This paper discusses an earlier emendation to fr. 54 GRF Funaioli from Varro's De bibliothecis and argues that, while the text et citro refers to cedar oil, it should not be emended to et cedro. A comparison with a passage from Pliny the Elder (HN 13.86) is used to support the view presented in the article.

This is the second of a series of papers that investigate fragments of quasi-Nelson logic (QNL) from an algebraic logic standpoint. QNL, recently introduced as a common generalization of intuitionistic and Nelson’s constructive logic with strong negation, is the axiomatic extension of the substructural logic |$FL_{ew}$| (full Lambek calculus with exchange and weakening) by the Nelson axiom. The algebraic counterpart of QNL (quasi-Nelson algebras) is a class of commutative integral residuated lattices (a.k.a. |$FL_{ew}$|-algebras) that includes both Heyting and Nelson algebras (...) and can be characterized algebraically in several alternative ways. The present paper focuses on the algebraic counterpart (a class we dub quasi-Nelson implication algebras, QNI-algebras) of the implication–negation fragment of QNL, corresponding to the connectives that witness the algebraizability of QNL. We recall the main known results on QNI-algebras and establish a number of new ones. Among these, we show that QNI-algebras form a congruence-distributive variety (Cor. 3.15) that enjoys equationally definable principal congruences and the strong congruence extension property (Prop. 3.16); we also characterize the subdirectly irreducible QNI-algebras in terms of the underlying poset structure (Thm. 4.23). Most of these results are obtained thanks to twist representations for QNI-algebras, which generalize the known ones for Nelson and quasi-Nelson algebras; we further introduce a Hilbert-style calculus that is algebraizable and has the variety of QNI-algebras as its equivalent algebraic semantics. (shrink)

We look at extensions (i.e., stronger logics in the same language) of the Belnap–Dunn four-valued logic. We prove the existence of a countable chain of logics that extend the Belnap–Dunn and do not coincide with any of the known extensions (Kleene’s logics, Priest’s logic of paradox). We characterise the reduced algebraic models of these new logics and prove a completeness result for the first and last element of the chain stating that both logics are determined by a single finite logical (...) matrix. We show that the last logic of the chain is not finitely axiomatisable. (shrink)

An erudite and witty collection of Umberto Eco's essays on mass culture from the 1960s through the 1980s, including major pieces which have not been translated into English before. The discussion is framed by opposing characterizations of current intellectuals as apocalyptic and opposed to all mass culture, or as integrated intellectuals, so much a part of mass culture as to be unaware of serving it. Organized in four main parts, "Mass Culture: Apocalypse Postponed," "Mass Media and the Limits of (...) Communication," "The Rise and Fall of Counter-Cultures," and "In Search of Italian Genius," Eco looks at a variety of topics and cultural productions, including the world of Charlie Brown, distinctions between highbrow and lowbrow, the future of literacy, Chinese comic strips, whether countercultures exist, Fellini's Ginger and Fred, and the Italian genius industry. (shrink)

In preference aggregation a set of individuals express preferences over a set of alternatives, and these preferences have to be aggregated into a collective preference. When preferences are represented as orders, aggregation procedures are called social welfare functions. Classical results in social choice theory state that it is impossible to aggregate the preferences of a set of individuals under different natural sets of axiomatic conditions. We define a first-order language for social welfare functions and we give a complete axiomatisation for (...) this class, without having the number of individuals or alternatives specified in the language. We are able to express classical axiomatic requirements in our first-order language, giving formal axioms for three classical theorems of preference aggregation by Arrow, by Sen, and by Kirman and Sondermann. We explore to what extent such theorems can be formally derived from our axiomatisations, obtaining positive results for Sen’s Theorem and the Kirman-Sondermann Theorem. For the case of Arrow’s Theorem, which does not apply in the case of infinite societies, we have to resort to fixing the number of individuals with an additional axiom. In the long run, we hope that our approach to formalisation can serve as the basis for a fully automated proof of classical and new theorems in social choice theory. (shrink)

Umberto Eco -- Stephen Jay Gould -- Jean-Claude Carrière -- Jean Delumeau.

