Guarded fragments of first-order logic were recently introduced by Andreka, van Benthem and Nemeti; they consist of relational first-order formulae whose quantifiers are appropriately relativized by atoms. These fragments are interesting because they extend in a natural way many propositional modal logics, because they have useful model-theoretic properties and especially because they are decidable classes that avoid the usual syntactic restrictions (on the arity of relation symbols, the quantifier pattern or the number of variables) of almost all other known decidable (...) fragments of first-order logic. Here, we investigate the computational complexity of these fragments. We prove that the satisfiability problems for the guarded fragment (GF) and the loosely guarded fragment (LGF) of first-order logic are complete for deterministic double exponential time. For the subfragments that have only a bounded number of variables or only relation symbols of bounded arity, satisfiability is EXPTIME-complete. We further establish a tree model property for both the guarded fragment and the loosely guarded fragment, and give a proof of the finite model property of the guarded fragment. It is also shown that some natural, modest extensions of the guarded fragments are undecidable. (shrink)

We identify the computational complexity of the satisfiability problem for FO 2 , the fragment of first-order logic consisting of all relational first-order sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity of its decision problem has not been pinpointed so far. In 1975 Mortimer proved that FO 2 has the finite-model property, which means that if an FO 2 -sentence is satisfiable, then it has a finite (...) model. Moreover, Mortimer showed that every satisfiable FO 2 -sentence has a model whose size is at most doubly exponential in the size of the sentence. In this paper, we improve Mortimer's bound by one exponential and show that every satisfiable FO 2 -sentence has a model whose size is at most exponential in the size of the sentence. As a consequence, we establish that the satisfiability problem for FO 2 is NEXPTIME-complete. (shrink)

It is a classical result of Mortimer that $L^2$ , first-order logic with two variables, is decidable for satisfiability. We show that going beyond $L^2$ by adding any one of the following leads to an undecidable logic:– very weak forms of recursion, viz.¶(i) transitive closure operations¶(ii) (restricted) monadic fixed-point operations¶– weak access to cardinalities, through the Härtig (or equicardinality) quantifier¶– a choice construct known as Hilbert's $\epsilon$ -operator.In fact all these extensions of $L^2$ prove to be undecidable both for satisfiability, (...) and for satisfiability in finite structures. Moreover most of them are hard for $\Sigma^1_1$ , the first level of the analytical hierachy, and thus have a much higher degree of undecidability than first-order logic. (shrink)

Rede und Gegenrede, pro und contra - jeweils von derselben Person zu einem bestimmten Thema? Wer kennt das nicht von sich selbst? Auch beim Philologen und Philosophen Friedrich Nietzsche finden sich solche Stellen in seinem Werk. Systematisch aufbereitet durch den Autor, umfasst das Buch 287 Schlagwörter und 5527 Zitate, geordnet nach pro und contra und ein Fundstellenverzeichnis. Das Buch will sein: Ein Zugang und Schlüssel zu Nietzsches Schriften Ein Nietzsche-Nachschlagewerk Ein Nietzsche-Brevier Eine Aufforderung an den Leser, von der Oberfläche der (...) Zitate in die Tiefen der Gedankengänge Nietzsches vorzudringen Ein Rüstzeug zum Selbst-Überdenken der Probleme Ein Buch von Studiendirektor i.R. Erich Frey-Teschen (1922 - 2016), posthum herausgegeben von Roman Seidl. (shrink)

We establish a general hierarchy theorem for quantifier classes in the infinitary logic L∞ωωon finite structures. In particular, it is shown that no infinitary formula with bounded number of universal quantifiers can express the negation of a transitive closure.This implies the solution of several open problems in finite model theory: On finite structures, positive transitive closure logic is not closed under negation. More generally the hierarchy defined by interleaving negation and transitive closure operators is strict. This proves a conjecture of (...) Immerman.We also separate the expressive power of several extensions of Datalog, giving new insight in the fine structure of stratified Datalog. (shrink)

In first order logic without equality, but with arbitrary relations and functions the ∃*∀∃* class is the unique maximal solvable prefix class. We show that the satisfiability problem for this class is decidable in deterministic exponential time The result is established by a structural analysis of a particular infinite subset of the Herbrand universe and by a polynomial space bounded alternating procedure.

From time to time medical ethicists bemoan the loss of a religious perspective in medical ethics. The discipline had its origins in the thinking of explicitly religious thinkers such as Paul Ramsey and Joseph Fletcher. Furthermore, many of those who contributed to the early development of the discipline had training in theology. One thinks of Daniel Callahan, Richard McCormick, Albert Jonsen, Sam. Banks. As the discipline becomes more and more self-reflective, with attention being paid to methodological and conditional concerns, it (...) is only natural that the roots are due for a reexamination. The time has therefore come for some reassessment. The first steps here are taken in the form of a dialogue between the coauthors to clarify authentic contributions and weed out unauthentic ones. (shrink)

