The differentiation of trait anxiety and depression in nonclinical and clinical populations is addressed. Following the tripartite model, it is assumed that anxiety and depression share a large portion of negative affectivity, but differ with respect to bodily hyperarousal and anhedonia. In contrast to the tripartite model, NA is subdivided into worry and dysthymia, which leads to a four-variable model of anxiety and depression encompassing emotionality, worry, dysthymia, and anhedonia. Item-level confirmatory factor analyses and latent class cluster analysis based on (...) a large nation-wide representative German sample substantiate the construct validity of the model. Further evidence concerning convergent and discriminant validity with respect to related constructs is obtained in two smaller nonclinical and clinical samples. Factors influencing the association between components of anxiety and depression are discussed. (shrink)

We study a notion ofpartial primitive recursion (p.p.r.) including the concept ofparallelism in the context of partial continuous functions of type level one in the sense of [Krei], [Sco82], [Ers]. A variety of subrecursive hierarchies with respect top.p.r. is introduced and it turns out that they all coincide.

In Homer’s account of the adventurous journey of Odysseus, the song of the sirens was so appealing and tempting that it lured sailors to their deaths. Warned by the goddess Kirke, Odysseus overcame the trap by plugging his crew’s ears with wax. An archaeo-acoustical research expedition undertaken by members of Humboldt University Berlin made sound propagation experiments at the supposedly historical scene at the Galli Islands where it’s said that the sirens originally sung. At the site we broadcasted both synthetic (...) signals and natural voices via loudspeakers in the direction Odysseus most probably should have approached the Siren’s island. Subjective listening as well as objective acoustic analysis of the recorded signals revealed evidence for a combination of site-specific acoustic effects, which may explain the nature and origin of the song of the sirens in Homer. The local arrangement of the three islands deforms the acoustic signals by amplification and by changes in timbre. Two female singers from the Berlin State Opera were asked to sing differently pitched musical intervals to be tested in the Li Galli environment. The experiment evinced that the first overtones would be merged by the echo of the rocks; yet when singing pure thirds and less consonant intervals, which yield higher orders in the overtone series, the voices appear recognisable as being two. As a result, and particularly because Homer stresses the number of exactly two sirens several times, the evidence of our research supports the musicological theory for a rather early existence of enharmonic tunings and most prominently a two-part polyphonic singing of Greek songs. Given that the rocky formation of the Galli Islands most likely didn’t change during the geological tick of just 2,700 years, we conclude that there has been a real acoustic basis for the myth reported by Homer and that a “song of the Sirens”, most probably based on natural voices, was transformed by the particular acoustic conditions of the landscape in such a way that signals were amplified and sent out in one concrete direction. Based on these results, we continue to discuss further leading acoustic theories that offer new insights into the mythology and which were essential to motivate our expedition in the first place. After all, the question remains open what kind of beings the first emitters of the song might have been. (shrink)

Is there still any importance of Husserl's Phenomenology for contemporary forms of philosophy of science? A comparison between Phenomenology and a prominent form of such modern philosophy of science, the so-called 'Critical Rationalism' of Karl Popper, may help to answer this question. Therefore, the different levels of argumentation have to be worked out to make the respective arguments applicable to one another. We are arguing for the following thesis: the strategy of corroboration in Critical Rationalism can be justified by (...) means of the phenomenological conception of 'intentionality of consciousness'. A typical example may illustrate how Popper's conception of taking the degree of corroboration as an indicator of the degree of verisimilitude can find its deeper foundation in Husserl's genetic interpretation of ordinary kinds of experience. (shrink)

