Interactive Theorem Proving with Indexed Formulas

Since more than two decades research in interactive theorem proving (ITP) has attracted growing interest. The primary application domains for ITPs range from hard- and software verification tools to mathematical tutor systems. To support communication with the user in an adequate way these systems depend on calculi that allow for the construction of human understandable and readable proofs. However, most calculi that are used in current ITPs fall still short of supporting the user in an optimal way. The reason is that they enforce the user to construct proofs at a level that is far more detailed than the one that can be found in human constructed proofs. Autexier [Aut03] has recently proposed a new theorem proving framework that allows to model different logics and calculi in an uniform way. In CORE, a proof-state is always represented as a single formula that can be manipulated by the application of replacement rules that are generated from the logical context of the subformula under transformation. This approach also facilitates proof construction at the assertion level which is considered as more closely matching the level at which humans construct proofs (see for instance [Hua94]). Together with COREs window inference technique this makes CORE a potentially well suited basis for interactive theorem proving. This thesis tries to excerpt COREs potential for interactive theorem proving by mapping important concepts of the established proof system ΩMEGA to CORE. A task structure is developed to present the context of a subformula in an intuitive way to the user and to assist him in structuring proofs. The development of a method interpreter makes it possible to specify abstract inference steps declaratively and to encode proof strategies for the use in CORE. The adaptation of ΩMEGAS agent-based suggestion mechanism ΩANTS to CORE helps the user with the identification of applicable methods and replacement rules.Interaktives Theorembeweisen hat in den letzten zwei Jahrzehnten zunehmend an Bedeutung gewonnen. Die Anwendungsbereiche von Systemen mit denen sich Beweise interaktiv führen lassen reichen von der Hard- und Software Verifikation bis zu mathematischen Tutor-Systemen. Die genannten Anwendungsgebiete machen es erforderlich das der Anwender bei der Beweisführung adequat untersützt wird. Um eine entsprechende Kommunikation mit dem Benutzer zu ermöglichen verwenden interaktive Beweissysteme Kalküle, in denen Beweise in einer für den Benutzer nachvollziehbaren Art und Weise, geführt werden können. Trotzdem kann man noch nicht davon sprechen, dass interaktive Beweiser den Benutzer optimal unterstützen. Der Hauptrgund hierfür ist, dass die eingesetzten Kalküle automatisch dazu führen, dass Beweise auf einer viel detailliertern Ebene geführt werden müssen, als man typischerweise in einem mathematischen Beweis finden würde. Autexier [Aut03]hat kürzlich eine neue logische Umgebung für die Beweissuche entwickelt, welche es ermöglicht verschiedene Logiken und Kalküle einheitlich zu modellieren. In CORE ist ein Beweiszustand immer als eine einzige Formel repräsentiert, welche durch das Anwenden von Ersetzungsregeln, die aus dem Kontext einer Teilformel abgeleitet werden, transformiert werden kann. Diese Herangehensweise erleichtert es auch, Beweise auf der sogenannten Assertion-Ebene (vgl. [Hua94]) zu führen, welche allgemein als eine natürlichere Ebene für die Beweisführung angesehen wird. Zusammen mit der Window-Inferenz Technik, die von CORE unterstützt, wird stellt CORE ein System dar das potentiell als eine verbesserte Grundlage für die interaktive Beweissuche angesehen werden kann. In dieser Arbeit geht es darum, das Potential von CORE im Hinblick auf die interaktive Beweiskonstruktion auszunutzen. Dieses geschieht zum einen dadurch, dass etablierte Konzepte im Bereich des interaktiven Beweisens, wie sie auch im Beweis-System ΩMEGA verwendet werden, auf das CORE-System abgebildet werden. Desweiteren wird eine Task-Srukture entwickelt, die es zum einen ermöglicht, den logischen Kontext einer Teilformel für den Benutzer verständlich aufzubereiten und darzustellen; zum anderen untersützt sie den Anwender auch darin, Beweise strukturiert zu führen. Der Entwurf eines Methoden-Interpreters ermöglicht es, abstrakte Beweisschritte zu kodieren und im System anzuwenden. Die Anpassung des Vorschlags-Mechanismus ΩANTS an CORE stellt eine weitere Unterstützung für den Benutzer bereit, indem sie automatisch Vorschläge über mögliche Fortsetzungen eines Beweises generiert

Essays in fiscal federalism - Welfare competition and the funding of higher education

This thesis considers several aspects of fiscal federalism. First, it addresses the problems arising in the presence of student mobility, when higher education is provided by sub-national governments. It is shown that preferential fee regimes that favor in-state students over out-of-state students reduce welfare compared to a situation with decentralized provision, but equal treatment of in- and out-of state students. The thesis also comprises an empirical part that quantifies the effect of the introduction of tuition fees in Germany on enrolment probabilities, suggesting that the introduction of tuition fees reduced enrolment probabilities in Germany. The last chapter of the thesis provides empirical evidence for the facts that the German counties engaged in welfare competition. The intensity of competition however declined after a welfare reform that led to a more centralized provision of welfare benefits

