We present a model of computation for string functions over single-sorted, total algebraic structures and study some basic features of a general theory of computability within this framework. Our concept generalizes the Blum-Shub-Smale setting of computability over the reals and other rings. By dealing with strings of arbitrary length instead of tuples of fixed length, some suppositions of deeper results within former approaches to generalized recursion theory become superfluous. Moreover, this gives the basis for introducing computational complexity in a BSS-like (...) manner. Relationships both to classical computability and to Friedman's concept of eds computability are established. Two kinds of nondeterminism as well as several variants of recognizability are investigated with respect to interdependencies on each other and on properties of the underlying structures. For structures of finite signatures, there are universal programs with the usual characteristics. For the general case of not necessarily finite signature, this subject will be studied in a separate, forthcoming paper. (shrink)

We study concepts of decidability for subsets of Euclidean spaces ℝk within the framework of approximate computability . A new notion of approximate decidability is proposed and discussed in some detail. It is an effective variant of F. Hausdorff's concept of resolvable sets, and it modifies and generalizes notions of recursivity known from computable analysis, formerly used for open or closed sets only, to more general types of sets. Approximate decidability of sets can equivalently be expressed by computability of the (...) characteristic functions by means of appropriately working oracle Turing machines. The notion fulfills some natural requirements and is hereditary under canonical embeddings of sets into spaces of higher dimensions. However, it is not closed under binary union or intersection of sets. We also show how the framework of resolvability and approximate decidability can be applied to investigate concepts of reducibility for subsets of Euclidean spaces. (shrink)

We present some characterizations of the members of Δta2, that class of the topological arithmetical hierarchy which is just large enough to include several fundamental types of sets of points in Euclidean spaces ℝk. The limit characterization serves as a basic tool in further investigations. The characterization by effective difference chains of effectively exhaustible sets yields only a hierarchy within a subfield of Δta2. Effective difference chains of transfinite (but constructive) order types, consisting of complements of effectively exhaustible sets, as (...) well as another closely related concept, yield a rich hierarchy within the whole class Δta2. The presentation always first reports analogies between Hausdorff's difference hierarchy within the Borel class ΔB2 and Ershov's hierarchy within the class Δ02 of the arithmetical hierarchy; after that the counterparts for Δta2 are developed. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

Continuing the paper [7], in which the Blum-Shub-Smale approach to computability over the reals has been generalized to arbitrary algebraic structures, this paper deals with computability and recognizability over structures of infinite signature. It begins with discussing related properties of the linear and scalar real structures and of their discrete counterparts over the natural numbers. Then the existence of universal functions is shown to be equivalent to the effective encodability of the underlying structure. Such structures even have universal functions satisfying (...) the s-m-n theorem and related features. The real and discrete examples are discussed with respect to effective encodability. Megiddo structures and computational extensions of effectively encodable structures are encodable, too. As further variants of universality, universal functions with enumerable sets of program codes and such ones with constructible codes are investigated. Finally, the existence of m-complete sets is shown to be independent of the effective encodability of structures, and the linear and scalar structures are discussed once more, under this aspect. (shrink)

We present some characterizations of the members of Δta2, that class of the topological arithmetical hierarchy which is just large enough to include several fundamental types of sets of points in Euclidean spaces ℝk. The limit characterization serves as a basic tool in further investigations. The characterization by effective difference chains of effectively exhaustible sets yields only a hierarchy within a subfield of Δta2. Effective difference chains of transfinite order types, consisting of complements of effectively exhaustible sets, as well as (...) another closely related concept, yield a rich hierarchy within the whole class Δta2. The presentation always first reports analogies between Hausdorff's difference hierarchy within the Borel class ΔB2 and Ershov's hierarchy within the class Δ02 of the arithmetical hierarchy; after that the counterparts for Δta2 are developed. (shrink)

