We define and study monadic MV-algebras as pairs of MV-algebras one of which is a special case of relatively complete subalgebra named m-relatively complete. An m-relatively complete subalgebra determines a unique monadic operator. A necessary and sufficient condition is given for a subalgebra to be m-relatively complete. A description of the free cyclic monadic MV-algebra is also given.

In this paper we define sheaf spaces of BL-algebras (or BL-sheaf spaces), we study completely regular and compact BL-sheaf spaces and compact representations of BL-algebras and, finally, we prove that the category of non-trivial BL-algebras is equivalent with the category of compact local BL-sheaf spaces.

In this paper we prove that the category of abelianl-groups is equivalent to the category of perfect MV-algebras. Furthermore, we give a finite equational axiomatization of the variety generated by perfect MV-algebras.

BL-algebras are the Lindenbaum algebras for Hájek's Basic Logic, just as Boolean algebras correspond to the classical propositional calculus. The finite totally ordered BL-algebras are ordinal sums of MV-chains. We develop a natural duality, in the sense of Davey and Werner, for each subvariety generated by a finite BL-chain, and we use it to describe the injective and the weak injective members of these classes.

In this paper we study and equationally characterize the subvarieties of BL, the variety of BL-algebras, which are generated by families of single-component BL-chains, i.e. MV-chains, Product-chain or Gödel-chains. Moreover, it is proved that they form a segment of the lattice of subvarieties of BL which is bounded by the Boolean variety and the variety generated by all single-component chains, called ŁΠG.

We present a stronger variation of state MV-algebras, recently presented by T. Flaminio and F. Montagna, which we call state-morphism MV-algebras. Such structures are MV-algebras with an internal notion, a state-morphism operator. We describe the categorical equivalences of such state MV-algebras with the category of unital Abelian ℓ-groups with a fixed state operator and present their basic properties. In addition, in contrast to state MV-algebras, we are able to describe all subdirectly irreducible state-morphism MV-algebras.

The MV-algebra S m w is obtained from the (m+1)-valued ukasiewicz chain by adding infinitesimals, in the same way as Chang's algebra is obtained from the two-valued chain. These algebras were introduced by Komori in his study of varieties of MV-algebras. In this paper we describe the finitely generated totally ordered algebras in the variety MV m w generated by S m w . This yields an easy description of the free MV m w -algebras over one generator. We characterize (...) the automorphism groups of the free MV-algebras over finitely many generators. (shrink)

In this paper we prove that the category of abelian l-groups is equivalent to the category of perfect MV-algebras. Furthermore, we give a finite equational axiomatization of the variety generated by perfect MV-algebras.

In this paper we study the notion of forcing for Łukasiewicz predicate logic (Ł∀, for short), along the lines of Robinson’s forcing in classical model theory. We deal with both finite and infinite forcing. As regard to the former we prove a Generic Model Theorem for Ł∀, while for the latter, we study the generic and existentially complete standard models of Ł∀.

We present a uniform version of Di Nola Theorem, this enables to embed all MV-algebras of a bounded cardinality in an algebra of functions with values in a single non-standard ultrapower of the real interval [0,1]. This result also implies the existence, for any cardinal α, of a single MV-algebra in which all infinite MV-algebras of cardinality at most α embed. Recasting the above construction with iterated ultrapowers, we show how to construct such an algebra of values in a (...) definable way, thus providing a sort of “canonical” set of values for the functional representation. (shrink)

In this paper we first provide a new axiomatization of algebraically closed MV-algebras based on McNaughtonʼs Theorem. Then we turn to sheaves, and we represent algebraically closed MV-algebras as algebras of global sections of sheaves, where the stalks are divisible MV-chains and the base space is Stonean.

In this paper we study the notion of forcing for Łukasiewicz predicate logic (Ł∀, for short), along the lines of Robinson’s forcing in classical model theory. We deal with both finite and infinite forcing. As regard to the former we prove a Generic Model Theorem for Ł∀, while for the latter, we study the generic and existentially complete standard models of Ł∀.

In this paper we give a representation of the free MV-algebra over one generator as a structure of functions having finite domain.

We prove that the m -generated free MV-algebra is isomorphic to a quotient of the disjoint union of all the m -generated free MV-algebras. Such a quotient can be seen as the direct limit of a system consisting of all free MV-algebras and special maps between them as morphisms.

We start from Marra–Spada duality between semisimple MV-algebras and Tychonoff spaces, and we consider the particular cases when the \-skeleta of the MV-algebras are restricted in some way. In particular we consider antiskeletal MV-algebras, that is, the ones whose \-skeleton is trivial.

