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 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 risposta all’ipotesi di estendere la categoria del falso valutativo alle motivazioni di una sentenza, l’articolo tenta una ricostruzione critica della progressiva apertura del falso intellettuale ad atti dispositivi e giudizi tecnici, ponendone in evidenza alcune aporie e proponendo specifici temperamenti. Tanto la teoria dei fatti psichici, quanto quella delle attestazioni implicite e del vero legale, nella loro congiunta sovrapposizione alla struttura della fattispecie penale, possono scadere in una violazione del divieto di analogia in materia penale. Il caso da cui (...) parte l’analisi attiene una procedura di selezione per la chiamata di professore universitario di prima fascia e la sentenza del T.A.R. che decide sul ricorso di un candidato. Falsity of the judicial decision. Implicit statements, legal truth and technical judgments. In response to the hypothesis of extending the category of "evaluative" falsehood to the motivations of a judicial decision, the paper attempts a critical reconstruction of the progressive evolution of these crimes in matter of acts of will and technical judgments, highlighting some aporias and proposing some corrections. Both the theory of psychic facts, as well as the theory of implicit attestations and the legal truth, in their joint action, can violate the prohibition of analogical interpretation in criminal matters. The controversial case from which the analysis starts concerns a public competition for a university professorship and the T.A.R.’s judgment that decides on a candidate's appeal. (shrink)
A discussion of the economic work of Genovesi, the first professor of political economy in Europe. Genovesi supports a physiocratic theory of value as the net produce of agricultural work; a theory of interest as the motive of human action, intermediate between the extreme poles of excessive self-love and benevolence; a doctrine of innate rights as a limit to the sovereign's action; a commercial policy that limits dependence on foreign countries. He also took a position in the eighteenth-century debate on (...) "luxury", taking a firm stance in favour of moderate luxury, considered not vice but virtue as the right means between excessive parsimony and prodigality. He also discusses the function of the classes not dedicated to "mechanical arts" and not producing "rents" but nevertheless useful to society (Adam Smith's "unproductive" workers) in which he includes the proprietary classes which he defends against Rousseau's radical criticism, limiting himself to advocating the abolition of inalienable properties. Finally, he advocates population growth as a way to increase public happiness, the development of agriculture, the freedom of grain trade and the interest rate. (shrink)
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 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.
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.
Hegel, nell’Enciclopedia, definisce la filosofia leibniziana come “la contraddizione” completamente sviluppata. Da sempre questa affermazione ha suscitato l’attenzione degli interpreti e nel tempo si è consolidata l’immagine storiografica di uno Hegel poco attento nei confronti di Leibniz, o semplicemente iniquo nella sua valutazione. Approfondendo tuttavia i termini concettuali del giudizio hegeliano e ripercorrendone insieme la genesi storica e sistematica, la questione appare teoreticamente ancora aperta e stimolante. Il vibrante dialogo che Hegel fin dai primi anni di Jena instaura con Leibniz (...) supera le anguste barriere di un confronto di “filologia storica”, ma si pone piuttosto come un momento assolutamente significativo in rapporto a quel processo di auto-comprensione che il pensiero moderno attua nei propri confronti e che rappresenta uno dei lasciti più preziosi sui quali si è oggi chiamati a riflettere. (shrink)
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)
An effective formalism is developed to handle decaying two-state systems. Herewith, observables of such systems can be described by a single operator in the Heisenberg picture. This allows for using the usual framework in quantum information theory and, hence, to enlighten the quantum features of such systems compared to non-decaying systems. We apply it to systems in high energy physics, i.e. to oscillating meson–antimeson systems. In particular, we discuss the entropic Heisenberg uncertainty relation for observables measured at different times at (...) accelerator facilities including the effect of $\mathcal{CP}$ violation, i.e. the imbalance of matter and antimatter. An operator-form of Bell inequalities for systems in high energy physics is presented, i.e. a Bell-witness operator, which allows for simple analysis of unstable systems. (shrink)
This study reviews and classifies the most common uses of the terms “enemy” and “enmity” within the context of traditional philosophical discourse. In order to contribute to a structured understanding of these concepts, we proceed in two steps. We first explore the auxiliary uses of the terms, which we distinguish from each other according to their axiological connotations. In a second part, we review the technical uses of the concepts known to philosophy of law. Here, we distinguish between two different (...) approaches to the concept, one of which defines it through qualitative criteria, and a second approach that uses the term as a quantifier. (shrink)
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 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.
This essay analyzes the reflection of Alfred Schütz on music. The first part will focus on the analysis of those that for Schütz are the constitutive elements of the phenomenology of music. The second part will focus on the idea of music as a social interaction and relationship of mutual harmony. The aim of the work is to demonstrate that Schütz’s reflection on music does not constitute an isolated element within his thought process, but rather it constitutes a fundamental element (...) of his reflection because music represents in an exemplary way the structure of the social relationship. Therefore, it will be demonstrated that music is for Schütz a relationship based on the sharing of space and time, or an intersubjective sharing of reality that allows simultaneous sharing in the experiences of one’s interlocutor. (shrink)
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.
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.
Among the tools of philosophical work, the dialogue, as form of live "transaction" between two or more persons, seems to have its beginning and its end with Socrates. Along the subsequent development of our philosophical tradition the dialogue reappears only as literary genre. The essay aims to suggest that the live philosophical dialogue, if offered in new forms as a distributed social practice arranged and supported by the professional skills of philosopher, shows some promise of widening the boundaries of the (...) examined life. (shrink)
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∀.
Leggett formulated an inequality that seems to generalize the Bell theorem to non-local hidden variable theories. Leggett inequality is violated by quantum mechanics, as was confirmed by experiment. However, a careful analysis reveals that the theory applies to a class of local theory. Contrary to what happens in the derivation of Bell inequality, it is not necessary to make the hypothesis of outcome independence to derive the Leggett inequality.
