The classical Feferman–Vaught Theorem for First Order Logic explains how to compute the truth value of a first order sentence in a generalized product of first order structures by reducing this computation to the computation of truth values of other first order sentences in the factors and evaluation of a monadic second order sentence in the index structure. This technique was later extended by Läuchli, Shelah and Gurevich to monadic second order logic. The technique has wide applications in decidability and (...) definability theory. Here we give a unified presentation, including some new results, of how to use the Feferman–Vaught Theorem, and some new variations thereof, algorithmically in the case of Monadic Second Order Logic MSOL . We then extend the technique to graph polynomials where the range of the summation of the monomials is definable in MSOL . Here the Feferman–Vaught Theorem for these polynomials generalizes well known splitting theorems for graph polynomials. Again, these can be used algorithmically. Finally, we discuss extensions of MSOL for which the Feferman–Vaught Theorem holds as well. (shrink)

We prove that compactness is equivalent to the amalgamation property, provided the occurrence number of the logic is smaller than the first uncountable measurable cardinal. We also relate compactness to the existence of certain regular ultrafilters related to the logic and develop a general theory of compactness and its consequences. We also prove some combinatorial results of independent interest.

We investigate the expressive power of second-order logic over finite structures, when two limitations are imposed. Let SAA ) be the set of second-order formulas such that the arity of the relation variables is bounded by k and the number of alternations of second-order quantification is bounded by n . We show that this imposes a proper hierarchy on second-order logic, i.e. for every k , n there are problems not definable in AA but definable in AA for some c (...) 1 , d 1 . The method to show this is to introduce the set AUTOSAT of formulas in F which satisfy themselves. We study the complexity of this set for various fragments of second-order loeic. For first-order logic FOL with unbounded alternation of quantifiers AUTOSAT is PSpace complete. For first-order logic FOL n with alternation of quantifiers bounded by n , AUTOSAT is definable in AA . AUTOSAT) is definable in AA for some c 1 , d 1. (shrink)

Graph polynomials are graph parameters invariant under graph isomorphisms which take values in a polynomial ring with a fixed finite number of indeterminates. We study graph polynomials from a model theoretic point of view. In this paper we distinguish between the graph theoretic (semantic) and the algebraic (syntactic) meaning of graph polynomials. Graph polynomials appear in the literature either as generating functions, as generalized chromatic polynomials, or as polynomials derived via determinants of adjacency or Laplacian matrices. We show that these (...) forms are mutually incomparable, and propose a unified framework based on definability in Second Order Logic. We show that this comprises virtually all examples of graph polynomials with a fixed finite set of indeterminates. Finally we show that the location of zeros and stability of graph polynomials is not a semantic property. The paper emphasizes a model theoretic view. It gives a unified exposition of classical results in algebraic combinatorics together with new and some of our previously obtained results scattered in the graph theoretic literature. (shrink)

We study the effects of Vopěnka's principle on properties of model theoretic logics. We show that Vopěnka's principle is equivalent to the assumption that every finitely generated logic has a compact cardinal. We show also that it is equivalent to the assumption that every such logic has a global Hanf number.

We show that the spectrum of a sentence ϕ in Counting Monadic Second Order Logic (CMSOL) using one binary relation symbol and finitely many unary relation symbols, is ultimately periodic, provided all the models of ϕ are of clique width at most k, for some fixed k. We prove a similar statement for arbitrary finite relational vocabularies τ and a variant of clique width for τ-structures. This includes the cases where the models of ϕ are of tree width at most (...) k. For the case of bounded tree-width, the ultimate periodicity is even proved for Guarded Second Order Logic GSOL. We also generalize this result to many-sorted spectra, which can be viewed as an analogue of Parikh's Theorem on context-free languages, and its analogues for context-free graph grammars due to Habel and Courcelle. Our work was inspired by Gurevich and Shelah (2003), who showed ultimate periodicity of the spectrum for sentences of Monadic Second Order Logic where only finitely many unary predicates and one unary function are allowed. This restriction implies that the models are all of tree width at most 2, and hence it follows from our result. (shrink)

Finitary sketches, i.e., sketches with finite-limit and finite-colimit specifications, are proved to be as strong as geometric sketches, i.e., sketches with finite-limit and arbitrary colimit specifications. Categories sketchable by such sketches are fully characterized in the infinitary first-order logic: they are axiomatizable by σ-coherent theories, i.e., basic theories using finite conjunctions, countable disjunctions, and finite quantifications. The latter result is absolute; the equivalence of geometric and finitary sketches requires (in fact, is equivalent to) the non-existence of measurable cardinals.

Global Media Ethics is the first comprehensive cross-cultural exploration of the conceptual and practical issues facing media ethics in a global world. A team of leading journalism experts investigate the impact of major global trends on responsible journalism. The first full-length, truly global textbook on media ethics; Explores how current global changes in media promote and inhibit responsible journalism; Includes relevant and timely ethical discussions based on major trends in journalism and global media; Questions existing frameworks in media ethics in (...) light of the impact of global media; Contributors are leading experts in global journalism and communication. (shrink)

v. 1. Nicomachean ethics. Politics. The Athenian Constitution. Rhetoric. On Poetics.--v. 2. Logic.--v. 3. Physics. Metaphysics. On the soul. Short physical treaties.--v. 4. On the heavens. On generation and corruption. Meteorology. Biological treatises.