A recent paper by Jakl, Jung and Pultr succeeded for the first time in establishing a very natural link between bilattice logic and the duality theory of d-frames and bitopological spaces. In this paper we further exploit, extend and investigate this link from an algebraic and a logical point of view. In particular, we introduce classes of algebras that extend bilattices, d-frames and N4-lattices to a setting in which the negation is not necessarily involutive, and we study corresponding logics. We (...) provide product representation theorems for these algebras, as well as completeness, algebraizability results for the corresponding logics. (shrink)

We introduce a modal expansion of paraconsistent Nelson logic that is also as a generalization of the Belnapian modal logic recently introduced by Odintsov and Wansing. We prove algebraic completeness theorems for both logics, defining and axiomatizing the corresponding algebraic semantics. We provide a representation for these algebras in terms of twiststructures, generalizing a known result on the representation of the algebraic counterpart of paraconsistent Nelson logic.

The world’s press may have lost interest in the ongoing enquiry into the deep‐rooted corruption in Italian business. But what exactly was going on, and what can be done to improve matters? The writers of this authoritative study are Faculty members of the prestigious Italian Business School, SDA Bocconi, Via F. Bocconi 8, 8‐20136 Milano, where Umberto Lago lectures in Strategy and Roberto Castoldi in Accounting. They both lecture on the Business Policy course at Bocconi University.

The world’s press may have lost interest in the ongoing enquiry into the deep‐rooted corruption in Italian business. But what exactly was going on, and what can be done to improve matters? The writers of this authoritative study are Faculty members of the prestigious Italian Business School, SDA Bocconi, Via F. Bocconi 8, 8‐20136 Milano, where Umberto Lago lectures in Strategy and Roberto Castoldi in Accounting. They both lecture on the Business Policy course at Bocconi University.

Neutrosophy has been introduced some years ago by Florentin Smarandache as a new branch of philosophy dealing with “the origin, nature and scope of neutralities, as well as their interactions with different ideational spectra”. A variety of new theories have been developed on the basic principles of neutrosophy: among them is neutrosophic logics, a family of many-valued systems that can be regarded as a generalization of fuzzy logics. In this paper we present a critical introduction to neutrosophic logics, focusing on (...) the problem of defining suitable neutrosophic propositional connectives and discussing the relationship between neutrosophic logics and other well-known frameworks for reasoning with uncertainty and vagueness, such as (intuitionistic and interval-valued) fuzzy systems and Belnap’s logic. (shrink)

L'étude du cycle carnavalesque de trois villages alpins, situés dans une enclave slave en Italie du nord (vallée de Resia), permet de suivre les étapes traversées par l'adolescente à l'intérieur de la fête, moment clef de son identification sexuelle et sociale. Les trois exemples choisis ont mis en lumière des stratégies différentes qui utilisent un couple de masques bäbac/maškira, couple qui correspond à l'opposition structurelle entre le modèle de la fille « sauvage » et celui de la demoiselle policée. Si (...) pour devenir une « jeune fille à marier », on doit passer par ces figures, l'identité ainsi acquise n'est pas fixée une fois pour toutes. En un jeu de miroirs, le sexe opposé et les autres classes d'âge éclairent ces parcours féminins sans cesse mouvants, au croisement des rites collectifs et du vécu singulier. (shrink)

Antonio Rosmini is considered by many to be greatest Italian - or even European - thinker of the nineteenth century. But for christians he is also a saint. Here, marking ten years since his beatification in 2007, is an updated biography.