Dieses Arbeitsinstrument bietet eine Aktualisierung des erstmals 1987 publizierten kritischen Überblicks über die Quellen zu dem im Titel genannten Streit. Es geht dem Verf. vor allem darum, den seit 1987 nicht unerheblichen Fortschritt in Editionen und Forschung zu dokumentieren. Die Regesten der Quellen werden zum einen durch einen knappen Bericht zur Forschungslage , zum Wert der Quellen , zum reichskirchlichen Ursprung des Streits im sog. Neuchalkedonismus , zu seinen politischen Hintergründen und zu seinem Verlauf eingeleitet und zum anderen durch prosopographische (...) Hinweise zu den Regesten erschlossen, die, wie der Verf. S. VII feststellt, „durch die Vorarbeiten“ in der PmbZ „wesentlich erleichtert“ wurden. Als Anhang bietet dieses Instrument eine Zeittafel, ein Glossar zu den wichtigsten Termini und ein Stellen- und Sachregister . Eingearbeitet hat der Verf. vor allem die Edition der ACO II,2 von R. Riedinger und der Scripta saeculi VII vitam Maximi Confessoris illustrantia, die P. Allen und B. Neil im Band 39 des CCSG vorgelegt haben . Auf Grund der bisher schwer zugänglichen Ausgabe von S.L. Epifanovic und ihrer Wiedergabe in der CPG sind zumindest zwei Dubletten in die Regesten aufgenommen worden. Denn die Texte Nr. 67, 67a ; Nr. 90 und Nr. 89 ; Nr. 91 sind jeweils nur verschiedene Rezensionen. – Die Regesten zur Vorgeschichte des Streits im 6. Jahrhundert , die als „Spitze eines Eisberges“ eingeführt werden , sind nicht vollständig; insbes. fehlen hier die Zeugnisse aus Kaiser Justinians Schriften . Zurecht betont der Verf., dass der Streit schon im Konzil von Chalkedon angelegt ist, sofern durch dessen „Verdammungen … der Grat für die weitere christologische Arbeit … sehr schmal geworden“ war . Dass hier die historische Forschung ansetzen und ihre Begriffe schärfen muss, hat der Rez. in Studia Patristica 34, 2001, 572–604, gezeigt. Ausführlich belegen die Regesten zum einen die Aussagen von Maximos dem Bekenner, sieht man von seinen „vielen beiläufigen Bemerkungen“ ab , und zum anderen den Streit der römischen Kirche seit „der Kampfansage“ unter Papst Johannes IV. . Dabei wird der Verf. der historischen Kritik an Maximos gerecht, die 1967 mit W. Lackner's Beurteilung der griechischen Vita des Maximos begann, 1973 durch die Publikation der syrischen Vita einen neuen Anstoß erhielt, 1985 mit R. Riedinger's Nachweis, dass die Akten der Lateransynode von 649 „ein Werk der Byzantiner um Maximos“ sind, der diese Synode als 6. Ökumenisches Konzil bezeichnet hat , und seit 1999 auf Grund der kritischen Ausgabe jener Dokumentation, die Maximos' Anhänger nach 655 publizierten zum Urteil geführt hat: „Maximos und seine Schüler“ sind „zu sehr einseitiger Darstellung und zu bewussten Irreführungen fähig gewesen“ . Dies gilt auch dann, wenn man in der Beurteilung der theologischen Intentionen des Maximos nicht dem Verf. , sondern W. Elert , dessen Verdienste der Verf. zurecht würdigt, und anderen Autoren folgt und vor allem eine Entwicklung in Maximos' Christologie aufweist. Eine solche zeigt sich z.B. in Maximos' Interpretation des Geschehens von Gethsemani und der Oratio 30,12 des Gregor von Nazianz. Hier wäre auch Maximos' Korrektur an der neuchalkedonischen Basis zu nennen, die eine Entwicklung von 633 über den Höhepunkt der Krise um 640 voraussetzt. Wenn es zur zuletzt genannten Quelle heißt, Anastasios I. von Antiochien werde hier „als völlig orthodox beurteilt“, dann sollte man hinzufügen, dass Maximos der Nachweis nur über eine höchst subtile Interpretation gelingt, die auf die durch Anastasios' Text gestellte Frage nach dem einen Subjekt des Wirkens nicht eingeht. Es sei hier die Bemerkung erlaubt, dass es der Maximos–Forschung gut täte, wieder nach Entwicklungen im Denken dieses bedeutenden Theologen zu fragen. – Im Vergleich zum vorgenannten Dossier ist jenes des Anastasios Sinaites nicht vollständig erfasst. Dies ist bedauerlich, weil dieser Autor kein Neuchalkedoniker ist und darum die Christologie Kyrills von Alexandrien und somit Chalkedon im Ausgang von der Unterscheidung von drei Klassen christologischer Aussagen der Bibel beurteilt, auf der die Union von 433 gründet, in der sich Kyrill mit den Orientalen verständigt hatte und auf die das Konzil von Chalkedon in der Einleitung zu seiner definitio fidei hinweist. Die dritte Klasse, jene der theandrischen Aussagen, erlaubte es Anastasios gegen seine reichskirchlichen Gegner in Ägypten und Syrien, von ihm Harmasiten genannt, den Tomus Leonis und so die antiochenische Christologie einzubringen und das Zeitalter Justinians und dessen Folgen einfach nicht zur Kenntnis zu nehmen, auch wenn er um das 5. Ökumenische Konzil von Konstantinopel wusste, dessen Sprache jene des sog. Neuchalkedonismus gewesen ist. Abschließend sei betont, dass dieses Arbeitsinstrument höchst sorgfältig zusammengestellt und eingeleitet ist. Dem Rez. ist nur eine Inkonsistenz aufgefallen. Der Verf. vertritt auf S. 23 als historisch gesichert, dass Kaiser Herakleios „später die Verantwortung für die Ekthesis von sich gewiesen hat“, und verweist dazu auf das in CPG 7736 wiedergegebene Zitat der Keleusis , dessen Authentizität er jedoch auf S. 97 zurecht bezweifelt. (shrink)

