Michael Benedikt

We revisit evaluation of logical formulas that allow both uninterpreted relations, constrained to be finite, as well as an interpreted vocabulary over an infinite domain. This formalism was denoted embedded finite model theory in the past. It is clear that the expressiveness and evaluating complexity of formulas of this type depend heavily on the infinite structure. If we embed in a wild structure like the integers with additive and multiplicative arithmetic, logic is extremely expressive and formulas are impossible to evaluate. On the other hand, for some well-known decidable structures, the expressiveness and evaluating complexity are similar to the situation without the additional infrastructure. The latter phenomenon was formalized via the notion of “Restricted Quantifier Collapse”: adding quantification over the infinite structure does not add expressiveness. Beyond these two extremes little was known. In this work we show that the possibilities for expressiveness and complexity are much wider. We show that we can get almost any possible complexity of evaluation while staying within a decidable structure. We also show that in some decidable structures, there is a disconnect between expressiveness of the logic and complexity, in that we cannot eliminate quantification over the structure, but this is not due to an ability to embed complex relational computation in the logic. We show failure of collapse for the theory of finite fields and the related theory of pseudo-finite fields, which will involve coding computation in the logic. As a by-product of this, we establish the first lower bounds for the complexity of decision procedures for several decidable theories of fields, including the theory of finite fields. This article includes material in the extended abstract “Embedded Finite Models: Beyond Restricted Quantifier Collapse,” that appeared in the Logic in Computer Science conference (LICS ’23).

Bd. 1, Pt. 1. Philosophie in Österreich (1400-1650); Vom Konstanzer Konzil zum Auftreten Luthers; Vom Beginn der Reformation bis zum Westfälischen Frieden / Michael Benedikt, Reinhold Knoll, Josef Rupitz (Hg.) -- Bd. 1, Pt. 2. Die Philosophie in Österreich zwischen Reformation und Aufklärung (1650-1750); Die Stärke des Barock / Michael Benedikt, Reinhold Knoll, Josef Rupitz (Hg.) -- [2. Bd.]. Österreichische Philosophie zur Zeit der Revolution und Restauration, 1750-1820 / Michael Benedikt (Hg.). -- 3. Bd. Bildung und Einbildung; Vom verfehlten Bürgerlichen zum Liberalismus; Philosophie in Österreich (1820-1880) / Michael Benedikt, Reinhold Knoll (Hg.) -- Bd. 4. Anspruch un Echo / Michael Benedikt, Endre Kiss, Reinhold Knoll (Hg.) -- Bd. 5. Im Schatten der Totalitarianismus : vom philosophischen Empiricismus zur kritischen Anthropologie : Philosophie in Österreich, 1920-1951 / Michael Benedikt, Reinhold Knoll, Cornelius Zehetner (Hg.) -- Bd. 6. Auf der Suche nach authentischem Philosophieren : Philosophie in Österreich, 1951-2000 / Michael Benedikt... [et al.] (Hg.).

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.

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.

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.

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.