Corruption as a global hindrance to promoting ethics,integrity, and sustainable development in Tanzania: the role of the anti-corruption agency

Corruption is the single greatest challenge that erodes and defeats efforts made by many nations, especially in the developing world, towards sustainable development and towards the promotion and strengthening of democratic institutions and values. This article lays out international norms of ethics and integrity, reflected also in Tanzanian norms. It argues that strategic decision is imperative and a ‘Good Governance Architecture' is meant to provide a working solution to curb unethical behaviour, corruption, and the culture of impunity. This working solution – which involves economic and institutional reforms, prevention strategies, enforcement, political will, transparency, accountability, popular participation, the rule of law, and the democratic space – goes further towards the root cause of the problem than legal norms do.     

Memory conjunction clusters: Influence of familiarity and recollection

In the memory conjunction paradigm, the number of times that constituents of conjunction lures were studied and the method of presentation were varied. In two experiments, participants were presented with eight parent items that could be recombined at test to form a conjunction lure. The constituents that were shared between the parent items and the conjunction lures were either presented in the same words (e.g., blackmail and jailbird presented four times each for the conjunction lure blackbird) or in different words (e.g., the targets footstool, footlocker, foothill, footbridge, baseball, softball, basketball, and golfball for the conjunction lure football). In both experiments, rates of false recognition were higher in the Different condition as opposed to the Same condition. These results provide evidence that participants in the Same condition were able to utilise a recall-to-reject strategy by remembering the repeatedly presented parent word. In the Different condition, participants were not able to utilise that strategy and instead relied on the familiarity of the repeatedly presented constituents which led to higher rates of false recognition.     

Understanding Asian parenting from a Rasch perspective

This study examines the factor structure of Asian child‐reported parenting from a Rasch perspective. Participants comprised 291 sixth graders (11 to 13 years) in Singapore. Six different aspects of parenting were measured, namely warmth, rejection, structure, chaos, autonomy support, and coercion. Rasch Analysis was used to transform ordinal data into linear measures; category functioning was examined; residual‐based principal components were analysed; differential item functioning was assessed; and items and subjects that were misfitting were removed. Results showed that parenting comprised six dimensions, namely warmth, autonomy support, structure‐control, structure‐warmth, chaos, and negative parenting. The findings suggest that it is important for Asian parents to provide guidance to their children (in structure‐control and structure‐warmth) and reaffirms the relevance of warmth in Asian parenting.     

Axiomatic world theory: An overview the general theory of evolution in brief

The world, its many subsystems and all their theories, starting with logic, can be reduced to two related functions: a combinatorial system generator and a hamiltonian system organizer. These can be derived, in turn, from an Axiom of Lawfulness, the expansion being guided by pseudo‐category and pseudo‐functor analysis to produce an axiomatic theory of the world or general theory of evolution. Specifically, world evolution is generated by a constrained combinatorial world generator, F:G_(X), deduced from two related axioms: I. The Axiom of World Lawfulness and II. The Axiom of World Constraint Constants, c = c₁, c₂, of primordial physical combinatee (substance), c₁, and physical combinator (motion), c₂.

Axiom I postulates a lawful analysis by an analyzer adhering to appropriate coordinate systems, CS, of a lawful analysand obeying a conservation law, X = X. The analysand consists of a base combinatee (the set and elements), X = {x₁, x₂,… x_n}, and a base combinator, namely, the universal Boolean operator, NOR = NOT + OR. Base combinatee and combinator both have attributes of quantity combinatorially generated by NOR operating on the universal number, 1, and of quality generated by NOR operating on the universal dimensions, MLT (mass, length, time), including the null sets.

Axiom II fixes the base constants, c, = c₁, c₂, thereby converting X to material substance using c₁ and NOR to material motion using c₂. This comprehensive, quality and quantity‐competent foundational science is called Universal Combinatorics. Its elements comprise the logical alphabet or metavector, A = {c, 1, MLT; X, NOR}, where c is obtained from the remaining terms. These give: (1) the attributive pseudo‐functor, F = P_(c,1,MLT), where P is the power set of the indicated attributes, and (2) the logic generator, G_(X), where G = NOR_(NOR). F then maps G_(X) into world evolution, F:G_(X) → world evolution, as follows:

Expanding the abstract generator, F₁:G,_(x), with world constants eliminated, i.e., c = 0, generates Universal Grammar consisting of (1) the substantive content of the abstract science chain running from linguistic grammar to mathematics and logic and (2) a comprehensive epistemology equivalent to an explicit theory of the strategic aspects of the scientific method, including a universal hamiltonian theory structure informally related to a mathematical category. The four epistemological theorems are:

1. I. The Combinatorial System Generator, F:G_(X), (read as “The attributive functor, F, maps the logic generator, G_(X), into world theory” or “The world is an attributive combinatorial function of logic").

