criar espaços de liberdade que correspondem aos ideais de emancipação social que sempre cruzaram o horizonte da modernidade ocidental. Através de vários estudos deste autor, incluindo contributos críticos à sua teoria, iremos desenvolver a sua reflexão epistemológica e a sua relevante contribuição para a renovação da teoria crítica alemã. Começaremos por apresentar a sua crítica ao positivismo, para depois convocar a disputa que protagonizou com Gadamer em torno (...) da hermenêutica. Habermas adota a hermenêutica, ainda que com algumas críticas, como facilitadora de autorreflexão que permita revelar às ciências sociais os erros quer da ciência social objetivista, quer da análise vulgar da linguagem. Segue-se a perspetiva deste pensador acerca dos interesses que orientam o conhecimento e, por fim, empreenderemos uma abordagem à teoria da racionalidade comunicativa, que afirma o otimismo universalista de Habermas, assente num saudável pluralismo que permite o consenso humano. (shrink)

Despite decades of study, mimicry continues to inspire and challenge evolutionary biologists. This essay aims to assess recent conceptual frameworks for the study of mimicry and to examine the links between mimicry and related phenomena. Mimicry is defined here as similarity in appearance and/or behavior between a mimic and a model that provides a selective advantage to the mimic because it affects the behavior of a receiver causing it to misidentify the mimic, and that evolved (or is maintained by selection) (...) because of those effects. Mimics copy cues or signals that are already in use as part of a stable communication system, but offer misleading information to receivers. Mimicry overlaps, both conceptually and evolutionarily, with camouflage and perceptual exploitation but the overlap is only partial, which may create some confusion. Certain types of camouflage (e.g. masquerade) conform to the definition of mimicry, while others (e.g. background matching) are not considered mimicry because they prevent detection rather than recognition of the camouflaged animal. Mimicry, on the other hand, works by exploiting peculiarities of the receiver at higher stages of sensory processing involving recognition and classification of stimuli. Perceptual exploitation models of trait evolution are also closely related to mimicry, and sensory traps in particular may act as a precursor for true mimicry to evolve. The common thread through these diverse phenomena is deception of a receiver by a mimic. Thus receiver deception (i.e. perceptual error) emerges as a key characteristic of mimicry shared with some types of camouflage and perceptual exploitation. (shrink)

ABSTRACT In this paper we introduce a set of six logical values, arising in the application of three-valued logics to time intervals, find its algebraic structure, and use it to define a six-valued logic. We then prove, by using algebraic properties of the class of De Morgan algebras, that this semantically defined logic can be axiomatized as Belnap's ?useful? four-valued logic. Other directions of research suggested by the construction of this set of six logical values are described.

No hay nada más evocador que un cuerpo filmado: los rasgos y la piel, pero también los gestos y movimientos. Y es uno de los privilegios del cine poder llevar a cabo esa misión como ningún otro arte pudo hacerlo antes. Porque a través de las películas vemos la labor del tiempo, su transcurso, su implacable trabajo de demolición. El cine contemporáneo se nos aparece ahora como el laboratorio ideal para la investigación sobre el cuerpo, sobre los contactos que establece (...) con otros cuerpos, sobre sus enfrentamientos, sobre su soledad y su decadencia. Pero también sobre su situación en los nuevos paisajes postindustriales, sobre su relación con la tecnología, sobre las fusiones que se ve obligado a realizar para sobrevivir. No estamos hablando solamente, pues, de relaciones humanas, o de desplazamientos en el espacio, o de las distintas maneras de sonreír y de mover las manos. También hablamos de las nuevas carnes metálicas, de otros cuerpos que hasta ahora nos eran desconocidos, por distancia geográfica o limitaciones de la imaginación. (shrink)