In this paper we define the hyper operations ⊗, ∨ and ∧ on a hyper MV -algebra and we obtain some related results. After that by considering the notions ofhyper MV -ideals and weak hyper MV -ideals, we prove some theorems. Then we determine relationships between hyper MV -ideals in a hyper MV -algebra and hyper K -ideals in a hyper K -algebra . Finally we give a characterization of hyper MV -algebras (...) of order 3 or 4 based on the hyper MV -ideals. (shrink)

The notions of a hyper MV-deductive system, a -hyper MV-deductive system, a - hyper MV-deductive system, a -hyper MV-deductive system, a -hyper MV-deductive system and a -hyper MV-deductive system are introduced, and then their relations are investigated.

In this paper we study the category of hyper MV-algebras and we prove that it has a terminal object and a coequalizer. We show that Jia's construction can be modified to provide a free hyper MV-algebra by a set. We use this to show that in the category of hyper MV-algebras the monomorphisms are exactly the one-to-one homomorphisms.

This paper introduces the concept of single-valued neutrosophic hyper \(BCK\)-subalgebras as a generalization and alternative of hyper \(BCK\)-algebras and on any given nonempty set constructs at least one single-valued neutrosophic hyper \(BCK\)-subalgebra and one a single-valued neutrosophic hyper \(BCK\)-ideal. In this study level subsets play the main role in the connection between singlevalued neutrosophic hyper \(BCK\)-subalgebras and hyper \(BCK\)-subalgebras and the connection between single-valued neutrosophic hyper \(BCK\)-ideals and hyper \(BCK\)-ideals. The congruence and (...) (strongly) regular equivalence relations are the important tools for connecting hyperstructures and structures, so the major contribution of this study is to apply and introduce a (strongly) regular relation on hyper \(BCK\)-algebras and to investigate their categorical properties (quasi commutative diagram) via single-valued neutrosophic hyper \(BCK\)-ideals. Indeed, by using the single-valued neutrosophic hyper \(BCK\)-ideals, we define a congruence relation on (weak commutative) hyper \(BCK\)-algebras that under some conditions is strongly regular and the quotient of any (single-valued neutrosophic)hyper \(BCK\)-(sub)algebra via this relation is a (single-valued neutrosophic)(hyper \(BCK\)-subalgebra) \(BCK\)-(sub)algebra. (shrink)

Generalizations of Boolean elements of a BL-algebra L are studied. By utilizing the MV-center MV(L) of L, it is reproved that an element x L is Boolean iff x x * = 1. L is called semi-Boolean if for all x L, x * is Boolean. An MV-algebra L is semi-Boolean iff L is a Boolean algebra. A BL-algebra L is semi-Boolean iff L is an SBL-algebra. A BL-algebra L is called hyper-Archimedean if for all x L, xn is (...) Boolean for some finite n 1. It is proved that hyper-Archimedean BL-algebras are MV-algebras. The study has application in mathematical fuzzy logics whose Lindenbaum algebras are MV-algebras or BL-algebras. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim). (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.

The notion of int-soft ideal in a pseudo MV -algebra is introduced, and related properties are investigated. Conditions for a soft set to be an int-soft ideal are provided. Characterizations of int-soft ideal are considered. The extension property for implicative int-soft ideal is established.

We look at a hierarchical arrangement of ideals in an MV -algebra. The principal classes of ideals studied are the maximals, the primes, the local and perfect ideals and the semi-locals. Beyond these special classes of ideals are the general ideals. Herein we study some relationships among these classes and, more specifically, the products of ideals of these classes. Among the results obtained are the square of a prime ideal is a local ideal, the finite product of prime ideals is (...) a semilocal ideal. We also show that the set of local ideals shares many of the properties of the class of prime ideals, as the Lying Over Theorem and the Going Up Theorem. (shrink)

In this paper we make an algebraic study of the variety of MV*-algebras introduced by C. C. Chang as an algebraic counterpart for a logic with positive and negative truth values.We build the algebraic theory of MV*-algebras within its own limits using a concept of ideal and of prime ideal that are very naturally related to the corresponding concepts in l-groups. The main results are a subdirect representation theorem, a completeness theorem, a study of simple and semisimple algebras, and a (...) characterization of the ideal of infinitesimals as an l-group. In the last section we develop a detailed proof a the one-dimensional theorem of McNaughton, that is, the free MV*-algebra in one generator is the algebra of McNaughton functions over [−1,1]. In contrast with the rest of the paper, this last result is based on work done for MV-algebras. (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.

