In this thesis, we discuss different techniques to bridge the gap between two different approaches to artificial intelligence: the symbolic and the connectionist paradigm. Both approaches have quite contrasting advantages and disadvantages. Research in the area of neural-symbolic integration aims at bridging the gap between them. Starting from a human readable logic program, we construct connectionist systems, which behave equivalently. Afterwards, those systems can be trained, and later the refined knowledge be extracted.

Wir untersuchen Feynman-Integrale in der Darstellung mit Schwinger-Parametern und leiten rekursive Integralgleichungen für masselose 3- und 4-Punkt-Funktionen her. Eigenschaften der analytischen (und dimensionalen) Regularisierung werden zusammengefasst und wir beweisen, dass in der Euklidischen Region jedes Feynman-Integral als eine Linearkombination konvergenter Feynman-Integrale geschrieben werden kann. Dies impliziert, dass man stets eine Basis aus konvergenten Masterintegralen wählen kann und somit divergente Integrale nicht selbst berechnet werden müssen. Weiterhin geben wir eine in sich geschlossene Darstellung der Theorie der Hyperlogarithmen und erklären detailliert die nötigen Algorithmen, um diese für die Berechnung mehrfacher Integrale anzuwenden. Wir definieren eine neue Methode um die Singularitäten solcher Integrale zu bestimmen und stellen ein Computerprogramm vor, welches die Integrationsalgorithmen implementiert. Unser Hauptresultat ist die Konstruktion unendlicher Familien masseloser 3- und 4-Punkt-Funktionen (diese umfassen unter anderem alle Leiter-Box-Graphen und deren Minoren), deren Feynman-Integrale zu allen Ordnungen in der epsilon-Entwicklung durch multiple Polylogarithmen dargestellt werden können. Diese Integrale können mit dem vorgestellten Programm explizit berechnet werden. Die Arbeit enthält interessante Beispiele von expliziten Ergebnissen für Feynman-Integrale mit bis zu 6 Schleifen. Insbesondere präsentieren wir den ersten exakt bestimmten Gegenterm in masseloser phi^4-Theorie, der kein multipler Zetawert ist sondern eine Linearkombination multipler Polylogarithmen, ausgewertet an primitiven sechsten Einheitswurzeln (und geteilt durch die Quadratwurzel aus 3). Zu diesem Zweck beweisen wir ein Paritätsresultat über die Zerlegbarkeit der Real- und Imaginärteile solcher Zahlen in Produkte und Beiträge geringerer Tiefe (depth). / We study Feynman integrals in the representation with Schwinger parameters and derive recursive integral formulas for massless 3- and 4-point functions. Properties of analytic (including dimensional) regularization are summarized and we prove that in the Euclidean region, each Feynman integral can be written as a linear combination of convergent Feynman integrals. This means that one can choose a basis of convergent master integrals and need not evaluate any divergent Feynman graph directly. Secondly we give a self-contained account of hyperlogarithms and explain in detail the algorithms needed for their application to the evaluation of multivariate integrals. We define a new method to track singularities of such integrals and present a computer program that implements the integration method. As our main result, we prove the existence of infinite families of massless 3- and 4-point graphs (including the ladder box graphs with arbitrary loop number and their minors) whose Feynman integrals can be expressed in terms of multiple polylogarithms, to all orders in the epsilon-expansion. These integrals can be computed effectively with the presented program. We include interesting examples of explicit results for Feynman integrals with up to 6 loops. In particular we present the first exactly computed counterterm in massless phi^4 theory which is not a multiple zeta value, but a linear combination of multiple polylogarithms at primitive sixth roots of unity (and divided by the square-root of 3). To this end we derive a parity result on the reducibility of the real- and imaginary parts of such numbers into products and terms of lower depth.

In this thesis, we discuss different techniques to bridge the gap between two different approaches to artificial intelligence: the symbolic and the connectionist paradigm. Both approaches have quite contrasting advantages and disadvantages. Research in the area of neural-symbolic integration aims at bridging the gap between them. Starting from a human readable logic program, we construct connectionist systems, which behave equivalently. Afterwards, those systems can be trained, and later the refined knowledge be extracted.

While in traditional computer game playing agents were designed solely for the purpose of playing one single game, General Game Playing is concerned with agents capable of playing classes of games. Given the game's rules and a few minutes time, the agent is supposed to play any game of the class and eventually win it. Since the game is unknown beforehand, previously optimized data structures or human-provided features are not applicable. Instead, the agent must derive a strategy on its own. One approach to obtain such a strategy is to analyze the game rules and create a state evaluation function that can be subsequently used to direct the agent to promising states in the match. In this thesis we will discuss existing methods and present a general approach on how to construct such an evaluation function. Each topic is discussed in a modular fashion and evaluated along the lines of quality and efficiency, resulting in a strong agent.

While in traditional computer game playing agents were designed solely for the purpose of playing one single game, General Game Playing is concerned with agents capable of playing classes of games. Given the game's rules and a few minutes time, the agent is supposed to play any game of the class and eventually win it. Since the game is unknown beforehand, previously optimized data structures or human-provided features are not applicable. Instead, the agent must derive a strategy on its own. One approach to obtain such a strategy is to analyze the game rules and create a state evaluation function that can be subsequently used to direct the agent to promising states in the match. In this thesis we will discuss existing methods and present a general approach on how to construct such an evaluation function. Each topic is discussed in a modular fashion and evaluated along the lines of quality and efficiency, resulting in a strong agent.:Introduction Game Playing Evaluation Functions I - Aggregation Evaluation Functions II - Features General Evaluation Related Work Discussion