We show that the complete first order theory of an MV algebra has equation image countable models unless the MV algebra is finitely valued. So, Vaught's Conjecture holds for all MV algebras except, possibly, for finitely valued ones. Additionally, we show that the complete theories of finitely valued MV algebras are equation image and that all ω-categorical complete theories of MV algebras are finitely axiomatizable and decidable. As a final result we prove that the free algebra on countably many generators (...) of any locally finite variety of MV algebras is ω-categorical. (shrink)

In this paper we study the set of MV-algebras with given prime spectrum and we introduce the class of spectral MV-algebras. An MV-algebra is spectral if it is generated by the union of all its prime ideals (or proper ideals, or principal ideals, or maximal ideals). Among spectral MV-algebras, special attention is devoted to bipartite MV-algebras. An MV-algebra is bipartite if it admits an homomorphism onto the MV-algebra of two elements. We prove that both bipartite MV-algebras and spectral MV-algebras can (...) be finitely axiomatized in first order logic. We also prove that there is only, up to isomorphism, a set of MV-algebras with given prime spectrum. A further part of the paper is devoted to some relations between bipartite MV-algebras and their states. Recall that a state on an MV-algebra is a generalization of a probability measure on a Boolean algebra. Particular states are the states with Bayes’ property. We show that an MV-algebra admits a state with the Bayes’ property if and only if it is bipartite. (shrink)

In this work we introduce a class of commutative rings whose defining condition is that its lattice of ideals, augmented with the ideal product, the semi-ring of ideals, is isomorphic to an MV-algebra. This class of rings coincides with the class of commutative rings which are direct sums of local Artinian chain rings with unit.

In [9] Mundici introduced a categorical equivalence Γ between the category of MV-algebras and the category of abelian [MATHEMATICAL SCRIPT SMALL L]-groups with strong unit. Using Mundici's functor Γ, in [8] the authors established an equivalence between the category of perfect MV-algebras and the category of abelian [MATHEMATICAL SCRIPT SMALL L]-groups. Aim of the present paper is to use the above functors to provide Yosida like representations of a large class of MV-algebras.

In this paper we show that the prime ideal space of an MV-algebra is the disjoint union of prime ideal spaces of suitable local MV-algebras. Some special classes of algebras are defined and their spaces are investigated. The space of minimal prime ideals is studied as well.

We describe a class of MV-algebras which is a natural generalization of the class of “algebras of continuous functions”. More specifically, we're interested in the algebra of frame maps Hom\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${_{\cal F}}$$\end{document} (Ω(A), K) in the category T of frames, where A is a topological MV-algebra, Ω(A) the lattice of open sets of A, and K an arbitrary frame.Given a topological space X and a topological MV-algebra A, we have the algebra C (...) (X, A) of continuous functions from X to A. We can look at this from a frame point of view. Among others we have the result: if K is spatial, then C(pt(K), A), pt(K) the points of K, embeds into Hom\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${_{\cal F}}$$\end{document} (Ω(A), K) analogous to the case of C (X, A) embedding into Hom\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${_{\cal F}}$$\end{document} (Ω(A), Ω (X)). (shrink)

ABSTRACT In this paper we shall prove that l-rings are categorally equivalent to the MV*-algebras, a subcategory of perfect MV-algebras. We shall use this equivalence in order to characterize l-rings as quotients of certain semirings of matrices over MV*-algebras. We shall establish a relation between l-ideals in l-rings and some ideals in MV*-algebras. This edlows us to study the MV* f-algebras, a subclass of the MV*-algebras corresponding to the f-rings.

The history of Fuzziness in Italy is varied and scattered among a num- ber of research groups. As a matter of fact, “fuzziness” spread in Italy through a sort of spontaneous diffusion, and, also subsequently, no one felt the need to cre- ate some “national” common structure like an Association or similar things. Since a cohesive retelling would be next to impossible, a few members of the Italian fuzzy community have been asked to recount their experience and express their hopes (...) for the future. (shrink)

In this paper we study the presence of elements related to Roman games in the work of the bishop Paulinus of Nola (355-431 AD). References to shows inhis work are not as abundant as they occurs among his contemporaries. Nevertheless, many of these references possess a great importance for us. Certainly, they are similar to other allusions made by his contemporaries; however they express the opinion of one of the most famous and prestigious bishops of the Late Antiquity about (...) these popular exhibitions. In his writings we can see his criticism of the waste of wealth in the organization of the Roman games, and also the use of a metaphorical language with ludical reminiscences whose origins go back to Paul of Tarsus. (shrink)

Soto Calderón, Andrea (2022)Imaginación materialSantiago de Chile: Metales Pesados, 149 p.ISBN 978-9566048923.