Let Γ be Mundici’s functor from the category $${\mathcal{LG}}$$ whose objects are the lattice-ordered abelian groups ( ℓ -groups for short) with a distinguished strong order unit and the morphisms are the unital homomorphisms, onto the category $${\mathcal{MV}}$$ of MV-algebras and homomorphisms. It is shown that for each strong order unit u of an ℓ -group G , the Boolean skeleton of the MV-algebra Γ ( G , u ) is isomorphic to the Boolean algebra of factor congruences of G.

A central frustration of recent political discourse is the consistent reduction of politically relevant factual and critical speech to mere expression of partisan commitment. Partisans of “the other side”—members of the other tribe—are viewed as de facto wrong, because partisans, even when their speech invokes mere facts or purportedly shared political principles. Ideally, democratic political discourse operates along at least two central dimensions: a dimension of shared factual, historical, and political assumptions, and a more contested dimension of interpretation, prioritization, and (...) evaluation that results in diverse and often competing understandings of what is good, and so of what is best to collectively pursue. Debates among advocates of competing conceptions of the good and partisans of diverse world views identifiable in terms of the second dimension are, on this picture, constrained and grounded by the shared factual and political commitments of the first, thus ensuring a meaningful basis for ongoing political engagement. While there is little reason to think this ideal has ever been perfectly realized, in recent political discourse statements that events have occurred, drugs are effective, or transparency is important in political conduct cannot seem to get uptake except as mere expressions of political partisanship any more than an actor on stage trying to convince her audience of the danger of a real fire that has broken out in the theater can get uptake for this claim except as an expression in a theatrical performance. In both cases, the real content and discursive intent of speech is undermined by the context in which it occurs. In the case of the actor on stage, the appropriate rules for uptake and interpretation are being followed, just to unfortunate effect. However, in the case of political discourse something seems to be wrong with the rules for uptake and interpretation that have come to dominate in many quarters. This essay relies on recent discussions of silencing and epistemic injustice to introduce the ideas of partisan silencing and hyper-partisan silencing in an attempt to say more precisely what has gone wrong with the rules for uptake and interpretation in political discourse. It then relies on Hannah Arendt’s analyses of truth and lies in politics to connect these phenomena to underlying features of political action and speech. Conditions of partisan and hyperpartisan silencing turn out to be a natural, if not inevitable, consequence of the relationship of truth-telling and deception to political action itself as Arendt understands this. Finally, the essay elaborates on two suggestive passages from Arendt’s 1967 essay “Truth and Politics” to propose potential strategies for resisting conditions of hyperpartisan silencing. Because hyper-partisan silencing itself imposes a certain discursive logic, there are kinds of political speech and action that might succeed in being understood as sincere and so in being persuasive—even in the face of hyper-partisan silencing—precisely because they challenge the assumptions that underpin this discursive logic itself. (shrink)

In this paper, inspired by methods of Bigard, Keimel, and Wolfenstein , we develop an approach to sheaf representations of MV-algebras which combines two techniques for the representation of MV-algebras devised by Filipoiu and Georgescu and by Dubuc and Poveda . Following Davey approach , we use a subdirect representation of MV-algebras that is based on local MV-algebras. This allowed us to obtain: a representation of any MV-algebras as MV-algebra of all global sections of a sheaf of local MV-algebras on (...) the spectruum of its prime ideals; a representation of MV-algebras, having the space of minimal prime ideals compact, as MV-algebra of all global sections of a Hausdorff sheaf of MV-chains on the space of minimal prime ideals, which is a Stone space; an adjunction between the category of all MV-algebras and the category of MV-algebraic spaces, where an MV-algebraic space is a pair , where X is a compact topological space and F is a sheaf of MV-algebras with stalks that are local. (shrink)

We initiate a study of two general concepts of semisimplicity for MV-algebras by replacing the standard MV-algebra with an arbitrary MV-chain. These generalised notions are called -semisimple MV-algebras and -semisimple MV-algebras. We obtain several of their characterisations and explore in more-depth the case of perfect MV-chains.

