Many logics considered in finite model theory have a natural notion of an arity. The purpose of this article is to study the hierarchies which are formed by the fragments of such logics whose formulae are of bounded arity.Based on a construction of finite graphs with a certain property of homogeneity, we develop a method that allows us to prove that the arity hierarchies are strict for several logics, including fixed-point logics, transitive closure logic and its deterministic version, variants of (...) the database language Datalog, and extensions of first-order logic by implicit definitions.Furthermore, we show that all our results already hold on the class of finite graphs. (shrink)

We prove an existential version of Gaifman's locality theorem and show how it can be applied algorithmically to evaluate existential first-order sentences in finite structures.

We discuss several possible extensions of the classical Löwenheim-Skolem Theorem to finite structures and give a counterexample refuting almost all of them.

In this paper we prove that thek-ary fragment of transitive closure logic is not contained in the extension of the (k−1)-ary fragment of partial fixed point logic by all (2k−1)-ary generalized quantifiers. As a consequence, the arity hierarchies of all the familiar forms of fixed point logic are strict simultaneously with respect to the arity of the induction predicates and the arity of generalized quantifiers.Although it is known that our theorem cannot be extended to the sublogic deterministic transitive closure logic, (...) we show that an extension is possible when we close this logic under congruence. (shrink)

Throughout the development of finite model theory, the fragments of first-order logic with only finitely many variables have played a central role. This survey gives an introduction to the theory of finite variable logics and reports on recent progress in the area.For each k ≥ 1 we let Lk be the fragment of first-order logic consisting of all formulas with at most k variables. The logics Lk are the simplest finite-variable logics. Later, we are going to consider infinitary variants and (...) extensions by so-called counting quantifiers.Finite variable logics have mostly been studied on finite structures. Like the whole area of finite model theory, they have interesting model theoretic, complexity theoretic, and combinatorial aspects. For finite structures, first-order logic is often too expressive, since each finite structure can be characterized up to isomorphism by a single first-order sentence, and each class of finite structures that is closed under isomorphism can be characterized by a first-order theory. The finite variable fragments seem to be promising candidates with the right balance between expressive power and weakness for a model theory of finite structures. This may have motivated Poizat [67] to collect some basic model theoretic properties of the Lk. Around the same time Immerman [45] showed that important complexity classes such as polynomial time or polynomial space can be characterized as collections of all classes of finite structures definable by uniform sequences of first-order formulas with a fixed number of variables and varying quantifier-depth. (shrink)

We observe that the W*-hierarchy, a variant (introduced by Downey, Fellows, and Taylor [7]) of the better known W-hierarchy, coincides with the W-hierarchy, though not level wise, but just as a whole hierarchy. More precisely, we prove that W[t] ⊆ W*[t] ⊆ W[2t − 2] for each t ≥ 2. It was known before that W[1] = W*[1] and W[2] = W*[2]. Our second main result is a new logical characterization of the W*-hierarchy in terms of "Fagin-definable problems." As a (...) by-product, we also obtain an improvement of our earlier characterization of the hierarchy in terms of model-checking problems. Furthermore, we obtain new complete problems for the classes W[3] and W*[3]. (shrink)

The model-checking problem for a logic L on a class C of structures asks whether a given L-sentence holds in a given structure in C. In this paper, we give super-exponential lower bounds for fixed-parameter tractable model-checking problems for first-order and monadic second-order logic. We show that unless PTIME=NP, the model-checking problem for monadic second-order logic on finite words is not solvable in time f·p, for any elementary function f and any polynomial p. Here k denotes the size of the (...) input sentence and n the size of the input word. We establish a number of similar lower bounds for the model-checking problem for first-order logic, for example, on the class of all trees. (shrink)

We study a refined framework of parameterized complexity theory where the parameter dependence of fixed-parameter tractable algorithms is not arbitrary, but restricted by a function in some family . For every family of functions, this yields a notion of -fixed-parameter tractability. If is the class of all polynomially bounded functions, then -fixed-parameter tractability coincides with polynomial time decidability and if is the class of all computable functions, -fixed-parameter tractability coincides with the standard notion of fixed-parameter tractability. There are interesting choices (...) of between these two extremes, for example the class of all singly exponential functions. In this article, we study the general theory of -fixed-parameter tractability. We introduce a generic notion of reduction and two classes -W[P] and -XP, which may be viewed as analogues of NP and EXPTIME, respectively, in the world of -fixed-parameter tractability. (shrink)