I hope you have had no trouble identifying this issue of our journal, even if the cover has been changed slightly. I would like to draw your attention to a more essential improvement in the journal's affairs: namely, that the Editorial Board has been enlarged by four new members. These are the following: Douglas Bridges , Ulrich Kohlenbach , H. Dugald Macpherson , and Pavel Pudlak . Please don't hesitate to contact a fellow editor, in particular the managing editor, if (...) you have suggestions for improving either the editorial procedures or the content and form of MLQ.The aims and scope of our journal are unchanged from the original ones developed by Günter Asser. His name is indissolubly connected with the former “Zeitschrift für Mathematische Logik und Grundlagen der Mathematik ”, now known as “Mathematical Logic Quarterly ”. He was one of the two founding editors and then the editor-in-chief of the journal until the 50th volume appeared about one year ago. Single-handedly, and almost incredibly, he showed that it is possible for one man to be the main editor of a successful highlevel scientific journal throughout half a century. He remains involved in and concerned with the editorial process of MLQ. For example, he carefully looks at every article to be published, faithfully checking almost every line of the final layout.On 26 February 2006, Professor Dr. Günter Asser celebrates his 80th birthday. I would like to take this opportunity, on behalf of the whole readership and of all fellow editors of ZML and MLQ throughout the last 51 years, to congratulate him cordially and to wish him good health and all the best for the future.The present issue starts with a paper directly related to G. Asser's spectrum conjecture. Then there are some papers specially dedicated to him, as well as further contributions, as always scrutinised and then recommended by expert referees. So this turns out to be an appropriate birthday issue. (shrink)

We consider the target-reaching problem in plane scenes for a point robot which has a tactile sensor and can locate the target ray. It might have a compass, too, but it is not able to perceive the coordinates of its position nor to measure distances. The complexity of an algorithm is measured by the number of straight moves until reaching the target, as a function of the number of vertices of the scene. It is shown how the target point can (...) be reached by exhaustive search without using a compass, with the complexity exp). Using a compass, there is a target-reaching algorithm, based on rotation counting, with the complexity O. The decision problem, to recognize if the target cannot be reached because it belongs to an obstacle, cannot be solved by our type of robot. If the behaviour of a robot without compass is periodic in a homogeneous environment, it cannot solve the target-reaching problem. (shrink)

Based on the computation mode introduced in [13], we deal with the time complexity of computations over arbitrary first-order structures.The main emphasis is on parameter-free computations. Some transfer results for solutions of P versus NP problems as well as relationships to quantifier elimination are discussed. By computation tree analysis using first-order formulas, it follows that P versus NP solutions and other results of structural complexity theory are invariant under elementary equivalence of structures.

It is shown that the classes of discrete parts, A ∩ ℕk, of approximately resp. weakly decidable subsets of Euclidean spaces, A ⊆ ℝk, coincide and are equal to the class of ω-r. e. sets which is well-known as the first transfinite level in Ershov's hierarchy exhausting Δ02.

The topological arithmetical hierarchy is the effective version of the Borel hierarchy. Its class Δta 2 is just large enough to include several types of pointsets in Euclidean spaces ℝ k which are fundamental in computable analysis. As a crossbreed of Hausdorff's difference hierarchy in the Borel class ΔB 2 and Ershov's hierarchy in the class Δ0 2 of the arithmetical hierarchy, the Hausdorff-Ershov hierarchy introduced in this paper gives a powerful classification within Δta 2. This is based on suitable (...) characterizations of the sets from Δta 2 which are obtained in a close analogy to those of the ΔB 2 sets as well as those of the Δ0 2 sets. A helpful tool in dealing with resolvable sets is contributed by the technique of depth analysis. On this basis, the hierarchy properties, in particular the strict inclusions between classes of different levels, can be shown by direct constructions of witness sets. The Hausdorff-Ershov hierarchy runs properly over all constructive ordinals, in contrast to Ershov's hierarchy whose denotation-independent version collapses at level ω 2. Also, some new characterizations of concepts of decidability for pointsets in Euclidean spaces are presented. (shrink)

Schon seit ihrer Gründung in den 1970er-Jahren ist die Reihe Germanistische Linguistik (RGL) exponiertes Forum des Faches, dessen Namen sie im Titel führt. Hinsichtlich der thematischen Breite (Sprachebenen, Varietäten, Kommunikationsformen, Epochen), der Forschungsperspektiven (Theorie und Empirie, Grundlagenforschung und Anwendung, Inter- und Transdisziplinarität) und des methodologischen Spektrums ist die Reihe offen angelegt. Das Aufgreifen neuer Trends hat in ihr ebenso Platz wie das Fortführen von Bewährtem. Die Publikationsformen reichen von Monographien und Sammelbänden bis zu Wörterbüchern. Wissenschaftlicher Beirat (ab November 2011): Prof. (...) Dr. Karin Donhauser (Berlin) Prof. Dr. Stephan Elspaß (Augsburg) Prof. Dr. Helmuth Feilke (Gießen) Prof. Dr. Jürg Fleischer (Marburg) Prof. Dr. Stephan Habscheid (Siegen) Prof. Dr. Rüdiger Harnisch (Passau). (shrink)