Pseudo MV-algebras are a non-commutative extension of MV-algebras introduced recently by Georgescu and Iorgulescu. We introduce states (finitely additive probability measures) on pseudo MV-algebras. We show that extremal states correspond to normal maximal ideals. We give an example in that, in contrast to classical MV-algebras introduced by Chang, states can fail on pseudo MV-algebras. We prove that representable and normal-valued pseudo MV-algebras admit at least one state.

In this paper, by considering the notion of MV-module, which is the structure that naturally correspond to lu-modules over lu-rings, we study injective MV-modules and we investigate some conditions for constructing injective MV-modules. Then we define the notions of essential A-homomorphisms and essential extension of A-homomorphisms, where A is a product MV-algebra, and we get some of there properties. Finally, we prove that a maximal essential extension of any A-ideal of an injective MV-module is an injective A-module, too.

ABSTRACTWe introduce the variety of Many-Valued-Weak rigs. We provide an axiomatisation and establish, in this context, basic properties about ideals, homomorphisms, quotients and radicals. This new class contains the class of product MV-algebras presented by Di Nola and Dvurečenskij in 2001 and by Montagna in 2005. The main result is the compactness of the prime spectrum of this new class, endowed with the co-Zariski topology as defined by Dubuc and Poveda in 2010.

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.

Neoliberalism is invariably presented as a governing regime of market and competition-based systems rather than as a set of migratory practices that are re-setting the ethical standards of the academy. This article seeks to explore the way in which neoliberalism is shifting the prevailing values of the academy by drawing on two illustrations: the death of disinterestedness and the obfuscation of authorship. While there was never a golden age when norms such as disinterestedness were universally practiced they represented widely accepted (...) aesthetic ideals associated with academic life. By contrast, neoliberal academics embrace a new set of assumptions and norms that stand in sharp relief to many of the values that were previously espoused. Practices that might have been regarded as ethically dubious by earlier generations of academics, such as grantsmanship, self-justificatory expressions of interestedness and tangential claims to authorship, are now regarded as legitimate and positive virtues in a more aggressive age of hyper-performativity. (shrink)

Neoliberalism is invariably presented as a governing regime of market and competition-based systems rather than as a set of migratory practices that are re-setting the ethical standards of the academy. This article seeks to explore the way in which neoliberalism is shifting the prevailing values of the academy by drawing on two illustrations: the death of disinterestedness and the obfuscation of authorship. While there was never a golden age when norms such as disinterestedness were universally practiced they represented widely accepted (...) aesthetic ideals associated with academic life. By contrast, neoliberal academics embrace a new set of assumptions and norms that stand in sharp relief to many of the values that were previously espoused. Practices that might have been regarded as ethically dubious by earlier generations of academics, such as grantsmanship, self-justificatory expressions of interestedness and tangential claims to authorship, are now regarded as legitimate and positive virtues in a more aggressive age of hyper-performativity. (shrink)

An equivalence between the category of MV-algebras and the category \ is given in Castiglioni et al. :67–92, 2014). An integral residuated lattice with bottom is an MV-algebra if and only if it satisfies the equations \ \vee = 1}\) and \ = a \wedge b}\). An object of \ is a residuated lattice which in particular satisfies some equations which correspond to the previous equations. In this paper we extend the equivalence to the category whose objects are pairs, where (...) A is an MV-algebra and I is an ideal of A. (shrink)

Societies are always gathered around a particular object or an idea that serves as its totem and its driving principle. This conscious arrangement of society, especially around an ideal, has been termed in history as utopias, which consciously moulds an individual’s behaviour inhabiting it for the desired future goal. However, in the hyper-humanistic period, called by James Scott as High-modernism, we can see a drastic truncation in the scope and range of those desired future forms, limited only to economic (...) and material wellbeing. The aim of this paper therefore is to look into an example of the utopian experiment that substantially differs from a high-modernist worldview. The paper will analyse one such futuristic spiritual experiment at Auroville and try to trace its similarities as well as its difference from the hyper-humanistic ideals of modernity. (shrink)

Simple idealized models seem to provide more understanding than opaque, complex, and hyper-realistic models. However, an increasing number of scientists are going in the opposite direction by utilizing opaque machine learning models to make predictions and draw inferences, suggesting that scientists are opting for models that have less potential for understanding. Are scientists trading understanding for some other epistemic or pragmatic good when they choose a machine learning model? Or are the assumptions behind why minimal models provide understanding misguided? (...) In this paper, using the case of deep neural networks, I argue that it is not the complexity or black box nature of a model that limits how much understanding the model provides. Instead, it is a lack of scientific and empirical evidence supporting the link that connects a model to the target phenomenon that primarily prohibits understanding. (shrink)