Significant individual differences exist in dream recall frequency but some variance is likely attributable to instrument choice in measuring DRF. Three hundred and fifty eight participants estimated their weekly DRF and recorded their dreams in either a narrative log or checklist log for 2–5 weeks. There was an early peak in DRF within the first week of both types of prospective logs after which DRF remained relatively stable. Although the two groups did not differ in their estimated DRF, significantly fewer (...) dreams were reported per week on the narrative logs and only checklist logs yielded significantly higher DRF than participants’ questionnaire estimates. The interactions between DRF measures did not vary across groups with low, medium or high baseline levels of DRF. Keeping a dream log does not necessarily increase DRF and narrative logs’ time consuming nature can impact subjects’ motivation to report all of their dreams over time. (shrink)

The cases of corruption reported by the media tend almost always to involve a private party (a citizen or a corporation) that pays, or promises to pay, money to a public party (a politician or a public official, for example) in order to obtain an advantage or avoid a disadvantage. Because of the harm it does to economic efficiency and growth, and because of its social, political and ethical consequences, private-to-public corruption has been widely studied. Private-to-private corruption, by contrast, has (...) been relatively neglected and only recently has started to receive the attention it deserves. The purpose of this paper is to offer some thoughts on the nature and importance of private-to-private corruption; the legal treatment it receives in some of the world''s leading countries; and the measures that companies can take to combat it, with special consideration of its ethical aspects. (shrink)

Machine consciousness is not only a technological challenge, but a new way to approach scientific and theoretical issues which have not yet received a satisfactory solution from AI and robotics. We outline the foundations and the objectives of machine consciousness from the standpoint of building a conscious robot.

Making use of facilitating payments is a very widespread form of corruption. These consist of small payments or gifts made to a person – generally a public official or an employee of a private company – to obtain a favour, such as expediting an administrative process; obtaining a permit, licence or service; or avoiding an abuse of power. Unlike the worst forms of corruption, facilitating payments do not usually involve an outright injustice on the part of the payer as they (...) are entitled to what they request. This may be why public opinion tends to condone such payments; often they are assumed to be unavoidable and are excused on the grounds of low wages and lack of professionalism among public officials and disorganisation in government offices. Many companies that take the fight against “grand” corruption very seriously are inclined to overlook these “petty” transgressions, which are seen as the grease that makes the wheels of the bureaucratic machine turn more smoothly. Despite this, facilitating payments have a pernicious effect on the working of public and private administrations: all too often they are the slippery slope to more serious forms of corruption; they impose additional costs on companies and citizens; and in the long run they sap the ethical foundations of organisations. Although many articles on corruption mention facilitating payments, there have been no systematic studies from a company’s point of view. This article thus focuses on facilitating payments from the point of view of the company that makes the payment, either as the active partner (when it is the company that takes the initiative) or as the passive partner (when the official or employee is the instigator). (shrink)

This article serves as an introduction to the collection of papers in this monographic issue on "What the European tradition can teach about Corporate Social Responsibility" and presents the rationale and the main hypotheses of the project. We maintain that corporate social responsibility (CSR) is an ethical concept, that the demands for socially responsible actions have been around since before the Industrial Revolution and that companies have responded to them, especially in Europe, and that the content of CSR has evolved (...) over time, depending on historical, cultural, political, and socio-economic drivers and particular conditions in different countries and also at different points in time. Therefore, there is not — and probably cannot be — a unique, precise definition of CSR: one global standard for CSR is unlikely. (shrink)

In our paper we aim to meditate on the concept of depth (profondeur) in the works of M. Merleau-Ponty, as it is a key notion to understand the French philosopher’s concept of space. Furthermore we will try to show that space plays a fundamental role in the development of Merleau-Ponty’s philosophy, allowing us to understand important features both of his phenomenological readings and ontological project.

As we turn to the lived experience of memory, we are confronted with an eerie and enigmatic possibility: the possibility to remember what we ourselves never lived. How to explain phenomenologically this enigmatic but fundamental level of spatialized memory? I would like to come back to these issues in order to face yet another fundamental question: Does a phenomenology of spatialized memory require any onto-phenomenological concretizations?

