Connections Between BCK-algebras and Difference Posetse

We discuss the interrelations between BCK-algebras and posets with difference. Applications are given to bounded commutative BCK-algebras, difference posets, MV-algebras, quantum MV-algebras and orthoalgebras.     

A Common Abstraction of MV-Algebras and Abelian l-groups

We investigate the class of strongly distributive pregroups, a common abstraction of MV-algebras and Abelian l-groups which was introduced by E.Casari. The main result of the paper is a representation theorem which yields both Chang's representation of MV-algebras and Clifford's representation of Abelian l-groups as immediate corollaries.     

Free Łukasiewicz and Hoop Residuation Algebras

Hoop residuation algebras are the {, 1}-subreducts of hoops; they include Hilbert algebras and the {, 1}-reducts of MV-algebras (also known as Wajsberg algebras). The paper investigates the structure and cardinality of finitely generated free algebras in varieties of k-potent hoop residuation algebras. The assumption of k-potency guarantees local finiteness of the varieties considered. It is shown that the free algebra on n generators in any of these varieties can be represented as a union of n subalgebras, each of which is a copy of the {, 1}-reduct of the same finite MV-algebra, i.e., of the same finite product of linearly ordered (simple) algebras. The cardinality of the product can be determined in principle, and an inclusion-exclusion type argument yields the cardinality of the free algebra. The methods are illustrated by applying them to various cases, both known (varieties generated by a finite linearly ordered Hilbert algebra) and new (residuation reducts of MV-algebras and of hoops).     

An Elementary Presentation of the Equivalence Between MV-algebras and l-groups With Strong Unit

Aim of this paper is to provide a self-contained presentation of the natural equivalence between MV-algebras and lattice-ordered abelian groups with strong unit.     

A non-commutative generalization of Łukasiewicz rings

The goal of the present article is to extend the study of commutative rings whose ideals form an MV-algebra as carried out by Belluce and Di Nola [1] to non-commutative rings. We study and characterize all rings whose ideals form a pseudo MV-algebra, which shall be called here generalized Łukasiewicz rings. We obtain that these are (up to isomorphism) exactly the direct sums of unitary special primary rings.     

The Dual Adjunction between MV-algebras and Tychonoff Spaces

We offer a proof of the duality theorem for finitely presented MV-algebras and rational polyhedra, a folklore and yet fundamental result. Our approach develops first a general dual adjunction between MV-algebras and subspaces of Tychonoff cubes, endowed with the transformations that are definable in the language of MV-algebras. We then show that this dual adjunction restricts to a duality between semisimple MV-algebras and closed subspaces of Tychonoff cubes. The duality theorem for finitely presented objects is obtained by a further specialisation. Our treatment is aimed at showing exactly which parts of the basic theory of MV-algebras are needed in order to establish these results, with an eye towards future generalisations.     

Frames and MV-algebras

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 (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 (Ω(A), K) analogous to the case of C (X, A) embedding into Hom (Ω(A), Ω (X)). 1991 Mathematics Subject Classification: 06F20, 06F25, 06D30 Presented by Ewa Orlowska     

Duality Theory and Skeleta for Semisimple MV-Algebras

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

The Intimate Relationship Between the McNaughton and the Chinese Remainder Theorems for MV-algebras

We show the intimate relationship between McNaughton Theorem and the Chinese Remaindner Theorem for MV-algebras. We develop a very short and simple proof of McNaughton Theorem. The arguing is elementary and right out of the definitions. We exhibit the theorem as just an instance of the Chinese theorem. Since the variety of MV-algebras is arithmetic, the Chinese theorem holds for MV-algebras. However, to make this paper self-contained and entirely elementary, we include a simple proof of this theorem inspired in Ferraioli and Lettieri (Math Logic Q 1:27–43, 2011).     

Quasivarieties Generated by Simple MV-algebras

In this paper we show that the quasivariety generated by an infinite simple MV-algebra only depends on the rationals which it contains. We extend this property to arbitrary families of simple MV-algebras.     

