SAGGI DI VITTORIO MARCHIS, UMBERTO BOTTAZZINI, FABIO TOSCANO, MASSIMO NEGROTTI, GIUSEPPE O. LONGO, STEFANO A. E. LEONI, ALBERTO CASADEI, SILVANO TAGLIAGAMBE.

We experience our own body through both touch and vision. We further see that others’ bodies are similar to our own body, but we have no direct experience of touch on others’ bodies. Therefore, relations between vision and touch are important for the sense of self and for mental representation of one’s own body. For example, seeing the hand improves tactile acuity on the hand, compared to seeing a non-hand object. While several studies have demonstrated this visual enhancement of touch (...) effect, its relation to the ‘bodily self’, or mental representation of one’s own body remains unclear. We examined whether VET is an effect of seeing a hand, or of seeing my hand, using the rubber hand illusion. In this illusion, a prosthetic hand which is brushed synchronously—but not asynchronously—with one’s own hand is felt to actually be one’s hand. Thus, we manipulated whether or not participants felt like they were looking directly at their hand, while holding the actual stimulus they viewed constant. Tactile acuity was measured by having participants judge the orientation of square-wave gratings. Two characteristic effects of VET were observed: cross-modal enhancement from seeing the hand was inversely related to overall tactile acuity, and participants near sensory threshold showed significant improvement following synchronous stroking, compared to asynchronous stroking or no stroking at all. These results demonstrate a clear functional relation between the bodily self and basic tactile perception. (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)

In this book, the Italian novelist and philosopher Umberto Eco presents a learned summary of medieval aesthetic ideas.

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)

Irrational debt decisions at the individual level may harm collective welfare. For this reason, regulators are committed to encourage information-based behaviours in order to enhance likelihood of appropriate indebtedness. We analyse, with a diff-in-diff estimator, the Italian case offered by the Legislative Decree that reformed the consumer credit market adopting European Directive 2008/48/ec, and that reinforced the mandatory information acquisition, jointly asked to lenders and borrowers, before granting/receiving consumer credit. By using micro-data on 60.000 consumer credit borrowers, in total, randomly (...) sampled from the most relevant Italian Credit Bureau, our findings support that, in the medium term, the new consumer credit regulation has improved borrowers’ repayment ability, enhancing the quality of credit distribution. Nevertheless, a simplistic ‘better information-better behaviour’ relationship cannot be assured. This success is likely due to conjunct adaptation of behaviours, with shared responsibilities experienced on both the demand and offer side of the consumer credit marketplace. (shrink)

La conoscenza che abbiamo del testo del Libellus ad Leonem X, noto anche come De Officio Pontificis ad Leonem X, redatto dai camaldolesi veneziani Tommaso Giustiniani e Vincenzo Querini , ruota intorno al codice che “extabat MS in Bibliotheca Monasterii S. Mariae Carcerum, nunc in Bibliotheca S. Michaelis Muriani”1 identificabile con il manoscritto Muraniano 1071, oggi conservato presso la Biblioteca del Monastero di Camaldoli.2 Si tratta del codice che è stato utilizzato, secondo quanto dichiarato dallo stesso Mittarelli,3 dai camaldolesi Giovanni (...) Benedetto Mittarelli e Anselmo Costadoni 4 per la loro edizione negli Annales Camaldulenses.5 Vi è una notazione .. (shrink)

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)

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 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 human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical (...) practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of “geometric judgments” from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) “space” should be revisited for the purposes of life sciences. (shrink)

"Eco wittily and enchantingly develops themes often touched on in his previous works, but he delves deeper into their complex nature... this collection can be read with pleasure by those unversed in semiotic theory." —Times Literary Supplement.

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)

Recent research on algebraic models of _quasi-Nelson logic_ has brought new attention to a number of classes of algebras which result from enriching (subreducts of) Heyting algebras with a special modal operator, known in the literature as a _nucleus_. Among these various algebraic structures, for which we employ the umbrella term _intuitionistic modal algebras_, some have been studied since at least the 1970s, usually within the framework of topology and sheaf theory. Others may seem more exotic, for their primitive operations (...) arise from algebraic terms of the intuitionistic modal language which have not been previously considered. We shall for instance investigate the variety of _weak implicative semilattices_, whose members are (non-necessarily distributive) meet semilattices endowed with a nucleus and an implication operation which is not a relative pseudo-complement but satisfies the postulates of Celani and Jansana’s strict implication. For each of these new classes of algebras we establish a representation and a topological duality which generalize the known ones for Heyting algebras enriched with a nucleus. (shrink)

De l'antiquité à la Renaissance, la notion de certitude est au coeur de la structuration de la pensée. Cet ouvrage réunit les contributions de spécialistes, qui explorent tous la littérature latine en mettant cette notion à l'épreuve de différentes disciplines et époques.

La traduction latine des Dialoghi della historia du philosophe néo-platonicien Francesco Patrizi da Cherso est publiée à Bâle en 1570. L’étude de la circulation de ce texte et des choix de traduction permet de mieux comprendre la réception des artes historicae italiennes dans le Nord de l’Europe et les fluctuations ou limites du latin face à la montée en puissance de l’italien vernaculaire comme langue philosophique.

La traduction latine des Dialoghi della historia du philosophe néo-platonicien Francesco Patrizi da Cherso est publiée à Bâle en 1570. L’étude de la circulation de ce texte et des choix de traduction permet de mieux comprendre la réception des artes historicae italiennes dans le Nord de l’Europe et les fluctuations ou limites du latin face à la montée en puissance de l’italien vernaculaire comme langue philosophique.

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.

In this paper we re-assess the philosophical foundation of Exactly True Logic ($$\mathcal {ET\!L}$$ ET L ), a competing variant of First Degree Entailment ($$\mathcal {FDE}$$ FDE ). In order to do this, we first rebut an argument against it. As the argument appears in an interview with Nuel Belnap himself, one of the fathers of $$\mathcal {FDE}$$ FDE, we believe its provenance to be such that it needs to be taken seriously. We submit, however, that the argument ultimately fails, (...) and that $$\mathcal {ET\!L}$$ ET L cannot easily be dismissed. We then proceed to give an overview of the research that was inspired by this logic over the last decade, thus providing further motivation for the study of $$\mathcal {ET\!L}$$ ET L and, more generally, of $$\mathcal {FDE}$$ FDE -related logics that result from semantical analyses alternative to Belnap’s canonical one. We focus, in particular, on philosophical questions that these developments raise. (shrink)