Interest in corporate social responsibility (CSR) is gaining momentum in academic and managerial circles. However, prior work in the area has paid little attention to how CSR initiatives should be implemented inside the organization. Against this backdrop, this study examines the impact of CSR initiatives on an important stakeholder group—employees. We build and test a comprehensive multilevel framework that focuses on whether employees derive job satisfaction from CSR programs. The proposed model predicts that a manager’s charismatic leadership influences employees’ interpretations (...) about the motives underlying their companies’ engagement in CSR initiatives (intrinsic and extrinsic CSR-induced attributions) which, in turn, influence employee job satisfaction. Hierarchical linear modeling of data from 47 organizational units comprising 438 employees from three world-leading manufacturing organizations shows that when employees think that their manager possesses charismatic leadership qualities, they tend to attribute the organization’s motives for engaging in CSR activities to intrinsic values, which, in turn, are positively associated with job satisfaction. Also, the extent to which managers are perceived as charismatic leaders relates positively to job satisfaction. Interestingly, CSR-induced extrinsic attributions are neither explained by charismatic leadership nor do they predict job satisfaction. Implications for both theory and practice are discussed. (shrink)

Two constructions for adding an involution operator to residuated ordered monoids are investigated. One preserves integrality and the mingle axiom x 2x but fails to preserve the contraction property xx 2. The other has the opposite preservation properties. Both constructions preserve commutativity as well as existent nonempty meets and joins and self-dual order properties. Used in conjunction with either construction, a result of R.T. Brady can be seen to show that the equational theory of commutative distributive residuated lattices (without involution) (...) is decidable, settling a question implicitly posed by P. Jipsen and C. Tsinakis. The corresponding logical result is the (theorem-) decidability of the negation-free axioms and rules of the logic RW, formulated with fusion and the Ackermann constant t. This completes a result of S. Giambrone whose proof relied on the absence of t. (shrink)

The purpose of this paper is first to show that if X is any locally compact but not compact perfect Polish space and stands for the one-point compactification of X, while E X is the equivalence relation which is defined on the Polish group C(X,R +*) by where f, g are in C(X,R +*), then E X is induced by a turbulent Polish group action. Second we show that given any if we identify the n-dimensional unit sphere S n with (...) the one-point compactification of R n via the stereographic projection, while E n , r is the equivalence relation which is defined on the Polish group C r (R n ,R +*) by where f, g are in C r (R n ,R +*), then E n , r is also induced by a turbulent Polish group action. (shrink)

This paper summarizes a theory of cognitive development and elaborates on its educational implications. The theory postulates that development occurs in cycles along multiple fronts. Cognitive competence in each cycle comprises a different profile of executive, inferential, and awareness processes, reflecting changes in developmental priorities in each cycle. Changes reflect varying needs in representing, understanding, and interacting with the world. Interaction control dominates episodic representation in infancy; attention control and perceptual awareness dominate in realistic representations in preschool; inferential control and (...) awareness dominate rule-based representation in primary school; truth and validity control and precise self-evaluation dominate in principle-based thought in adolescence. We demonstrate that the best predictors of school learning in each cycle are the cycle’s cognitive priorities. Also learning in different domains, e.g., language and mathematics, depends on an interaction between the general cognitive processes dominating in each cycle and the state of the representational systems associated with each domain. When a representational system is deficient, specific learning difficulties may emerge, e.g., dyslexia and dyscalculia. We also discuss the educational implications for evaluation and learning at school. (shrink)

This is also where we begin investigating lattices of logics and varieties, rather than particular examples.

What does ‘care’ mean in contemporary society? How are caring relationships practised in different contexts? What resources do individuals and collectives draw upon in order to care for, care with and care about themselves and others? How do such relationships and practices relate to broader social processes? Care shapes people’s everyday lives and relationships and caring relations and practices influence the economies of different societies. This interdisciplinary book takes a nuanced and context-sensitive approach to exploring caring relationships, identities and practices (...) within and across a variety of cultural, familial, geographical and institutional arenas. Grounded in rich empirical research and discussing key theoretical, policy and practice debates, it provides important, yet often neglected, international and cross-cultural perspectives. It is divided into four sections covering: caring within educational institutions; caring amongst communities and networks; caring and families; and caring across the life-course. Contributing to broader theoretical, philosophical and moral debates associated with the ethics of care, citizenship, justice, relationality and entanglements of power, _Critical Approaches to Care_ is an important work for students and academics studying caring and care work in the fields of health and social care, sociology, social policy, anthropology, education, human geography and politics. (shrink)