Patience and Inflation

Monetary policy makers constantly face an inter-temporal choice problem. By gener- ating surprise inflation they can temporarily increase employment and output. These short-run gains have however to be weighed against the long-run costs associated with higher inflation and a loss of reputation. More patient countries should therefore choose to implement lower inflation. Using cross-country data for up to 88 advanced and emerging economies, we provide empirical evidence that more patient countries had indeed lower average inflation rates over our sample period from 1961 to 2009. To address the possibility that patience may be endogenous to past inflation rates we use information on how the language spoken in a country encodes future time as an instrument for patience. Our results show that patience has a statistically and economically significant impact on inflation

Patience and Inflation

Monetary policy makers constantly face an inter-temporal choice problem. By gener- ating surprise inflation they can temporarily increase employment and output. These short-run gains have however to be weighed against the long-run costs associated with higher inflation and a loss of reputation. More patient countries should therefore choose to implement lower inflation. Using cross-country data for up to 88 advanced and emerging economies, we provide empirical evidence that more patient countries had indeed lower average inflation rates over our sample period from 1961 to 2009. To address the possibility that patience may be endogenous to past inflation rates we use information on how the language spoken in a country encodes future time as an instrument for patience. Our results show that patience has a statistically and economically significant impact on inflation

Throughput Analysis for Layout Optimisation of Modular Conveyor Systems

In this paper, objective functions for the optimisation of modular conveyor systems will be introduced. Modular conveyor systems consist of conventional as well as modular conveyor hardware, which are arranged in form of matrix-like layouts. The aim of an ongoing research project is to provide small and medium-sized enterprises with a user-friendly decision support for the selection and planning of modular conveyor systems. For this purpose, the conveyor systems should be evaluated according to the objectives throughput and space requirement. Therefore, mathematical equations have been developed, which enable a fast and precise evaluation of layouts. The paper focuses mainly on the efficient calculation of the throughput. The result quality of the evaluation equations regarding the throughput was proven by a simulation of example systems

Development of a Method for Decision Support on Participation in Capacity Sharing for Manufacturing SMEs

A volatile, non-transparent market environment leads to fluctuations in the load on production capacities in the manufacturing sector, which are reflected within production in the over- or underutilization of machines and persons. Small and midsized enterprises (SMEs) are expecting increasing volatility, which is accompanied by an increase in the frequency of market and economic cycles. For SMEs it is difficult to cope with these fluctuations. Capacity sharing platforms can be a solution for this challenge. Platforms are available in different forms, but not used by companies often, because of prevailing scepticism in different fields. Therefore, a methodology will be developed to provide a decision support for or against platform usage. Additionally, the platform type choice will be supported, and the changes of logistic and economic indicators will be considered. With this information companies can make a qualitative decision, and the existing inhibitions can be alleviated

Endowashers: an overlooked risk for possible post-endoscopic infections

Background: Prevention of post-endoscopy infections is an important objective to assure patient safety. Endowashers, or high throughput irrigation water pumps, are a frequently used device on endoscopes. Recommendations published by professional bodies and regulatory health agencies cover not only adequate reprocessing of fiber-endoscopes but also state accepted methods of regular microbial sampling. Although major instruments like endoscopes are covered by these recommendations, other devices used as optional add-ons for endoscopes are not included

Observation of ultrafast solid-density plasma dynamics using femtosecond X-ray pulses from a free-electron laser

The complex physics of the interaction between short pulse high intensity lasers and solids is so far hardly accessible by experiments. As a result of missing experimental capabilities to probe the complex electron dynamics and competing instabilities, this impedes the development of compact laser-based next generation secondary radiation sources, e.g. for tumor therapy [Bulanov2002,ledingham2007], laboratory-astrophysics [Remington1999,Bulanov2015], and fusion [Tabak2014]. At present, the fundamental plasma dynamics that occur at the nanometer and femtosecond scales during the laser-solid interaction can only be elucidated by simulations. Here we show experimentally that small angle X-ray scattering of femtosecond X-ray free-electron laser pulses facilitates new capabilities for direct in-situ characterization of intense short-pulse laser plasma interaction at solid density that allows simultaneous nanometer spatial and femtosecond temporal resolution, directly verifying numerical simulations of the electron density dynamics during the short pulse high intensity laser irradiation of a solid density target. For laser-driven grating targets, we measure the solid density plasma expansion and observe the generation of a transient grating structure in front of the pre-inscribed grating, due to plasma expansion, which is an hitherto unknown effect. We expect that our results will pave the way for novel time-resolved studies, guiding the development of future laser-driven particle and photon sources from solid targets