2. II. The Hamiltonian System Operating Theorem, h (an abstract theory‐category structure).

3. III. The System Stability Theorem, PI?, where PI is the extremal Performance Index or controlling law.

4. IV. The Intersystem Abstraction Ranking Theorem given by the Attributive Functor/ Function, F.

F₂ admits the world constants, c > 0, to materialize the grammar generator, G_(X), to an homologous concrete Euler combinatorial physical wave generator, namely, the superstring equation of quantum theory, E_(NI) = A(σ,τ), where E is the permutational function, NI, is the set of nonintegers and the solution is the dual amplitude, σ,τ. Expanding generates the elementary particles of nonadaptive physics and, by inference, the substantive content of Universal Physics consisting of three additional primary systems comprising the world, where a primary system is defined as one having a distinct but derivative extremal controlling law:

1. I. Nonadaptive physics and chemistry (harmonic hamiltonian wave systems) : Minimize Action, subject to conservation constraints.

2. II. Adaptive physics or biology (membrane bound duplicating polymer‐copolymer hamiltonian systems) : Maximize Survival, subject to energy constraints.

3. III. Sentient physics or sociopsychology (neuromatrix hamiltonian systems) : Maximize subjective Happiness, subject to survival constraints and

4. IV. Representational physics or language (a symbolic combinatorial routine): Maximizes the Information Gain, subject to happiness constraints.

The world can then be viewed as a perpetual superfluid computer implicitly using the epistemology of Axiom I as a world program to process the physical data base, c > 0, of Axiom II into world evolution. After evolving through Systems I and II, mankind, i.e., System III, evolves as an internal metacomputer which makes the combinatorial program explicit and uses it to put all four primary systems in standard hamiltonian theory (pseudo‐category) format and terminology. This can be viewed as a generalization of the Darwinian variation‐and‐selection theme in which combinatorial‐variation is recursively hamiltonian‐selected thereby incrementing world logic and logic constraints on successive primary systems. Because Universal Physics and Universal Grammar are functor‐related homologous concrete and abstract combinatorial pseudocategories, related by a pseudo‐functor, thus, differing only in the presence and absence, respectively, of the World Constants, c ≥ 0, they constitute, ipso facto, Universal Science (Formal Philosophy, World Evolution, World Unification, Explicit Theory of Everything, ETOE, or Axiomatic World Theory).

QED: Because intricate verified predictions, ranging from particles to personality types, mental disorders, political parties and the abstract sciences, result from a system which is merely expanding to fill its possibility set, it is concluded that the world is lawful and that this means it is an object deterministic but not fully analytically determinable combinatorial system. In the object domain, the world is system‐number complete at four. Dually, in the analytical codomain, understanding of it is approximately complete, as measured by a world information gain function. Hence, the dualistic, analysand‐analyzer world program is finite and has dualistic completion criteria, as required of an involuted program.     

The relationship between parental involvement,self-regulated learning,and reading achievement of fifth graders: a path analysis using the ECLS-K database

This study examined the relationship between parental involvement, self-regulated learning (SRL), and reading achievement through analyzing the fifth grade data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998–1999 (ECLS-K). The results identified six dimensions of parental involvement that are likely to foster SRL of fifth graders: School Involvement, TV Rules, Homework Help, Homework Frequency, Parental Education Expectations, and Extracurricular Activities. Of these three dimensions, Parental Education Expectations, School Involvement, and Homework Help, were found to have stronger effects on SRL; Parental Education Expectations was found to have the strongest beneficial effect on SRL. The results also suggest that SRL mediates the relationship between parental involvement and reading achievement. These results provide a framework for parents to help their children develop SRL skills and guide educators and school administrators as they intend to increase parental involvement and its effectiveness.     

