The Guarded Negation Fragment (GNFO) is a fragment of first-order logic that contains all positive existential formulas, can express the first-order translations of basic modal logic and of many description logics, along with many sentences that arise in databases. It has been shown that the syntax of GNFO is restrictive enough so that computational problems such as validity and satisfiability are still decidable. This suggests that, in spite of its expressive power, GNFO formulas are amenable to novel optimizations. In this (...) article we study the model theory of GNFO formulas. Our results include effective preservation theorems for GNFO, effective Craig Interpolation and Beth Definability results, and the ability to express the certain answers of queries with respect to a large class of GNFO sentences within very restricted logics. (shrink)
We study classes of ultrafilters on ω defined by a natural property of the Loeb measure in the Nonstandard Universe corresponding to the ultrafilter. This class, the Property M ultrafilters, is shown to contain all ultrafilters built up by taking iterated products over collections of pairwise nonisomorphic selective ultrafilters. Results on Property M ultrafilters are applied to the construction of extensions of probability measures, and to the study of measurable reductions between ultrafilters.
Buildings are meaningful parts of the environment; and when they are architecture, they aspire to greater meaning. Several accounts of architectural semiosis have been offered based on analogies to biology and language. These are critiqued. Critiqued, too, are accounts of semiosis generally that use systems-theoretical concepts and language. The essay goes on to outline what could be a contribution to biosemiotics from the work of perception psychologist, J. J. Gibson, as brought through architecture in the form of isovist field theory. (...) This theory is not treated as an example of systems thinking as it usually is, but, with the help of philosopher Martin Buber as well as Jesper Hoffmeyer, as a way out of it—able to describe the meaning of objects and space phenomenologically and ecologically at once. (shrink)
Der Verfassungsrechtler und Rechtsphilosoph Carl Schmitt (1888–1985) ist ohne Zweifel ein faszinierender Autor. Die von ihm ausgehende Suggestion basiert auf der Virtuosität seines polemischen Stils, der oft vergessen macht, welch sachliche Kritik von Zeitgenossen an seinen Theorien geübt wurde. Erstmals liegt nun eine kritische Auseinandersetzung mit den wichtigsten Aspekten seines Werkes vor, die die Nähe seines konservativen Denkens zum Nationalsozialismus systematisch aufzeigt. Gegenüber der vorherrschenden biografischen Behandlung dieses Verhältnisses lassen sich damit auch aktuelle politische Theoreme und Positionen sehr viel deutlicher (...) verorten. Ziel des Buches ist es, dem Leser sowohl die Komplexität dieses außergewöhnlichen Denkens als auch dessen Konsequenzen vor Augen zu führen. (shrink)
We settle a number of questions concerning definability in first order logic with an extra predicate symbol ranging over semi-linear sets. We give new results both on the positive and negative side: we show that in first-order logic one cannot query a semi-linear set as to whether or not it contains a line, or whether or not it contains the line segment between two given points. However, we show that some of these queries become definable if one makes small restrictions (...) on the semi-linear sets considered. (shrink)
We study relations between measure-theoretic classes of ultrafilters, such as the Property M ultrafilters of , with other well-known ultrafilter classes. We define several classes of measure theoretic ultrafilters, of which the Property M ultrafilters are the strongest. We show which containments are provable in ZFC between these measure-theoretic ultrafilters and boolean combinations of well-known ultrafilters such as the selective, semi-selective, and P-point ultrafilters. We also list some of the containment results between measure-theoretic ultrafilters and several other ultrafilter classes, such (...) as the Arrow and Property C ultrafilters. (shrink)
This work deals with the expressive power of logics on finite graphs with access to an additional "arbitrary" linear order. The queries that can be expressed this way are the order-invariant queries for the logic. For the standard logics used in computer science, such as first-order logic, it is known that access to an arbitrary linear order increases the expressiveness of the logic. However, when we look at the separating examples, we find that they have satisfying models whose Gaifman Graph (...) is complex -unbounded in valence and in treewidth. We thus explore the expressiveness of order-invariant queries over well-behaved graphs. We prove that first-order order-invariant queries over strings and trees have no additional expressiveness over first-order logic in the original signature. We also prove new upper bounds on order-invariant queries over bounded treewidth and bounded valence graphs. Our results make use of a new technique of independent interest: the application of algebraic characterizations of definability to show collapse results. (shrink)
Abstract Does the contemporary built environment?the ensemble of our humanly created surroundings?make us happy? This question prompts a consideration of the psychological dimensions of economic value, and of Tibor Scitovsky's revisions of standard economic theory. With Scitovsky as a starting point, a model of value based on modern complexity theory and a Maslow?like rendition of human needs can account for some of the more important exceptions to the law of diminished marginal utility, including those that may undermine the built environment (...) in a market economy. (shrink)