The Legitimacy of Pseudo‐Expert Discourse in the Public Sphere

This article examines the role of expertise in public debate, specifically the ways in which expertise can be mimicked and deployed as “pseudo‐expert discourse” to generate legitimacy for views that have otherwise been discredited. The article argues that pseudo‐expert discourse having a clear public health or safety impact should be regulated. There have been some attempts to legally regulate this speech through various means; however, these attempts at regulation have been met with fierce resistance, because of free‐speech concerns. The article suggests that these appeals to free speech in the context of pseudo‐expert discourse are both misguided and misplaced. Moreover, because speakers with the relevant expertise or perceived expertise are able to secure uptake of their views, they have a moral responsibility to not deceive or mislead audiences, and may also have various legal responsibilities.     

Perfect MV-algebras are categorically equivalent to abelianl-groups

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.Presented byDaniele Mundici     

Qualia im Knotenpunkt zwischen Leib und Seele: „Argumentatives“ Dilemma in der gegenwärtigen Diskussion über die Subjektivität mentaler Zustände

Qualia in the node-point between mind and body: Dilemma of present discussion about the subjectivity of mental states. The present discussion about qualia shows a bewildering variety of different positions. We show implicit assumptions about brain, subject, and qualia of this complex discussion. By means of three assumptions we divide the discussion about qualia into three different positions (proposition, opposition, intermediate solutions). These positions and their exemplaric authors are briefly presented along the lines of the three assumptions. The next step shows how each position solves the dilemma which arises if one relates all three assumptions by eliminating at least one of the three assumptions. Finally, general problems in the discussion of qualia are shown by means of which the dilemma of the relation between brain, subject and qualia may be brought closer to a solution without eliminating one assumption.     

Set-Theoretic Absoluteness and the Revision Theory of Truth

We describe the solution of the Limit Rule Problem of Revision Theory and discuss the philosophical consequences of the fact that the truth set of Revision Theory is a complete 1/2 set.     

Having a voice and getting a hearing: An educational perspective on free speech in a plural society

This paper examines Ronald Dworkin's claim that the right to free speech does not include a right to circumstances that encourage citizens to speak nor a right to competent and sympathetic understanding on the part of listeners. Drawing on familiar arguments for the existence of other human rights, the paper challenges Dworkin's claim. Even if, however, the challenge fails and it is not possible to show that there is such a right, that is not the end of the story. It is argued that democratic societies should try to foster conditions in which citizens are encouraged to speak and are listened to sympathetically in the interests of the well-being and flourishing of the polity. The important role education has to play in this is explored.     

Bounded contraction and Gentzen-style formulation of Łukasiewicz logics

In this paper, we consider multiplicative-additive fragments of affine propositional classical linear logic extended with n-contraction. To be specific, n-contraction (n 2) is a version of the contraction rule where (n+ 1) occurrences of a formula may be contracted to n occurrences. We show that expansions of the linear models for (n + 1)- valued ukasiewicz logic are models for the multiplicative-additive classical linear logic, its affine version and their extensions with n-contraction. We prove the finite axiomatizability for the classes of finite models, as well as for the class of infinite linear models based on the set of rational numbers in the interval [0, 1]. The axiomatizations obtained in a Gentzen-style formulation are equivalent to finite and infinite-valued ukasiewicz logics.Presented by Jan Zygmunt     

Desires in Palliative Medicine. Five Models of the Physician‐Patient Interaction on Palliative Treatment Related to Hellenistic Therapies of Desire

In this paper, we explore the desires that play a role at the palliative stage and relate them to various approaches to patient autonomy. What attitude can physicians and other caregivers take to the desires of patients at the palliative stage? We examine this question by introducing five physicians who are consulted by Jackie, an imaginary patient with metastatic lung carcinoma. By combining the models of the physician-patient relationship developed by Emanuel and Emanuel (1992) and the Hellenistic approaches to desires analyzed by Nussbaum (1994), five different ways of dealing with desires in the context of palliative care are sketched. The story of Jackie shows that desires are to a certain extent responsive to reasoning. In the palliative process, that can be a reason to devote attention to the desires of patients and caregivers and to determine which desires need to be fulfilled, which are less important, and how they are linked to emotions the patient has.