The aim of the paper is to present and evaluate Bolzano's theory of grounding, that is, his theory of the concept expressed and the relation brought into play by 'because'. In the first part of the paper (Sections 1-4) the concept of grounding is distinguished from and related to three other concepts: the concept of an epistemic reason}, the concept of causality, and the concept of deducibility (i.e., logical consequence). In its second part (Sections 5-7) Bolzano's positive account of grounding (...) is reconstructed in axiomatic form and critically discussed. (shrink)

This study focuses on the altars of the major annual Hopi ceremonials which display ritual objects, the possession and use of which give religious and secular power. With the importance of such objects in mind, an iconographic study of Hopi religion is particularly illuminating. This study aims to demonstrate how to view Hopi altars and is supplemented by a theory of the mechanics of efficacy in the Hopi altar context. The text provides a general introduction to Hopi religious practice and (...) distinguishes three levels of information: 1) the calendrical and ritual contexts of Hopi altars, 2) the functions of these altars within those contexts, and 3) the iconography and iconology of the altars, understood here in a literal sense as the study of the forms and structures of the altars on the one hand and the study of the implicit and explicit symbology of the altars on the other. The book provides keys to understanding through exemplification and typology, and is meant to be of particular use to museums and research libraries. (shrink)

The 18 contributions to this volume deal with a variety of 'tropes', such as metaphor, metonymy, synecdoche, irony, euphemism, antonomasia and hyperbole. Using various approaches or paradigms the authors aim to find answers to the crucial epistemological questions, namely whether and to what extent utterances containing tropes can be said to be true or false.

In a number of very influential publications, Epstein and Hoover (among other authors) have recently argued that a thoroughly micro-foundationalist approach towards economics is unconvincing for metaphysical reasons. However, as we show in this article, this metaphysical/social ontological approach to the debate fails to resolve the status of micro-foundations in the practice of economic modelling. To overcome this, we argue that endogenizing a model—that is, providing micro-foundations for it—correlates with making that model more complex. Specifically, we show that models with (...) more micro-foundations tend to have more parameters or variables. This matters, as there are well-established methodological reasons for preferring models with fewer parameters or variables—ceteris paribus. We therefore conclude that, from a practice-based point of view, micro-foundations are only defensible to the extent that they significantly improve the ability of the relevant model to fit the data of interest. In this way, we arrive at a practice-based, methodological reconceptualization of the debate surrounding the need for micro-foundations in economics. (shrink)

Recent findings suggest that medical students’ moral competence decreases throughout medical school. This pilot study gives preliminary insights into the effects of two educational interventions in ethics classes on moral competence among medical students in Munich, Germany. Between 2012 and 2013, medical students were tested using Lind’s Moral Competence Test prior to and after completing different ethics classes. The experimental group participated in principle-based structured case discussions and was compared with a control group with theory-based case discussions. The pre/post C-scores (...) were compared using a Wilcoxon Test, ANOVA and effect-size calculation. The C-score improved by around 3.2 C-points in the EG, and by 0.2 C-points in the CG. The mean C-score difference was not statistically significant for the EG or between the two groups. There was no statistical significance for the teachers’ influence on C-score. In both groups, students with below-average C-scores improved and students with above-average C-scores regressed. The increase of the C-Index was greater in the EG than in the CG. The absolute effect-size of the EG compared with the CG was 3.0 C-points, indicating a relevant effect. Teaching ethics with PBSCDs did not provide a statistically significant influence on students’ moral competence, compared with TBCDs. Yet, the effect size suggests that PBSCDs may improve moral competence among medical students more effectively. Further research with larger and completely randomized samples is needed to gain definite explanations for the results. (shrink)

Business Ethics: A European Review, EarlyView.

