An l-hemi-implicative semilattice is an algebra \\) such that \\) is a semilattice with a greatest element 1 and satisfies: for every \, \ implies \ and \. An l-hemi-implicative semilattice is commutative if if it satisfies that \ for every \. It is shown that the class of l-hemi-implicative semilattices is a variety. These algebras provide a general framework for the study of different algebras of interest in algebraic logic. In any l-hemi-implicative semilattice it is possible to define an (...) derived operation by \ \wedge \). Endowing \\) with the binary operation \ the algebra \\) results an l-hemi-implicative semilattice, which also satisfies the identity \. In this article, we characterize the commutative l-hemi-implicative semilattices. We also provide many new examples of l-hemi-implicative semilattice on any semillatice with greatest element. Finally, we characterize congruences on the classes of l-hemi-implicative semilattices introduced earlier and we characterize the principal congruences of l-hemi-implicative semilattices. (shrink)

This work extend to residuated lattices the results of [7]. It also provides a possible generalization to this context of frontal operators in the sense of [9].Let L be a residuated lattice, and f : Lk → L a function. We give a necessary and sufficient condition for f to be compatible with respect to every congruence on L. We use this characterization of compatible functions in order to prove that the variety of residuated lattices is locally affine complete.We study (...) some compatible functions on residuated lattices which are a generalization of frontal operators. We also give conditions for two operations P(x, y) and Q(x, y) on a residuated lattice L which imply that the function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x \mapsto min\{y \in L : P(x, y) \leq Q(x, y)\}}$$\end{document} when defined, is equational and compatible. Finally we discuss the affine completeness of residuated lattices equipped with some additional operators. (shrink)

Citizens need accurate news to govern themselves effectively in a democratic society. Journalists argue editorial independence is necessary to ensure that the integrity of news is not compromised. However, the economic characteristics of news create conflicts between the ideal of independence and the need to pay production costs. This study analyzes those conflicts and the economic tools for resolving them. The analysis suggests ways to balance independence and economic necessity without violating mutual ethical obligations shared by journalists, audiences, and advertisers. (...) Independence, along with a good budget, tends to make for quality journalism. —Michael Wolff, The Man Who Owns the News (p. 225). (shrink)

A subresiduated lattice is a pair, where A is a bounded distributive lattice, D is a bounded sublattice of A and for every there exists the maximum of the set, which is denoted by. This pair can be regarded as an algebra of type (2, 2, 2, 0, 0), where. The class of subresiduated lattices is a variety which properly contains the variety of Heyting algebras. In this paper we study the subvariety of subresiduated lattices, denoted by, whose members satisfy (...) the equation. Inspired by the fact that in any subresiduated lattice whose order is total the previous equation and the condition for every are satisfied, we also study the subvariety of generated by the class whose members satisfy that for every. (shrink)

This study compares two uniquely developed tools for engaging undergraduate business ethics students in case discussions: paper-based cases and interactive digital games. The cases we developed address borderline instances of sexual harassment and racism in the workplace and were used to facilitate students’ affective appreciation of the content of course lectures and readings. The purpose of the study was to assess the relative effectiveness of these two tools as teaching aids in increasing affective learning. Pre- and post-test surveys thus focused (...) on affective learning outcomes. These included change in student perceptions of the importance of the topics, feelings of agency, perceptions of improved self-reliance, and confidence. Results showed that digital cases are at least as effective as static cases in terms of their affective learning efficacy, and that digital serious games spur students to reflect on themselves and others more effectively than static cases. (shrink)

We study some operations that may be defined using the minimum operator in the context of a Heyting algebra. Our motivation comes from the fact that 1) already known compatible operations, such as the successor by Kuznetsov, the minimum dense by Smetanich and the operation G by Gabbay may be defined in this way, though almost never explicitly noted in the literature; 2) defining operations in this way is equivalent, from a logical point of view, to two clauses, one corresponding (...) to an introduction rule and the other to an elimination rule, thus providing a manageable way to deal with these operations. Our main result is negative: all operations that arise turn out to be Heyting terms or the mentioned already known operations or operations interdefinable with them. However, it should be noted that some of the operations that arise may exist even if the known operations do not. We also study the extension of Priestley duality to Heyting algebras enriched with the new operations. (shrink)

In this paper we introduce and study a variety of algebras that properly includes integral distributive commutative residuated lattices and weak Heyting algebras. Our main goal is to give a characterization of the principal congruences in this variety. We apply this description in order to study compatible functions.

A história do livro é uma invenção alemã nascida das celebrações de Gutenberg, festejadas anualmente naquele país. No último terço do século XIX, em França, Durkheim desenvolveu uma escola sociológica influente que pretendeu anexar a história. Contra o que se opôs um dos seus companheiros da Escola superior normal, Henri Berr. Desde logo acompanhado pelo jovem Lucien Febvre, criou a Revue de synthèse que abriu caminho aos Annales e fundou a colecção da Evolution de L'Humanité, cujos cem volumes deveriam estudar (...) os grandes momentos da história humana. De entre os volumes previstos, figurava um dedicado à Apparition du Livre que demorou a surgir. Paralelamente Berr e Febvre organizaram um trabalho interdisciplinar fecundo, o primeiro com o Centre de Synthése, o segundo com a publicação de uma Encyclo­pédie française, o que renovou a escola histórica francesa. A Apparition du Livre, publicada em 1959, inscreve-se neste contexto, mas ficou de certa forma incompleta na medida em que se deveria ter inscrito, mais claramente, no quadro de uma história geral das comunicações que se começa hoje a desenvolver. (shrink)

Review of Spiritual Treasures: Esotericism in the Finnish Art World 1890–1950, edited by Nina Kokkinen and Lotta Nylund.

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)