Die vorliegenden, bisher nicht veröffentlichten Briefe, Post-karten, Widmungen, Anzeigen und Telegramme von Prof. Dr. Martin Heidegger und seiner Frau Elfride an Walter Schloss aus den Jahren 1950 bis 1976 sind zusammen mit einigen Briefentwürfen von Schloss Teile einer Korrespondenz, die Schloss dem Herausgeber vererbte. Es geht darin um Danksagungen, Wünsche, Termine für Besuche bei Heidegger und zur Verfügung stehende Zeit, um Angaben zur Anwesenheit, Widmungen, auch um Angaben zum gesundheitlichen Befinden und Älterwerden, um Anmerkungen zur Anhängerschaft und zum Persönlichkeitskult, (...) um einige Bemerkungen zum Wesen des Denkens und vor allem um den Berliner Heidegger-Kreis, den Schloss gegründet hatte. (shrink)

Enth. u. a.: S. 57-68: Berliner "Exil" und Schweizer "Heimat": Johann Georg Zimmermanns Reflexionen über die Rolle des Schweizer Gelehrten / Simone Zurbuchen. - S. 137-150: Medizinische Aufklärung bei Johann Georg Zimmermann : zum Verhältnis von Macht und Wissen bei einem Arzt der Aufklärung / Martin Dinges.

In lieu of an abstract, here is a brief excerpt of the content:INTENTIONAL ACTIONS AND THE MEANING OF OBJECT: A REPLY TO RICHARD McCORMICK MARTIN RHONHEIMER Roman Athenaeum of the Holy Cross Rome, Italy I N HIS ARTICLE, " Some Early Reactions to Veritatis Splendor," 1 Richard McCormick discusses my article on Veritatis Splendor and its teaching about intrinsically evil acts.2 He challenges my defence of the encyclical's views and poses some concrete questions for me. At the same time, (...) McCormick complains once more about what he calls the encyclical's misrepresentation of the proportionalists' views, as well as about a general misunderstanding on the part of critics of what proportionalism, consequentialism, and their teleological approach are really about. To begin with, I find it somewhat surprising that McCormick presents intentional understanding of human acts and their objects as something discovered by proportionalists. By this he obscures the fact that most critics of proportionalism, consequentialism, and so-called " teleological ethics " (I will not further distinguish these different labels) work with what is precisely an intentional conception of moral objects.3 For example, my own 1 Theological Studies 55 (1994): 481-506; see 500-502; 504. 2 Martin Rhonheimer, " ' Intrinsically Evil Acts' and the Moral Viewpoint: Clarifying a Central Teaching of Veritatis Splendor," The Thomist 58 (1994) : 1-39. 3 There may be some exceptions, for example, Russell Rittinger; see his article, "The Pope and the Theorists," Crisis 11 (December 1993) : 31-36. G. E. M. Anscombe, one of the first and most incisive critics of consequentialism, attacked it on the grounds of an intentional concept of action, developed in her famous study Intention (Oxford: Basil Blackwell, 1957; 2nd ed. 1963). Cf. Anscombe, Contraception and Chastity (London: Catholic Truth Society, 1975). 279 280 MARTIN RHONHEIMER position, situated in the context of virtue ethics,4 is one in which an intentional conception action plays a crucial role. McCormick seems to evade this level of argument, however, and in this way appears to beg the question about one of the central issues in the debate. At the same, it is not entirely surprising that McCormick had some difficulty in dealing with the central point of my argument (and of similar arguments),5 because his methodology is so entangled in the categories of the strongly legalistic and casuistic manual tradition.6 In my article, I explicitly dealt with the difficulty of understanding a virtue and first-person-centered view from the perspective of the manual tradition: It will, however, never be possible to render intelligible this moral methodology on the grounds of an ethic which from the beginning is concerned with justifying " moral norms." This is so because in such an approach the distinction between " object" and further intentions necessarily drops out of view. The only thing which a norm ethic can produce in the way of an action theory are the particular " occurrences " ("actions ") on the one hand, and the consequences 4 See Martin Rhonheimer, "'Ethics of Narms' and the Lost Virtues. Searching the Roots of the Crisis of Ethical Reasoning," Anthropotes IX, 2 (1993) : 231-243; La prospettiva della morale. Fondamenti dell'etica philosophica (Rome: Armando, 1994) ; Praktische Vernunft und Verniinftigkeit der Praxis. Handlungstheorie bei Thomas van Aquin in ihrer Entstehimg aus dem Problemlwntext der aristotelischen Ethik (Berlin: Akademie Verlag, 1994). Contrary to the impression which McCormick gives in his article, I do not share the Grisez-Finnis theory about basic goods and practical reason, nor do I argue on its grounds, in spite of many important common views. 5 See William E. May, Moral Absolutes. Catholic Tradition, Citrrent Trends, and the Truth (Milwaukee, Wisc: Marquette University Press, 1989) ; John Finnis, Moral Absolutes: Tradition, Revision, and Truth (Washington, D.C.: The Catholic University of America Press, 1991); Alasdair Macintyre, "How Can We Learn What Veritatis Splendor Has To Teach?" The Thomist 58 (1994) : 171-195. See also Robert P. George's and Hadley's Arkes's contributions to " The Splendor of Truth: A Symposium," published in First Things (January 1994) and rather unfairly criticized in McCormick's article. 6 This is also the case with Bruno Schuller and his disciples; see the recent paper by Werner Wolbert, " Die 'in sich schlechten' Handlungen und der Konsequentialismus," M oraltheologie im Abseitsf Antwort auf die Enzyklika... (shrink)