Wittgensteins Philosophie ist nicht auf die „Überwindung der Metaphysik" hin angelegt, sondem auf diejenige ihrer Überwindung. Insofem ist der Schritt zurück zu Wittgenstein zugleich ein Schritt hinaus über die analytische Philosophie. Beherrschendes Ziel des frühen wie des späten Wittgenstein ist es, den Innenraum des sinnvoll Sagbaren auszumessen und dadurch einen Blick auf das Unsagbare zu erhaschen, d. h. die Grenze des Sinnsi durch minutiöse Beschreibung der physischen Welt der Tatsachen bzw. der sozialen Welt der „Sprachspiele" zu bestimmen. Das eigentlich Wertvolle (...) ist für ihn aber das, was sich nicht „sagen", sondem nur - gleichsam gegen die Regeln der Sprache - in „unsinnigen" Sätzen „zeigen" läßt: Ethik/Ästhetik, Logik/Semantik, Kunst und Religion. Scheinbar paradoxerweise wird der „Unsinn" für Wittgenstein dadurch zum eigentlichen Sinn2. Seine Philosophie zeigt sich als das, was sie immer wieder thematisiert: „Anrennen an die Grenze der Sprache", die in der Verstehbariceit von Metaphern liegt. (shrink)

Wittgensteins Philosophie ist nicht auf die „Überwindung der Metaphysik" hin angelegt, sondem auf diejenige ihrer Überwindung. Insofem ist der Schritt zurück zu Wittgenstein zugleich ein Schritt hinaus über die analytische Philosophie. Beherrschendes Ziel des frühen wie des späten Wittgenstein ist es, den Innenraum des sinnvoll Sagbaren auszumessen und dadurch einen Blick auf das Unsagbare zu erhaschen, d. h. die Grenze des Sinnsi durch minutiöse Beschreibung der physischen Welt der Tatsachen bzw. der sozialen Welt der „Sprachspiele" zu bestimmen. Das eigentlich Wertvolle (...) ist für ihn aber das, was sich nicht „sagen", sondem nur - gleichsam gegen die Regeln der Sprache - in „unsinnigen" Sätzen „zeigen" läßt: Ethik/Ästhetik, Logik/Semantik, Kunst und Religion. Scheinbar paradoxerweise wird der „Unsinn" für Wittgenstein dadurch zum eigentlichen Sinn2. Seine Philosophie zeigt sich als das, was sie immer wieder thematisiert: „Anrennen an die Grenze der Sprache", die in der Verstehbariceit von Metaphern liegt. (shrink)

Dynamic stability of the knee and weakness of the extensor muscles are considered to be the most important functional limitations after anterior cruciate ligament injury, probably due to changes at the central level of motor control rather than at the peripheral level. Despite general technological advances, fewer contraindicative surgical procedures, and extensive postoperative rehabilitation, up to 65% of patients fail to return to their preinjury level of sports, and only half were able to return to competitive sport. Later, it becomes (...) clear that current rehabilitation after knee surgery is not sufficient to address the functional limitations after ACL reconstruction even years after surgery. Therefore, new therapeutic tools targeting the central neural system, i.e., the higher centers of motor control, should be investigated and integrated into current rehabilitation practice. To improve motor performance when overt movement cannot be fully performed, several techniques have been developed to increase physical and mental activation without the need to perform overt movements. Among the most popular cognitive techniques used to increase physical performance are motor imagery and action observation practices. This review, which examines the available evidence, presents the underlying mechanisms of the efficacy of cognitive interventions and provides guidelines for their use at home. (shrink)

Recent research has detailed the use of neuroscience in several jurisdictions, but Australia remains a notable omission. To fill this substantial void we performed a systematic review of neuroscience in Australian criminal cases. The first section of this article reports the results of our review by detailing the purposes for which neuroscience is admitted into Australian criminal courts. We found that neuroscience is being admitted pre-trial, at trial, and during sentencing. In the second section, we evaluate these applications. We generally (...) found that courts admit neuroscience cautiously, and to supplement more well-established forms of evidence. Still, we found some instances in which the court seemed to misunderstand the neuroscience. These cases ranged from interpreting neuroscience as “objective” evidence to admitting neuroscience when the same non-neuroscientific psychiatric evidence would be inadmissible for being common sense. Furthermore, in some cases, neuroscientific evidence presents a double-edged sword; it may serve to either aggravate or mitigate a sentence. Thus, the decision about whether or not to tender this evidence is risky. (shrink)