Maximum likelihood estimation of the joint covariance matrix for sections of tests given to distinct samples with application to test equating

Consider an old testX consisting ofs sections and two new testsY andZ similar toX consisting ofp andq sections respectively. All subjects are given testX plus two variable sections from either testY orZ. Different pairings of variable sections are given to each subsample of subjects. We present a method of estimating the covariance matrix of the combined test (X ₁, ...,X _s ,Y ₁, ...,Y _p ,Z ₁, ...,Z _q ) and describe an application of these estimation techniques to linear, observed-score, test equating.The author is indebted to Paul W. Holland and Donald B. Rubin for their encouragement and many helpful comments and suggestions that contributed significantly to the development of this paper.This research was supported by the Program Statistics Research Project of the ETS Research Statistics Group.     

The Melancholy Boy and the Religion of Humor: The Case of S. S. Adams

Drawing on earlier writings (Capps, Men, religion, and melancholia: James, Otto, Jung, and Erikson, 1997, 2004) in which I argue that male melancholia has its origins in the boy’s emotional separation from his mother at age 3–5 years old, and that the three main forms of male religion—honor, hope, and humor—are responses to this loss, I focus in this article on S. S. Adams, the inventor of several practical jokes, as an illustration of the religion of humor. I suggest that Adams, son of Danish immigrants, coped with his melancholia through the invention of practical jokes, including the Dribble Glass, the Razzberry Cushion, and the Joy Buzzer. I contend that these inventions have similar iconic value in the religion of male melancholia to the prayer cards, rosary beads, and votive candles of traditional Christianity. I also propose that the S. S. Adams Factory in Neptune, NJ, USA may be viewed as a pilgrimage site for devotees of male melancholic religion.     

Differential Method of Characterizing Gait Strategies From Step Lengths and Frequencies: Strategy of Velocity Modulation

The differential method consists of the analysis of the variation of gait parameters length, frequency, and velocity with respect to their mean values, respectively, ΔL = L — L_m , Δf = f — f_m , and Δv = v – v_m , where L_m , f_m , and v_m represent the mean values of those parameters. Assuming that the strategy of modulation of velocity implies that L and f are functions of v and that statistical analyses of ratios ΔL/Δv and Δf/Δv have established that there is a very significant linear correlation, close to 1, between those ratios, the mathematical procedure allows one to determine the equation of step length, L = a · f + b · v + K, where a and b are the slope and the intercept of the linear regression and K is close to L_m . The equation was experimentally tested on 140 gait sequences performed by 6 participants and for gait velocities ranging from 0.6 to 2.2 m/s and was found to be very representative of all individual values. The differential method provides another way of using the derivative of velocity, v = L·f, to characterize the strategy of velocity modulation, which then permits one to determine the linear equation of velocity, v = f · L_m + L · f_m — L_m · f_m , and to show that the respective parts played by each parameter in the progression velocity are approximately equal. The author establishes the uniqueness of the different linear adjustments and discusses the differential method's own modes of use, that is, interindividually or globally.     

REVIEWS

Books Reviewed in this Article: Religion and Philosophy, by FREDERICK C. COPLESTON. A History of Philosophy. Volume IX: Maine de Biran to Sartre, by FREDERICK C. COPLESTON. Friedrich Nietzsche, Philosopher of Culture, by FREDERICK C. COPLESTON. The Gay Science, by FRIEDRICH NIETZSCHE, translated with commentary by WALTER KAUFMANN. Nietzsche, Philosopher, Psychologist, Antichrist, by WALTER KAUFM ANN, 4th Edition. Critique of Earth (Gifford Lectures, Second Series), by AREND TH. VAN LEEUWEN. Critique of Heaven (Gifford Lectures, First Series), by AREND TH. VAN LEEUWEN. Collected Works: Vol. I: Marx; 1835–1843, by KARL MARX and FREDERICK ENGELS. Roads to Consciousness, by SYDNEY MENDEL. Art and the Imagination, A Study in the Philosophy of Mind, by ROGER SCRUTON. Dealing with Deviants, by STUART WHITELEY, DENNIE BRIGGS and MERFYN TURNER. Two Old Testament Theologies. A Comparative Evaluation of the Contributions of Eichrodt and von Rad to our Understanding of the Nature of Old Testament Theology, by D.G. SPRIGGS. Christian Initiation, by HUGH M. RILEY. Idem. Vol. 6, Crescentianus - Innocentia. Lexikon der christlichen Ikonogruphie, edited by WOLFGANG BRAUNFELS. Vol. 5, Ikonographie der Heiligen, Aaron - Crescentianus. Idem, Vol 7, lnnozenz - Melchisedech. Christian Political Theory and Church Politics in the Mid-Twelfth Century: The Ecclesiology of Gratian's Decretum, by STANLEY CHODOROW. La Teoria del Naturale e del Soprannaturale secondo S. Tommaso d'Aquino, by GIACOMO CROSIGNANI. Consubstantiel et Transsubstantiation, by PAUL-LAURENT CARLE, O.P. The Covenant Sealed: The Development of Puritan Sacramental Theology in Old and New England, 1570–1720, by E. BROOKS HOLIFIELD. The Eucharist Today: Studies in Series 3, edited by R.C.D. JASPER. Le Ralliement du Clergé Français à la Morale Liguorienne, by JEAN GUERBER. New Perspectives in Moral Theology, by CHARLES E. CURRAN. Christian Ethics and the Problems of Society, by ROGER CHARLES, SJ. Origins of the Theology of Hope, by M. DOUGLAS MEEKS. International Glossary of Abbreviations for Theology and Related Subjects, compiled by SIEGFRIED SCHWERTNER.     

