With the aim of reflecting on a Pedagogy of the Franciscan Schools, the Franciscan Itinerary took place from February to December 2022, with the participation of collaborators and teachers from the schools maintained by the Charitable and Literary Society of St. Francis of Assisi - North Zone (SCALIFRA - ZN). The training consisted of webinars and evaluative activities, with themes extracted from works from the Franciscan writings. This experience report describes how the Itinerary was planned, as well as its main (...) results. (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)

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)

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)

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.

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)

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)

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)

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)

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.

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 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)

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)

Em tempos plurais hodiernos, reproduz-se um contexto em que coexistem diferentes concepções de verdade, de justiça e de vida digna. Versões de mundo e cosmovisões completamente díspares são paulatinamente legitimadas no grande processo globalizante de inscrição do outro, o que demanda um tipo de racionalidade retórica e argumentativa, única capaz de adaptar-se aos diversos topoi de um mundo cada vez mais multicultural. A proposta é acompanhar esse debate e concluir que a defesa do respeito aos direitos humanos só é possível (...) descomprometendo-se com pressupostos metafísicos excludentes, pseudolaicos, incapazes de gerar respeito mútuo e solidariedade entre todos os interlocutores. (shrink)

Las diferencias entre Francisco Suárez y Juan de Mariana son notables, empezando por sus caracteres personales. En particular, en el tratamiento de una cuestión de tanta importancia en la teoría política de la época como el tema del derecho de resistencia y el tiranicidio, y pese a ciertos rasgos similares que los enemigos de los jesuitas se encar-garán de acentuar, un somero estudio puede revelar una serie de diferencias. No obstante, merece la pena examinar dichas diferencias tomando como referencia una (...) cuestión práctica que podría arrojar luz sobre el grado de profundidad de esas divergencias. En efecto, pese a las evidencias que demuestran que Mariana y Suárez se conocían, y a la dificultad de sostener la idea de que el segundo desconociese la obra de Mariana, el granadino no cita en ningún momento al talaverano al tratar el tema que concita nuestro interés. Más allá de la presencia evidente de cuestiones de estrategia política en dicho silencio, no cabe duda de que Suárez debía entender también que su teoría no coincidía con la de Marian. (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)

The fact that monstrous births were not represented in independent learned publications of the eighteenth century, except for the case of hermaphrodites, does not mean that the interest in them had disappeared or that they were no more considered proper objects of inquiry. This paper focuses on the medical understanding of monstrosity at the Royal Society of London. I point to the use of monstrous births in strengthening the authority of medical practitioners and lecturers. I also show some of their (...) uses in providing new questions for the scenes of medical inquiry of the period and as crucial evidence in the understanding of regular physiological phenomena. I discuss some of the reasons why monstrous formations continued to defy an 'Enlightenment' approach to nature based on the search for order and regularity. (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)

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)

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)

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)

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.

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)

Jose Marti contributed greatly to Cuba's struggle for independence from Spain with words as well as revolutionary action. Although he died before the formation of an independent republic, he has since been hailed as a heroic martyr inspiring Cuban republican traditions.

Neste artigo pretendemos investigar a origem e o alcance do conceito de Economia Política da Natureza, quando aplicado à luta indígena pela demarcação de seus territórios, em confronto com a dinâmica dos interesses da mercantilização capitalista da terra e dos chamados 'recursos naturais', através da análise dos fundamentos da economia política, com ênfase na sua conceitualização do trabalho. A seguir faremos um levantamento da leitura histórico-materialista destes fenômenos, para finalmente comparar estas teorias com a perspectiva antropológica do “valor” do trabalho (...) e da divisão social das riquezas em sociedades não articuladas pelo mercado auto-regulado. (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)

In her well-known book, Rasiowa states without proof that in implicative algebras there is a one-to-one correspondence between kernels of epimorphisms and the so-called special implicative filters, and that in the logic whose algebraic counterpart is the class of implicative algebras the deductive filters coincide with the special implicative filters. We show that neither claim is true, and how to repair the situation by redefining some of the notions involved. We answer other questions concerning special implicative filters, taking the theory (...) of algebraizable logics of Blok and Pigozzi as a framework to approach the question in a systematic way. (shrink)