Notions of democracy and nationhood constitute the pivotal legacy of the American Revolution, but to understand their development one must move beyond a purely American context. Citizens of a Common Intellectual Homeland explores the simultaneous emergence of modern concepts of democracy and the nation on both sides of the Atlantic during the age of revolutions. Armin Mattes argues that in their origin the two concepts were indistinguishable because they arose from a common revolutionary impulse directed against the prevailing hierarchical (...) political and social order. The author shows how the reconceptualization of democracy and the nation, which resulted from this revolutionary impulse, received its decisive form from the French Revolution. Although the French Revolution was instrumental in redefining the two terms, however, neither were these changes confined to France, nor did the new meanings merely radiate from France to other countries. To illustrate the transatlantic emergence of these ideas, Mattes considers the works of pairs of prominent intellectual contemporaries--one in America and the other in Europe--each writing on a common topic. The thinkers and topics include Thomas Paine and Edmund Burke on the transatlantic revolutions, John Adams and Friedrich von Gentz on the mixed constitution, James Madison and Immanuel Kant on perpetual peace, and Thomas Jefferson and Destutt de Tracy on the nation. Mattes's approach highlights the significant impact that the French Revolution had on the evolution of thought in the period, demonstrating that the emergence and early development of modern concepts of democracy and the nation in America were intimately tied to revolutionary events and processes in the larger Atlantic world. Preparation of this volume has been supported by the Thomas Jefferson Foundation. Jeffersonian America. (shrink)

Introduction The analytical way of thinking has been one of the most fruitful paradigms in this century in philosophy and in different sciences, ...

Certain strands of contemporary media theory are concerned with the ways in which computational environments exploit the ‘missing half-second’ of human perception and thereby influence, control or exploit humans at an affective level. The ‘technological unconscious’ of our times is often understood to work at this affective level, and high-frequency trading is regularly provided as a primary illustrative example of the contagious dynamics it produces. We challenge and complicate this account of the relation between consciousness, affect and media technologies by (...) drawing on the recent work of N. Katherine Hayles and by focusing in detail on the ways in which the ‘costs of consciousness’ are accounted for and negotiated in high-frequency trading. We suggest that traders actively develop modes of awareness accounting for the costs of consciousness, and that the necessary ‘stupidity’ of high-frequency trading algorithms as well as competition pose limits to the full automation of financial markets. (shrink)

Business schools have become implicated in the widespread demonisation of the financial classes. By educating those held most responsible for the crisis – financial traders and speculators – they are said to have produced ruthlessly talented graduates who have ambition in abundance but little sense for social responsibility or ethics. This ethical lack thrives upon the trading floor within a compelling critique of the complicity of the pedagogy of the business school with the financial crisis of the global economy. An (...) ethical turn within the curriculum is now widely encouraged as a counteractive force. Within this paper, however, we argue that taking this ethical turn is not enough. For business ethicists to learn from the financial crisis, the crisis' legacy needs to be taken account of, and financialisation needs to be taken seriously. Pedagogical reform cannot bracket itself off from the crisis as if it were coincidental with or separate from it. Post-crisis pedagogy must rather take the fact that it is requested now, in light of the crisis, as its very point of departure. The financial crisis must not be understood as something to be resisted in the name of Business Ethics. Instead, the financial crisis must be understood as the very foundation for contemporary Business Ethics in particular and for contemporary business and management education more generally. (shrink)

Business schools have become implicated in the widespread demonisation of the financial classes. By educating those held most responsible for the crisis – financial traders and speculators – they are said to have produced ruthlessly talented graduates who have ambition in abundance but little sense for social responsibility or ethics. This ethical lack thrives upon the trading floor within a compelling critique of the complicity of the pedagogy of the business school with the financial crisis of the global economy. An (...) ethical turn within the curriculum is now widely encouraged as a counteractive force. Within this paper, however, we argue that taking this ethical turn is not enough. For business ethicists to learn from the financial crisis, the crisis' legacy needs to be taken account of, and financialisation needs to be taken seriously. Pedagogical reform cannot bracket itself off from the crisis as if it were coincidental with or separate from it. Post‐crisis pedagogy must rather take the fact that it is requested now, in light of the crisis, as its very point of departure. The financial crisis must not be understood as something to be resisted in the name of Business Ethics. Instead, the financial crisis must be understood as the very foundation for contemporary Business Ethics in particular and for contemporary business and management education more generally. (shrink)