Effects of response type on pigeons' sensitivity to variation in reinforcer amount and reinforcer delay

Twelve pigeons, divided into two groups, responded on concurrent nonindependent variable-interval schedules to obtain access to grain by either pecking keys or pressing treadles. Either the amount of grain or the delay to the receipt of grain was varied in separate conditions to determine the sensitivity of relative responding to variation in reinforcer amount (s_A), the sensitivity to variation in reinforcer delay (s_D), and s_A/s_D, a measure related to self-control. There were no significant differences between the two groups in the values of s_A, s_D, and s_A/s_D. These results suggest that the values of s_A, s_D, and s_A/s_D for pigeons may be similar across these two types of responses.     

Calculating Impact Factor: How Bibliographical Classification of Journal Items Affects the Impact Factor of Large and Small Journals

As bibliographical classification of published journal items affects the denominator in this equation, we investigated how the numerator and denominator of the impact factor (IF) equation were generated for representative journals in two categories of the Journal Citation Reports (JCR). We performed a full text search of the 1st-ranked journal in 2004 JCR category “Medicine, General and Internal” (New England Journal of Medicine, NEJM, IF = 38.570) and 61st-ranked journal (Croatian Medical Journal, CMJ, IF = 0.690), 1st-ranked journal in category “Multidisciplinary Sciences” (Nature, IF = 32.182) and journal with a relative rank of CMJ (Anais da Academia Brasileira de Ciencias, AABC, IF = 0.435). Large journals published more items categorized by Web of Science (WoS) as non-research items (editorial material, letters, news, book reviews, bibliographical items, or corrections): 63% out of total 5,193 items in Nature and 81% out of 3,540 items in NEJM, compared with 31% out of 283 items in CMJ and only 2 (2%) out of 126 items in AABC. Some items classified by WoS as non-original contained original research data (9.5% in Nature, 7.2% in NEJM, 13.7% in CMJ and none in AABC). These items received a significant number of citations: 6.9% of total citations in Nature, 14.7% in NEJM and 18.5% in CMJ. IF decreased for all journals when only items presenting original research and citations to them were used for IF calculation. Regardless of the journal’s size or discipline, publication of non-original research and its classification by the bibliographical database have an effect on both numerator and denominator of the IF equation. Preliminary results of the study were presented at the 2006 ORI Research Conference on Research Integrity, Tampa, FL, December 1–3, 2006.     

Reasons and Entailment

What is the relation between entailment and reasons for belief? In this paper, I discuss several answers to this question, and I argue that these answers all face problems. I then propose the following answer: for all propositions p ₁,…,p _n and q, if the conjunction of p ₁,…, and p _n entails q, then there is a reason against a person’s both believing that p ₁,…, and that p _n and believing the negation of q. I argue that this answer avoids the problems that the other answers to this question face, and that it does not face any other problems either. I end by showing what the relation between deductive logic, reasons for belief and reasoning is if this answer is correct.     