Two simply typed term systems $\sf {PR}_1$ and $\sf {PR}_2$ are considered, both for representing algorithms computing primitive recursive functions. $\sf {PR}_1$ is based on primitive recursion, $\sf {PR}_2$ on recursion on notation. A purely syntactical method of determining the computational complexity of algorithms in $\sf {PR}_i$ , called $\mu$ -measure, is employed to uniformly integrate traditional results in subrecursion theory with resource-free characterisations of sub-elementary complexity classes. Extending the Schwichtenberg and Müller characterisation of the Grzegorczyk classes ${\mathcal{E}}_n$ for $n\ge (...) 3$ , it is shown $\mathcal{E}_{n+1} = \mathcal{R}^n_1 $ for $ n\ge 1 $, where $ \mathcal{R}^n_i$ denotes the \emph{ $n$ th modified Heinermann class} based on $\mu$ . The proof does not refer to any machine-based computation model, unlike the Schwichtenberg and Müller proofs. This is due to the notion of modified recursion lying on top of each other provided by $\mu$ . By Ritchie's result, $\mathcal{R}^1_1$ characterises the linear-space computable functions. Using the same method, a short and straightforward proof is presented, showing that $\mathcal{R}^1_2$ characterises the polynomial time computable functions. Furthermore, the classes $\mathcal{R}^n_2$ and $\mathcal{R}^n_1$ coincide at and above level 2. (shrink)

The paper builds on both a simply typed term system ${\cal PR}^\omega$ and a computation model on Scott domains via so-called parallel typed while programs (PTWP). The former provides a notion of partial primitive recursive functional on Scott domains $D_\rho$ supporting a suitable concept of parallelism. Computability on Scott domains seems to entail that Kleene's schema of higher type simultaneous course-of-values recursion (scvr) is not reducible to partial primitive recursion. So extensions ${\cal PR}^{\omega e}$ and PTWP $^e$ are studied that (...) are closed under scvr. The twist are certain type 1 Gödel recursors ${\cal R}_k$ for simultaneous partial primitive recursion. Formally, ${\cal R}_k\vec{g}\vec{H}xi$ denotes a function $f_i \in D_{\iota\to\iota}$ , however, ${\cal R}_k$ is modelled such that $f_i$ is finite, or in other words, a partial sequence. As for PTWP $^e$ , the concept of type $\iota\to\iota$ writable variables is introduced, providing the possibility of creating and manipulating partial sequences. It is shown that the PTWP $^e$ -computable functionals coincide with those definable in ${\cal PR}^{\omega e}$ plus a constant for sequential minimisation. In particular, the functionals definable in ${\cal PR}^{\omega e}$ denoted ${\cal R}^{\omega e}$ can be characterised by a subclass of PTWP $^e$ -computable functionals denoted ${\rm PPR}^{\omega e}$ . Moreover, hierarchies of strictly increasing classes ${\cal R}^{\omega e}_n$ in the style of Heinermann and complexity classes ${\rm PPR}^{\omega e}_n$ are introduced such that $\forall n\ge 0. {\cal R}^{\omega e}_n ={\rm PPR}^{\omega e}_n$ . These results extend those for ${\cal PR}^\omega$ and PTWP [Nig94]. Finally, scvr is employed to define for each type $\sigma$ the enumeration functional $E^\sigma$ of all finite elements of $D_\sigma$. (shrink)