The areas of interest of the scholar of religious studies, Karl E. Grozinger, are diverse. His research is concentrated on the religious and cultural history of Judaism throughout the ages: Israel in antiquity, the era of rabbinical traditional literature, philosophy of religion during the Middle Ages, the kabbalistic tradition, as well as Jewish thinkers and devout movements in contemporary times. On the occasion of Professor Grozinger's seventieth birthday, numerous scholars present the first fruits of their current research as a first (...) look into the tendencies of future research in Jewish studies. In accordance with this scholar's broad interests, the volume Jewish Lifeworlds and Jewish Thought, edited by Nathanael Riemer, is comprised of contributions to a wide variety of topics of Jewish cultural history.With contributions by Hermann Lichtenberger, Hanna Liss, Ronit Meroz, Yoav Elstein, Susanne Talabardon, Nathanael Riemer, Giuseppe Veltri, Dirk Westerkamp, Thomas Meyer, Daniel Jutte, Frederek Musall, Robert Jutte, J. Friedrich Battenberg, Admiel Kosman, Rella Kushelevsky, Elvira Grozinger, Simon Bronner, Avidov Lipsker, Jascha Nemtsov, Rebekka Denz, Micha Brumlik, Micha? Galas, Manja Herrmann, Hans-Michael Haussig, Anat Feinberg, Adam Lipszyc, Vivian Liska, Julius H. Schoeps, Edward D'browa, Ewa Geller, Manfred Voigts, Mordechai Lewy and Stanislaw Krajewski. (shrink)

Motivated by the search for a logic for polynomial time, we study rank logic which extends fixed-point logic with counting by operators that determine the rank of matrices over finite fields. WhileFPRcan express most of the known queries that separateFPCfromPtime, almost nothing was known about the limitations of its expressive power.In our first main result we show that the extensions ofFPCby rank operators over different prime fields are incomparable. This solves an open question posed by Dawar and Holm and also (...) implies that rank logic, in its original definition with a distinct rank operator for every field, fails to capture polynomial time. In particular we show that the variant of rank logic${\text{FPR}}^{\text{*}}$with an operator that uniformly expresses the matrix rank over finite fields is more expressive thanFPR.One important step in our proof is to consider solvability logicFPSwhich is the analogous extension ofFPCby quantifiers which express the solvability problem for linear equation systems over finite fields. Solvability logic can easily be embedded into rank logic, but it is open whether it is a strict fragment. In our second main result we give a partial answer to this question: in the absence of counting, rank operators are strictly more expressive than solvability quantifiers. (shrink)

We design functional algebras that characterize various complexity classes of global functions. For this purpose, classical schemata from recursion theory are tailored for capturing complexity. In particular we present a functional analog of first-order logic and describe algebras of the functions computable in nondeterministic logarithmic space, deterministic and nondeterministic polynomial time, and for the functions computable by AC 1 -circuits.

In an analysis of Fichte’s theoretical reflections read in the light of decisive biographical events, the present paper examines the following question: to what extent are we to assent to Fichte’s own assertion that his system is from the very outset a system of freedom? Kant’s philosophy provided the catalyst for the young Fichte because it promised a way out of the impasse of determinism. I will argue that the ultimate goal of Fichte’s lifelong struggle was to furnish a foundation (...) for genuine freedom. In reaction to both Jacobi and Schelling, Fichte’s philosophical and political investigations pursue at once the problem of grounding the “Absolute” and the relationship between individual freedom and reason as a whole.—These tensions are especially visible in Fichte’s path from the Addresses To the German Nation to the virtually unknown “Philosophical Diaries” of the final days of his life. (shrink)

The unity of thinking and acting (saying and doing) will be assumed as a fundamental hypothesis for a biography of Fichte, allowing one to understand the different stages in J.G. Fichte’s life. Die Einheit von Denken und Handeln (Sagen und Tun) wird als Grundhypothese für eine Biographie Fichtes angenommen, aus der sich die Etappen des Lebens von J.G. Fichte verstehen lassen sollen.

Der Jesuit Erich Przywara (1889-1972) und Gertrud von le Fort (1876-1971) lernten sich Mitte der 1920-er Jahre kennen, zur Zeit der Konversion le Forts zum katholischen Glauben. Seither standen sie in einem durchgehenden, wenn auch losen Briefwechsel, vor allem in den beiden Jahrzehnten nach dem Zweiten Weltkrieg. Die von Manfred Lochbrunner herausgegebene Korrespondenz ist das berührende Dokument einer freundschaftlichen Beziehung zwischen der angesehenen Dichterin und dem nicht minder bedeutenden Religionsphilosophen und Theologen mit eigenen dichterischen Ambitionen. In einem Einführungsessay werden (...) die wesentlichen Briefinhalte kurz vorgestellt. Anmerkungen kommentieren den Text der Briefe. Abgerundet wird die Edition durch drei biographische Exkurse zu nahestehenden Personen und Anhänge, etwa zu gegenseitigen Widmungen, sowie ein Literaturverzeichnis"-- Back cover. (shrink)

In On Repentance, noted scholar Pinchas Peli has gathered the major points of Rabbi Soloveitchik's teachings on teshuvah (repentance), based on the annual series of lectures on the theme of teshuvah, presented on the anniversary of his ...

This book explores the theory of value structure, or axiology, in metaethics and defends the thesis that aspects of “better than” comparisons may outrank each other and that value cannot always be summed up neatly.