In recent years, several Vygotskian computer-based learning activities (VCBLAs) were designed in the context of (mathematics) education and implemented on Moodle platform. However, Moodle does not allow users to visualize all chats on a single browser page, and they are forced to open multiple browser windows and switch among them very frequently. This paper describes the features of a plugin for Moodle, called “Quick Chat,” which allows to manage in a single browser window both the narrative flow of a VCBLA (...) and all chats. Some results of an experimentation with PhD students, engaged in solving two mathematical tasks, are shown. (shrink)

We introduce a new product bilattice con- struction that generalizes the well-known one for interlaced bilattices and others that were developed more recently, allowing to obtain a bilattice with two residuated pairs as a certain kind of power of an arbitrary residuated lattice. We prove that the class of bilattices thus obtained is a variety, give a finite axiomatization for it and characterize the congruences of its members in terms of those of their lat- tice factors. Finally, we show how (...) to employ our product construction to define first-order definable classes of bi- lattices corresponding to any first-order definable subclass of residuated lattices. (shrink)

We look at extensions (i.e., stronger logics in the same language) of the Belnap–Dunn four-valued logic. We prove the existence of a countable chain of logics that extend the Belnap–Dunn and do not coincide with any of the known extensions (Kleene’s logics, Priest’s logic of paradox). We characterise the reduced algebraic models of these new log- ics and prove a completeness result for the first and last element of the chain stating that both logics are determined by a single finite (...) logical matrix. We show that the last logic of the chain is not finitely axiomatisable. (shrink)

Cet article vise à exposer le travail que juristes, magistrats et experts ont dû effectuer – parfois au prix de leur vie – pour soutenir l’énoncé selon lequel la mafia existe, et montre les implications de cette assertion pour les « économies morales » de la société italienne. Après un détour historique destiné à décrire le processus conduisant, en septembre 1982, à une définition juridique de la mafia comme « association criminelle » – préalable nécessaire à l’aboutissement de toute action (...) en justice contre cette société secrète – ce texte se penche sur les mises à l’épreuve judiciaire de l’affirmation de la nature organisée et centralisée du phénomène mafieux, et sur les multiples revirements auxquels cette théorisation – appelée « le théorème Buscetta » du nom du repenti ayant permis de la formuler – a été soumise. Les controverses que suscitent de nos jours encore les procès anti-mafia dans le prétoire, les bureaux d’instruction ou les médias, incitent à saisir les enjeux politiques et moraux de telle ou telle définition de la « mafia » et du « mafieux », et à poser la question de la limite entre ce qui est acceptable ou intolérable au sein d’une démocratie. (shrink)

Cet article vise à exposer le travail que juristes, magistrats et experts ont dû effectuer – parfois au prix de leur vie – pour soutenir l’énoncé selon lequel la mafia existe, et montre les implications de cette assertion pour les « économies morales » de la société italienne. Après un détour historique destiné à décrire le processus conduisant, en septembre 1982, à une définition juridique de la mafia comme « association criminelle » – préalable nécessaire à l’aboutissement de toute action (...) en justice contre cette société secrète – ce texte se penche sur les mises à l’épreuve judiciaire de l’affirmation de la nature organisée et centralisée du phénomène mafieux, et sur les multiples revirements auxquels cette théorisation – appelée « le théorème Buscetta » du nom du repenti ayant permis de la formuler – a été soumise. Les controverses que suscitent de nos jours encore les procès anti-mafia dans le prétoire, les bureaux d’instruction ou les médias, incitent à saisir les enjeux politiques et moraux de telle ou telle définition de la « mafia » et du « mafieux », et à poser la question de la limite entre ce qui est acceptable ou intolérable au sein d’une démocratie. (shrink)

À San Juan de Plan, village des Hautes-Pyrénées espagnoles, le jour de la Sainte-Agathe, trois générations féminines s’affairent autour d’une préparation culinaire : el chocolate, le chocolat. Quelle relation peut-on établir entre la sainte aux seins coupés, les femmes, qui en Espagne lui vouent un culte tout particulier, et la boisson chaude qu’elles élaborent? Éclairé à la lumière de la biographie de sainte Agathe, ce rite alimentaire nous découvre quelques-unes des propriétés symboliques du chocolat et fait apparaître, dans ses multiples (...) facettes, une capacité propre à l’être féminin : celle de transmettre. (shrink)