Genetic associations with reflexive visual attention in infancy and childhood

This study elucidates genetic influences on reflexive (as opposed to sustained) attention in children (aged 9–16 years; N = 332) who previously participated as infants in visual attention studies using orienting to a moving bar (Dannemiller, 2004). We investigated genetic associations with reflexive attention measures in infancy and childhood in the same group of children. The genetic markers (single nucleotide polymorphisms and variable number tandem repeats on the genes APOE, BDNF, CHRNA4, COMT, DRD4, HTR4, IGF2, MAOA, SLC5A7, SLC6A3, and SNAP25) are related to brain development and/or to the availability of neurotransmitters such as acetylcholine, dopamine, or serotonin. This study shows that typically developing children have differences in reflexive attention associated with their genes, as we found in adults (Lundwall, Guo & Dannemiller, 2012). This effort to extend our previous findings to outcomes in infancy and childhood was necessary because genetic influence may differ over the course of development. Although two of the genes that were tested in our adult study (Lundwall et al., 2012) were significant in either our infant study (SLC6A3) or child study (DRD4), the specific markers tested differed. Performance on the infant task was associated with SLC6A3. In addition, several genetic associations with an analogous child task occurred with markers on CHRNA4, COMT, and DRD4. Interestingly, the child version of the task involved an interaction such that which genotype group performed poorer on the child task depended on whether we were examining the higher or lower infant scoring group. These findings are discussed in terms of genetic influences on reflexive attention in infancy and childhood.     

The Two Faces of Evidentialism

In this paper I hope to demonstrate two different (and seemingly independent) ways of interpreting the tenets of evidentialism and show why it is important to distinguish between them. These two ways correspond to those proposed by Feldman (Philosophy and Phenomenological Research, 60, 667–695, 2000, Evidentialism: Essays in epistemology, Oxford University Press, 2004) and Adler (Midwest Studies in Philosophy, 23, 267–285, 1999, Beliefs own ethics, MIT Press, 2002). Feldman’s way of interpreting evidentialism makes evidentialism a principle about epistemic justification, about what we ought to believe. Adler’s, on the other hand, makes evidentialism a principle about how we come to believe, what it is, broadly speaking, rational for us to believe. Having identified this difference, I consider two complaints levied against evidentialism, namely what I call the threshold problem and what I call the availability problem, and hope to show that: (a) only an independent, bracketed justification principle of evidentialism can deal with those problems; (b) the rationality principle of evidentialism is not in fact independent from the justification principle; (c) the rationality principle is hard to motivate; and that (d) in the final analysis the argument for the justification principle depends on the rationality principle. I thus conclude that although it may be convenient for evidentialists to treat these two principles as independent, such an independence cannot be maintained.

List of contributors

Abstract

Integrity and Change: Mental Health in the Marketplace, Eileen Smith (ed.), London: Routledge, 1997, 200 pp., £45 hb., £14.99 pb.

Staff Supervision in a Turbulent Environment: Managing Process and, Task in Front-line Services, Lynette Hughes and Paul Pengelly, London: Jessica Kingsley Publishers, 1997, 150 pp., £14.95 pb.

An Introduction to Object Relations, Lavina Gomez, London: Free Association Books, 1997, 245 pp., £15.95 pb.

Countertransference in Psychoanalytic Psychotherapy with Children and Adolescents, John Tsiantis, Anne Marie Sandier, Dimitris Anastasopolous and Brian Martindale (eds), London: Karnac, 1996, 176 pp., £17.95 pb.

Working with Drug Family Support Groups, Paul Lockley, London: Free Association Books, 1996, 275 pp., £15.95 pb.

The Cradle of Violence, Stephen Wilson, Oxford: Jessica Kingsley Publishers, 1995, 157 pp., £14.95 pb.

Art, Psychotherapy and Psychosis, Katherine Killick and Joy Schaverien (eds), London: Routledge, 1997, 267 pp., £50 hb., £16.99 pb.     

Coordination of Emotions in Mother–Infant Dialogues

Eleven infant–mother dyads in Crete were videod during spontaneous interactions at home, from the second to the sixth month of life. Micro‐analysis was used to investigate‘coordination'and ‘non‐matching’ of facial expressions of emotion. ‘Emotional coordination’ was evaluated with four measures: matching of facial expressions, completion when one responded to the other with ‘pleasure’ or ‘interest’, synchrony by matching frequency of change or rhythm of emotional expressions, and attunement when shifts of emotional intensity of the two partners were in the same direction.‘Emotional non‐matching'was coded when neither the infant nor the mother showed interest in interacting with the other. In emotional coordination or non‐matching between mother and infant, who performed first was also recorded. We obtained evidence of emotional matching, synchrony, and attunement. Importantly, the probability of emotional non‐matching by the infant was higher than the probability of emotional matching and completion, indicating a tendency for thoughtful attention or playful rivalry in the responses of infants, who also initiated emotional matching, completion, and non‐matching more frequently than mothers. The probability of expression of emotional matching, completion, and non‐matching changed with age. Both mothers and infants act to obtain sympathetic complementarity of feelings and co‐operative inter‐synchrony of actions. Copyright © 2016 John Wiley & Sons, Ltd.     