We investigate a simply typed term system ℘R ω aimed at defining partial primitive recursive functionals over arbitrary Scott domains . A hierarchy of complexity classes R n ω for functionals definable in ℘R ω is given based on a hierarchy of term classes ℘R n ωpn denoting the n th class of so-called prenormal terms . They come into play by the key observation that every term t can be transformed by what we call higher type modularization as a (...) kind of inversion of normalization into an αβη equal term t ′ having almost no structural complexity. However, it turns out that normalization of a prenormal term may increase its structural complexity with respect to the classes ℘R n ωpn , and conversely, ground type modularization being still possible may reduce it. Thus the structural complexity of a prenormal term t defined as the least n with t ϵ ℘R n ωpn depends strongly on the representation of t . We present a measure denoted μ = n rel v , ϱ for prenormal terms t to be read as t is of complexity n with valued free variables v and valued type π . It is shown that μ is stable on αβη equal terms and furthermore, μ ⩽ min {n |∃t′ ϵ ℘R n ω pn .t′ = αβη t} . Moreover, if t is in a certain μ- normal form 2, the estimate above is even true with equality, that is μ yields the structural complexity of the maximal modularization of t , clearly the best a purely structural measure can do. μ-normal forms 2 do not always exist. The counterexample we give, however, clearly shows that μ does not only take into account the structural complexity of a prenormal term but also the nature and computationl complexity of the algorithm it represents. (shrink)

We investigate a simply typed term system ℘R ω aimed at defining partial primitive recursive functionals over arbitrary Scott domains . A hierarchy of complexity classes R n ω for functionals definable in ℘R ω is given based on a hierarchy of term classes ℘R n ωpn denoting the n th class of so-called prenormal terms . They come into play by the key observation that every term t can be transformed by what we call higher type modularization as a (...) kind of inversion of normalization into an αβη equal term t ′ having almost no structural complexity. However, it turns out that normalization of a prenormal term may increase its structural complexity with respect to the classes ℘R n ωpn , and conversely, ground type modularization being still possible may reduce it. Thus the structural complexity of a prenormal term t defined as the least n with t ϵ ℘R n ωpn depends strongly on the representation of t . We present a measure denoted μ = n rel v , ϱ for prenormal terms t to be read as t is of complexity n with valued free variables v and valued type π . It is shown that μ is stable on αβη equal terms and furthermore, μ ⩽ min {n |∃t′ ϵ ℘R n ω pn .t′ = αβη t} . Moreover, if t is in a certain μ- normal form 2, the estimate above is even true with equality, that is μ yields the structural complexity of the maximal modularization of t , clearly the best a purely structural measure can do. μ-normal forms 2 do not always exist. The counterexample we give, however, clearly shows that μ does not only take into account the structural complexity of a prenormal term but also the nature and computationl complexity of the algorithm it represents. (shrink)

The paper studies a simply typed term system Mω providing a primitive recursive concept of parallelism in the sense of Plotkin. The system aims at defining and computing partial continuous functionals. Some connections between denotational and operational semantics → for Mω are investigated. It is shown that → is correct with respect to the denotational semantics. Conversely, → is complete in the sense that if a program denotes some number k, then it is reducible to the numeral nk. Restricting to (...) the primitive recursive kernel Rω of Mω, it is shown that → is strongly normalising with uniquely determined normal forms. The twist is the design of fixed point style conversion rules for constants accounting for parallelly bounded parallel search such that correctness and strong normalisation hold. Thereupon, minor alternations to → bring about that every reduction sequence for a program of Rω terminates either in a numeral nk if the program denotes k, or in the term 0 if the program denotes the “undefined” object. Thus, Rω can be considered a primitive recursive version of Plotkin's PA+·. (shrink)

It is shown how to restrict recursion on notation in all finite types so as to characterize the polynomial-time computable functions. The restrictions are obtained by using a ramified type structure, and by adding linear concepts to the lambda calculus.