In the present paper, i propose, first, to present some aspects of what we may call a type of "phenomenology" of the image contained in the Berlin lectures on transcendental logic – notably, in the second of these courses in Berlin. Second, i would like to return to the problem of the relationship between logic and philosophy, starting from these indications with regard to the "image", and, if possible, outline some parallel with certain theses on the same subject (...) from the Jena years. Finally, in what i consider a novelty concerning these lessons, i would like to conclude my exposition by raising the question of the foundational character of Fichte’s project. (shrink)

The intellectual Huguenot Refuge is one of the most important movements in Early modern Europe. This volume provides new information about one of its centres: about Berlin, and on the extremely important role Huguenot scholars played disseminating Enlightened thought.

Revisiting the 1927 Solvay conference and the early interpretation of quantum mechanics Content Type Journal Article Category Essay Review Pages 1-5 DOI 10.1007/s11016-011-9555-z Authors Martin Jähnert, Max Planck Institute for the History of Science, Boltzmannstraße 22, 14195 Berlin, Germany Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.

Little attention has been paid to Hegel’s version of the sublime. I argue that the sublime plays a very marginal role in the Berlin lectures on aesthetics and on religion; in particular, Hegel ignores the “Romantic” sublime popular among his contemporaries. The sublime he locates in Persian poetry and more properly in Biblical Psalmody. After surveying his various articulations of the sublime, I turn to Hegel’s careful analysis of how the Psalms achieve their peculiar effects and note his focus (...) on the “individual.” Paradoxically, while close to Romantic “subreption”, their complex play with voice—and Hegel’s explication—both keep a safe distance, I contend. Turning finally to the question of anachronism and the sublime as a historical category, I suggest in a brief postscript how effects analogous to the Psalms’ rhetoric may nevertheless be detected in Terry Malick films. (shrink)

Little attention has been paid to Hegel’s version of the sublime. I argue that the sublime plays a very marginal role in the Berlin lectures on aesthetics and on religion; in particular, Hegel ignores the “Romantic” sublime popular among his contemporaries. The sublime he locates in Persian poetry and more properly in Biblical Psalmody. After surveying his various articulations of the sublime, I turn to Hegel’s careful analysis of how the Psalms achieve their peculiar effects and note his focus (...) on the “individual.” Paradoxically, while close to Romantic “subreption” (Kant’s term for subjective projection on objective world or word), their complex play with voice—and Hegel’s explication—both keep a safe distance, I contend. Turning finally to the question of anachronism and the sublime as a historical category, I suggest in a brief postscript how effects analogous to the Psalms’ rhetoric may nevertheless be detected in Terry Malick films. (shrink)

Contents: K. Ludeking, The Body and the Letters Albrecht Durer s self-portrait from 1500; E. Osterkamp, Spartacus under the Germans on the history of a literary legacy; F. Forster-Hahn, German, Modern and Jewish Max Liebermann s 1906 exhibitions in Berlin and London; U. Haselstein, A Genealogy of Modernity Flaubert, Cezanne, and Gertrude Stein; C. Asendurf, Bodies in Force Fields Art War and Spatial Theory in Classical Modernity.".