Peer Commentaries on James Russell’s Cognitive Development as an Executive Process – in part: A Homeopathic Dose of Piaget

Peter R. Hobson Beyond Agency: Commentary on ‘Cognitive Development as an Executive Process’, p.271 Olivier HoudéExecutive Performance/Competence, and Inhibition in Cognitive Development. Object, Number, Categorization and Reasoning, p.273 Marco W. Battacchi Commentary on ‘Cognitive Development as an Executive Process’, p.275 Peter Bryant Executive Control – A Cause or a Product or Both?, p.276 Jeremy I.M. Carpendale Symbols and Side Effects: Commentary on ‘Cognitive Development as an Executive Process’, p.278 Willis F. Overton Nativism, Empiricism and Developmental Dynamic Action Systems, p.280 Pierre Mounoud What is Homeopathic when you Overdose?, p.282 Joëlle Proust Experience, Action and Theory of Mind, p.285 Elisabeth Pacherie Action Monitoring: Lower, Higher and Intermediate Levels, p.287     

Evidence for morphological composition at the form level in speech production

We investigated in two picture–word-interference experiments whether there is evidence for composition during compound production (Experiment 1). In Experiment 2, we tried to determine the level at which composition takes place. In Experiment 1, shared morphemes between distractor and target (HANDTASCHE, handbag) sped up naming regardless of category membership: semantically opaque (Plaudertasche, chatterbox) and semantically transparent distractors (Reisetasche, travelling bag) facilitated picture naming to a comparable degree. In Experiment 2, targets (BROTMESSER, bread knife) were combined with a simple word distractor (Kuchen, cake) categorically related to a target compound constituent but not related to the compound as a whole. This target was further paired with a categorically related compound distractor (Kochlöffel, wooden spoon). The simple word distractor was also paired with a categorically related compound constituent (BROT, bread). Whenever distractor (e.g., Kochlöffel, Kuchen) and target (BROTMESSER, BROT, respectively) were categorically related, semantic inhibition was observed. Distractors (e.g., Kuchen) related to only one compound constituent did not affect compound production. Taken together, our results indicate that during compound production a single lemma node is activated and that morphological composition takes place at the form level of representation. Current lexical selection mechanisms in language production models are not supported by these data.     

Reviews

Books reviewed: Science and Theology: An Introduction, by JohnPolkinghorne Genesis, Genes, and God: Values and Their Origins in Naturaland Human History, by Holmes Rolston, III Playing God? Genetic Determinism and Human Freedom, by Ted Peters Green Space, Green Time: The Way of Science, by Connie Barlow Reconstructing Nature: The Engagement of Science and Religion , by John Brooke and GeoffreyCantor Whatever Happened to the Soul? Scientific and Theological Portraits ofHuman Nature, Edited by Warren S. Brown, Nancey Murphy, and H.Newton Malony The Turn of the Millennium: An Agenda for Christian Religion in an Age of Science, by Jeffrey G. Sobosan God without the Supernatural: A Defense of Scientific Theism, by Peter Forrest Religion and Creation, by Keith Ward     

On Categorical Equivalences of Commutative BCK-algebras

A commutative BCK-algebra with the relative cancellation property is a commutative BCK-algebra (X;*,0) which satisfies the condition: if a ≤ x, a ≤ y and x * a = y * a, then x = y. Such BCK-algebras form a variety, and the category of these BCK-algebras is categorically equivalent to the category of Abelian ℓ-groups whose objects are pairs (G, G ₀), where G is an Abelian ℓ-group, G ₀ is a subset of the positive cone generating G ⁺ such that if u, v ∈ G ₀, then 0 ∨ (u - v) ∈ G ₀, and morphisms are ℓ-group homomorphisms h: (G, G ₀) → (G′,G′₀) with f(G ₀) ⫅ G′₀. Our methods in particular cases give known categorical equivalences of Cornish for conical BCK-algebras and of Mundici for bounded commutative BCK-algebras (= MV-algebras). This revised version was published online in June 2006 with corrections to the Cover Date.