How can educators create space for students to practice making the worlds we are trying to collectively build? Inspired by genealogies that are grounded in and emerge from social movements, this paper uplifts the possibilities, tensions, and new questions that emerge when we take seriously the role of our classroom pedagogies. The authors offer a reflexive, methodological approach that pushes against the theory/practice divide and that stays with the importance of inhabiting theory through practice. They reflect on the role their (...) classroom pedagogies in enacting their commitments to justice, organizing their offerings around the following themes: (1) Enter, or how their learnings from previous teaching experiences shape praxis through the pauses, recalibrations, and persistent questions they provoke; (2) how they Open and create space in their classrooms through rituals and routines, and toward what ends; and finally, (3) how they aim to Build with their students within and beyond the bounds of the classroom. The authors share the guiding questions that prompted these reflections, as well as the echoes across their offerings, inviting readers to reflect on their own teaching practice in community. (shrink)

Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices.

Equivalences and translations between consequence relations abound in logic. The notion of equivalence can be defined syntactically, in terms of translations of formulas, and order-theoretically, in terms of the associated lattices of theories. W. Blok and D. Pigozzi proved in [4] that the two definitions coincide in the case of an algebraizable sentential deductive system. A refined treatment of this equivalence was provided by W. Blok and B. Jónsson in [3]. Other authors have extended this result to the cases of (...) k-deductive systems and of consequence relations on associative, commutative, multiple conclusion sequents. Our main result subsumes all existing results in the literature and reveals their common character. The proofs are of order-theoretic and categorical nature. (shrink)

Given a positive universal formula in the language of residuated lattices, we construct a recursive basis of equations for a variety, such that a subdirectly irreducible residuated lattice is in the variety exactly when it satisfies the positive universal formula. We use this correspondence to prove, among other things, that the join of two finitely based varieties of commutative residuated lattices is also finitely based. This implies that the intersection of two finitely axiomatized substructural logics over FL + is also (...) finitely axiomatized. Finally, we give examples of cases where the join of two varieties is their Cartesian product. (shrink)

We develop a general algebraic and proof-theoretic study of substructural logics that may lack associativity, along with other structural rules. Our study extends existing work on substructural logics over the full Lambek Calculus [34], Galatos and Ono [18], Galatos et al. [17]). We present a Gentzen-style sequent system that lacks the structural rules of contraction, weakening, exchange and associativity, and can be considered a non-associative formulation of . Moreover, we introduce an equivalent Hilbert-style system and show that the logic associated (...) with and is algebraizable, with the variety of residuated lattice-ordered groupoids with unit serving as its equivalent algebraic semantics. Overcoming technical complications arising from the lack of associativity, we introduce a generalized version of a logical matrix and apply the method of quasicompletions to obtain an algebra and a quasiembedding from the matrix to the algebra. By applying the general result to specific cases, we obtain important logical and algebraic properties, including the cut elimination of and various extensions, the strong separation of , and the finite generation of the variety of residuated lattice-ordered groupoids with unit. (shrink)

Με αφορμή ένα γεωμετρικό αμφορέα του επιγάστριου αττικο-κυκλαδικού τύπου από το νεκροταφείο της Ελεύθερνας, διακοσμημένο με τρεις μετόπες ομόκεντρων κύκλων στη ζώνη της κοιλιάς, συζητούνται τα προβλήματα τυπολογίας και προέλευσης αυτής της χαρακτηριστικής κατηγορίας αγγείων στο φως της νεότερης έρευνας. Η τεχνοτροπία όλων των αμφορέων αυτού του τύπου, δηλ. με δύο ή με τρεις μετόπες ομοκέντρων κύκλων, ακολουθεί πάντοτε τον αττικό ρυθμό, αλλά ενώ η αττική καταγωγή των διμετο- πικών αμφορέων του τύπου ουδέποτε αμφισβητήθηκε, η καταγωγή των τριμετοπικών αμφορέων, που (...) παρουσιάζουν ευρύτατη διάδοση στο Αιγαίο και κυρίως στις Κυκλάδες, άλλοτε αποδίδεται στην Αττική και άλλοτε στις Κυκλάδες. Στη μελέτη αυτή επιχειρείται ένας επαναπροσδιορισμός της τυπολογίας του επιγάστριου ομοκεντρικού αμφορέα και συζητείται διεξοδικά η κατηγορία των αμφορέων με τρεις μετόπες. (shrink)

All known structural extensions of the substructural logic $\textbf{FL}_{\textbf{e}}$, the Full Lambek calculus with exchange/commutativity (corresponding to subvarieties of commutative residuated lattices axiomatized by $\{\vee, \cdot, 1\}$ -equations), have decidable theoremhood; in particular all the ones defined by knotted axioms enjoy strong decidability properties (such as the finite embeddability property). We provide infinitely many such extensions that have undecidable theoremhood, by encoding machines with undecidable halting problem. An even bigger class of extensions is shown to have undecidable deducibility problem (the (...) corresponding varieties of residuated lattices have undecidable word problem); actually with very few exceptions, such as the knotted axioms and the other prespinal axioms, we prove that undecidability is ubiquitous. Known undecidability results for non-commutative extensions use an encoding that fails in the presence of commutativity, so and-branching counter machines are employed. Even these machines provide encodings that fail to capture proper extensions of commutativity, therefore we introduce a new variant that works on an exponential scale. The correctness of the encoding is established by employing the theory of residuated frames. (shrink)

We provide an alternative proof of the decidability of the equational theory of lattices. The proof presented here is quite short and elementary.