For several decades, historians have realized the limitations of analysing the historical past of science as a mere succession of theories. One of the most stimulating messages that the reinvention of the discipline has launched is that although there are obvious intellectual elements that promote the development and progress of science, there are also social, economic, and institutional aspects to consider. The history of science is no longer just a history of scientific ideas and theories, but also a history of (...) institutions, communities, spaces, objects, and practices as well as a history of the complex interaction among all these dimensions. Accompanying this new panorama is a broad consensus among scholars to accept that major social changes have inexorably some impact on scientific practice and vice versa. This premise, now widespread, is especially relevant to the history of early modern science and the question of its roots because it has allowed the introduction of new agents and spaces previously excluded from the domain of scientific development. In other words, this enriched perspective has multiplied both the processes of knowledge construction and the arenas in which these processes were undertaken. More specifically, historical research is no longer limited to spaces traditionally linked to the construction of science; it now embraces less orthodox ones. Within this broadened field of inquiry, practical knowledge and the objects of material culture have come to occupy a central place. This special issue explores how the new directions in which the history of science has expanded have a direct impact on the study of Iberian science in the Atlantic world. (shrink)

Corruption is a serious economic, social, political, and moral blight, especially in many emerging countries. It is a problem that affects companies in particular, especially in international commerce, finance, and technology transfer. And it is becoming an international phenomenon in scope, substance, and consequences. That is why, in recent years, there has been a proliferation of international efforts to tackle the problem of corruption. One such international cooperative initiative is the United Nations Convention against Corruption, signed in 2003, which came (...) into force in December 2005. This is the first truly global instrument to prevent and combat corruption, built on a broad international consensus. The purpose of this article is to explain the origin and content of the Convention, what it adds to existing international instruments for combating corruption, and its strengths and weaknesses, mainly from the point of view of companies. (shrink)

En este artículo nos proponemos exponer, a partir de los límites conceptuales encontrados a los planteamientos arqueo-genealógicos de Michel Foucault, la posibilidad de plantear, en dos momentos –arqueo-genealógico y gubernamental–, una “ética de la insubordinación reflexiva”. Es decir, una “ética de la libertad inmanente” al débil que al decir su palabra, denuncia y al denunciar cuestiona al tirano y su mundo al habar y actuar con –y por– los otros. Esta ética de la intersubjetividad planteada como una ética de la (...) insumisión concertada, crítica y deliberada, pensamos, puede derivar de ciertas “condiciones enunciativas” encontradas en las dos últimas investigaciones concernientes al “decir veraz” o el “hablar franco” expuestos en El gobierno de sí y de los otros y El coraje de la verdad. (shrink)

Our economic system, the market economy, is a part of a broader system or “society.” We frequently study the operation of the market economy as if it were autonomous, even though there are many complex and mutual relationships between society, the economic system and the other systems – political, cultural, religious, legal, etc. – that form part of society. In a market economy we may identify several components: a frame or background in which the economic activity takes place, a set (...) of ideas and theories, the values shared by this society, the set of institutions, norms and rules that control the economic behavior of people, and the incentives or motivations of the economic agents. The play of these elements defines the operation of a market economy. Is ethics an institution, or does it belong to the set of values and ideas? In this paper I will discuss the role of institutions, norms and rules in society, with special reference to the economic system, in order to gain insight into the relationship between institutions and ethics. I study first the concept and features of social institutions and norms; second, institutional change, and third, the relationship between ethics and institutions. (shrink)

The ‘bat and ball’ is one of the problems most frequently employed as a testbed for research on the dual-system hypothesis of reasoning. Frederick (J Econ Perspect 19:25–42, 2005) is the first to envisage the possibility that different numerical arrangements of the ‘bat and ball’ problem could lead to different dynamics of activation of the dual-system, and so to different performances of subjects in task accomplishment. This possibility has triggered a strand of research oriented to accomplish ‘sensitivity analyses’ of the (...) ‘bat and ball’ problem. The scope of this paper is to test experimentally the specific hypothesis that numerals are responsible for the selective activation of the two systems of reasoning in this task. In particular, we argue that their role goes beyond and cannot be reduced to that of numbers conceived as magnitudes. To test our hypothesis, we devise an experimental setting in which the role of numbers (as magnitudes) is rendered irrelevant. We find experimental results consistent with our hypothesis. We further provide a link between the literature on mathematical problem-solving and that on mathematical cognition research, in particular that branch labeled embodied mathematical cognition. (shrink)