We define a new class of pseudo effect algebras, called kite pseudo effect algebras, which is connected with partially ordered groups not necessarily with strong unit. In such a case, starting even with an Abelian po-group, we can obtain a noncommutative pseudo effect algebra. We show how such kite pseudo effect algebras are tied with different types of the Riesz Decomposition Properties. Kites are so-called perfect pseudo effect algebras, and we define conditions when kite pseudo effect algebras have the least (...) non-trivial normal ideal. (shrink)

This book contends that the crises of well-being, distress, and dysfunction currently afflicting the legal profession, other professions, and our politics can best be addressed by encouraging people to pursue a flourishing life of meaning and purpose in communities of excellence and virtue. It draws centrally upon the work of Alasdair MacIntyre, arguably the most famous living moral philosopher and notorious for his critique of liberal democracy, its capitalist, large-scale market economy, and hyper-individualism in late Modernity. Constructing a fishing (...) village called Piscopolis as a central image and theoretical ideal, the book integrates relevant aspects of MacIntyre's Thomistic-Aristotelianism into a clear, comprehensible, and original synthesis that also significantly expands and supplements MacIntyre's theoretical approach, including insights drawn from Heideggerian phenomenology. It examines the legal polis, the "fishing village of the law" called Juropolis, to illustrate how the Piscopolis ideal challenges members of the professions and suggests how the ideal might be deployed more broadly to organically transform the liberal democratic state into a "republic of virtue." With the Covid-19 pandemic starkly revealing the need for such transformation, the book will interest both the MacIntyrean expert and novice alike and appeal broadly to moral and political philosophers, ethicists, theologians, legal professionals, and scholarly lay readers. (shrink)

Heidegger presciently diagnosed the current crisis in higher education. Contemporary theorists like Bill Readings extend and update Heidegger's critique, documenting the increasing instrumentalization, professionalization, vocationalization, corporatization, and technologization of the modern university, the dissolution of its unifying and guiding ideals, and, consequently, the growing hyper-specialization and ruinous fragmentation of its departments. Unlike Heidegger, however, these critics do not recognize such disturbing trends as interlocking symptoms of an underlying ontological problem and so they provide no positive vision for the future (...) of higher education. By understanding our educational crisis 'ontohistorically', Heidegger is able to develop an alternative, ontological conception of education which he hopes will help bring about a renaissance of the university. In a provocative reading of Plato's famous 'allegory of the cave', Heidegger excavates and appropriates the original Western educational ideal of Platonic paideia, outlining the pedagogy of an ontological education capable of directly challenging the 'technological understanding of being' he holds responsible for our contemporary educational crisis. This notion of ontological education can best be understood as a philosophical perfectionism, a re-essentialization of the currently empty ideal of educational 'excellence' by which Heidegger believes we can reconnect teaching to research and, ultimately, reunify and revitalize the university itself. (shrink)

Behavioural variant frontotemporal dementia (bvFTD) is characterized by an absence of obvious cognitive impairment and presence of symptoms such as disinhibition, social inappropriateness, personality changes, hyper-sexuality, and hyper-orality. Affected individuals do not feel concerned enough about their actions to be deterred from violating social norms, and their antisocial behaviours are most likely caused by the neurodegenerative processes in the frontal and anterior temporal lobes. BvFTD patients present a challenge for the traditional notion of autonomy and the medical and (...) criminal justice systems. Antisocial behaviour is often the earliest recognized manifestation of bvFTD. Given that the symptoms are not specific and that atrophy of the frontal lobes is only observable with structural neuroimaging in the later stages of the disease, it is hard to ascertain their autonomy. Recently proposed re-conceptualizations of autonomy (Dworkin’s, Jaworska’s, and Dubljević’s) can, however, be sufficiently redefined to provide explicit rules and offer nuanced guidance in such cases. A combination of notions of autonomy gives the most nuanced guidance with three modifications: 1) including socio-moral judgement in the notion of “normal cognitive competence,” 2) excluding in-principle un-endorsable ideals from the notion of “capacity to value,” and 3) redefining ideal-typical degrees of compulsion (mild, severe, and total). (shrink)