Much of the progress in the fields constituting cognitive science has been based upon the use of explicit information processing models, almost exclusively patterned after conventional serial computers. An extension of these ideas to massively parallel, connectionist models appears to offer a number of advantages. After a preliminary discussion, this paper introduces a general connectionist model and considers how it might be used in cognitive science. Among the issues addressed are: stability and noise‐sensitivity, distributed decision‐making, time and sequence problems, and (...) the representation of complex concepts. (shrink)

In this paper we attempt to sharpen and to provide an answer to the question of when human beings first become conscious. Since it is relatively uncontentious that a capacity for raw sensation precedes and underpins all more sophisticated mental capacities, our question is tantamount to asking when human beings first have experiences with sensational content. Two interconnected features of our argument are crucial. First, we argue that experiences with sensational content are supervenient on facts about electrical activity in the (...) cerebral cortex which can be ascertained through EEG readings. Second, we isolate from other notions of a‘functioning brain’that which is required to underpin the view that a cortex is functioning in a way which could give rise to rudimentary conscious experiences. We investigate the development in the human fetus of the anatomical and chemical pathways which underpin cortical activity and the growth and maturation of the electrical circuitry specifically associated with sensational content in adult experience. We conclude that a fetus becomes conscious at about 30 to 35 weeks after conception; an answer based on a careful analysis of EEG readings at various stages of cortical development. Finally, we survey the possible ethical ramifications of our answer. (shrink)

Forty years’ experience as a bacterial geneticist has taught me that bacteria possess many cognitive, computational and evolutionary capabilities unimaginable in the first six decades of the twentieth century. Analysis of cellular processes such as metabolism, regulation of protein synthesis, and DNA repair established that bacteria continually monitor their external and internal environments and compute functional outputs based on information provided by their sensory apparatus. Studies of genetic recombination, lysogeny, antibiotic resistance and my own work on transposable elements revealed multiple (...) widespread bacterial systems for mobilizing and engineering DNA molecules. Examination of colony development and organization led me to appreciate how extensive multicellular collaboration is among the majority of bacterial species. Contemporary research in many laboratories on cell–cell signaling, symbiosis and pathogenesis show that bacteria utilise sophisticated mechanisms for intercellular communication and even have the ability to commandeer the basic cell biology of ‘higher’ plants and animals to meet their own needs. This remarkable series of observations requires us to revise basic ideas about biological information processing and recognise that even the smallest cells are sentient beings. Previous article in issue. (shrink)

ABSTRACT In this paper we attempt to sharpen and to provide an answer to the question of when human beings first become conscious. Since it is relatively uncontentious that a capacity for raw sensation precedes and underpins all more sophisticated mental capacities, our question is tantamount to asking when human beings first have experiences with sensational content. Two interconnected features of our argument are crucial. First, we argue that experiences with sensational content are supervenient on facts about electrical activity in (...) the cerebral cortex which can be ascertained through EEG readings. Second, we isolate from other notions of a‘functioning brain’that which is required to underpin the view that a cortex is functioning in a way which could give rise to rudimentary conscious experiences. We investigate the development in the human fetus of the anatomical and chemical pathways which underpin (immature) cortical activity and the growth and maturation of the electrical circuitry specifically associated with sensational content in adult experience. We conclude (tentatively) that a fetus becomes conscious at about 30 to 35 weeks after conception; an answer based on a careful analysis of EEG readings at various stages of cortical development. Finally, we survey the possible ethical ramifications of our answer. (shrink)

In The Face of Emotions, which was Carroll Izard’s first major attempt at elaborating his differential emotions theory, he stated that the book “presents a theoretical framework for the study of emotions and their role in personality and interpersonal processes.” Yet, over the years, his contribution to personality theory has generally been overshadowed by the attention focused on his views on facial expressions and the structure of emotions. This article will begin with a brief overview of the DET perspective on (...) personality development. Then, it will examine how the DET framework can be used to organize recent findings from three lines of research on adult personality. It will conclude with suggestions for future research as well as some personal recollections. (shrink)

Was Metaphysik ist, läßt sich nicht apriorisch bestimmen, sondern zeigt sich erst in den denkerischen Entwürfen eines Ersten und Grundlegenden. Metaphysik ist, wie Philosophie überhaupt, von ihrer Geschichte nicht trennbar. Die philosophische Bedeutung der Periode des Mittelalters für den Gang der abendländischen Metaphysik ist in den letzten Jahrzehnten durch zwei klassische Studien herausgestellt worden.

A simple transposition in the text would, I venture to suggest, remove one or two of the many difficulties of this obscure chapter.

This book offers a sustained re-evaluation of the most central and perplexing themes of Leibniz's metaphysics. In contrast to traditional assessments that view the metaphysics in terms of its place among post-Cartesian theories of the world, Jan Cover and John O'Leary-Hawthorne examine the question of how the scholastic themes which were Leibniz's inheritance figure - and are refigured - in his mature account of substance and individuation. From this emerges a fresh and sometimes surprising assessment of Leibniz's views on modality, (...) the Identity of Indiscernibles, form as an internal law, and the complete-concept doctrine. As a rigorous philosophical treatment of a still-influential mediary between scholastic and modern metaphysics, their study will be of interest to historians of philosophy and contemporary metaphysicians alike. (shrink)

Im Jahrgang LXV der Recherches de Théologie et Philosophie médiévales wurde die Reihe «Entretiens» inauguriert, in der angesehene Forscher auf dem Gebiet der mittelalterlichen Theologie und Philosophie zu ihrem persönlichen Werdegang als Forscher, zu ihren Forschungsschwerpunkten und zur Zukunft der Mittelalterforschung Auskunft geben. Das zweite Interview führten Jan A. Aertsen und Andreas Speer mit Wolfgang Kluxen, emeritierter Ordinarius für Philosophie in Bonn, von 1972 bis 1982 Präsident, später président d’honneur der Société Internationale pour l’Étude de la Philosophie Médiévale.