It is well known that classical propositional logic can be interpreted in intuitionistic propositional logic. In particular Glivenko's theorem states that a formula is provable in the former iff its double negation is provable in the latter. We extend Glivenko's theorem and show that for every involutive substructural logic there exists a minimum substructural logic that contains the first via a double negation interpretation. Our presentation is algebraic and is formulated in the context of residuated lattices. In the last part (...) of the paper, we also discuss some extended forms of the Kolmogorov translation and we compare it to the Glivenko translation. (shrink)

Background:Withdrawal of treatment is a common practice in intensive care units when treatment is considered futile. Compassion is an important aspect of care; however, it has not been explored much within the context of treatment withdrawal in intensive care units.Objectives:The aim was to examine how concepts of compassion are framed, utilised and communicated by intensive care nurses in the context of treatment withdrawal.Design:The study employed a qualitative approach conducting secondary analysis of an original data set. In the primary study, 13 (...) nurses were recruited from three intensive care units within a large hospital in United Kingdom. Deductive framework analysis was used to analyse the data in relation to compassionate care.Ethical considerations:The primary study was approved by the local Research Ethics Committee and the hospital’s Research and Development services.Findings:Compassionate care was mostly directed to the patient’s family and was demonstrated through care and emotional support to the family. It was predominantly expressed through attempts to maintain the patient’s dignity by controlling symptoms, maintaining patient cleanliness and removing technical apparatus.Conclusion:This study’s findings provide insight about compassionate care during treatment withdrawal which could help to understand and develop further clinicians’ roles. Prioritising the family over the patient raised concerns among nurses, who motivated by compassion, may feel justified in taking measures that are in the interests of the family rather than the patient. Further work is needed to explore the ethics of this. (shrink)

La cité de Panopeus (alias Phanoteus) en Phocide, réputée à l’époque impériale être indigente d’après un célèbre passage de Pausanias – lequel appelle cependant encore commentaire –, peut désormais être mieux connue grâce aux progrès récents de l’exploration archéologique et épigraphique. Ces progrès montrent notamment deux césures au seuil et vers la fin de l’époque classique, en lien respectivement avec l’invasion perse de 480 et la 3e guerre sacrée (356‑346 av. J.‑C.). Parmi les cités phocidiennes, Panopeus demeura à l’époque hellénistique (...) sans doute une cité moyenne, dont la vie est rendue manifeste par deux nouvelles inscriptions, une dédicace à Héraklès et un texte érotique. (shrink)

Seize plaques de marbres du gymnase d’Andros ont été trouvées à l’état fragmentaire. De longueur et largeur irrégulières, mais de hauteur constante, elles vont s’épaississant régulièrement d’un long côté à l’autre. Des graffiti sont inscrits sur le côté vertical et étroit de ces plaques, plus rarement aussi sur un autre côté. Ces plaques rappellent les bancs des gymnases et des palestres où, dans ce que l’on appelle l’ephebeion, les jeunes gens assistaient aux leçons. Les graffiti trouvés dans cette pièce reflètent (...) la vanité des éphèbes. Le soin de la gravure sur deux des plaques (n° 1-2) permet de déduire que les graffiti ont d’abord été inscrits sous les auspices d’un magistrat tel que le gymnasiarque. Le nom de l’éphèbe parvenu à l’âge adulte pouvait être effacé et remplacé par un autre nom, mais la gravure ne révèle plus le même soin. L’étude de la prosopographie d’Andros et du contexte historique permet de dater les plaques du début du IIe s. av. J.-C. leur utilisation s’étendant au cours des IIe et Ier s. av. J.-C. (shrink)

If X is a locally compact Polish space, then LSC denotes the compact Polish space of lower semi-continuous real-valued functions on X equipped with the topology of epi-convergence.Our purpose in this article is to prove the following: if –∞ < α < β < ∞ and –∞ < a < b < ∞, while r ∈ ℕ \ {0}, then the set CV of all f ∈ LSC for which there is u ∈ Cr such that for any v ∈ (...) Cr we have that ∫αβf , v ′)dx ≥ ∫αβf , v )dx is not Borel. (shrink)