Editors’ Introduction to [Algorithmic Learning Theory: 18th International Conference, ALT 2007, Sendai, Japan, October 1-4, 2007. Proceedings]

Learning theory is an active research area that incorporates ideas, problems, and techniques from a wide range of disciplines including statistics, artificial intelligence, information theory, pattern recognition, and theoretical computer science. The research reported at the 18th International Conference on Algorithmic Learning Theory (ALT 2007) ranges over areas such as unsupervised learning, inductive inference, complexity and learning, boosting and reinforcement learning, query learning models, grammatical inference, online learning and defensive forecasting, and kernel methods. In this introduction we give an overview of the five invited talks and the regular contributions of ALT 2007

Computability Theory

Computability and computable enumerability are two of the fundamental notions of mathematics. Interest in effectiveness is already apparent in the famous Hilbert problems, in particular the second and tenth, and in early 20th century work of Dehn, initiating the study of word problems in group theory. The last decade has seen both completely new subareas develop as well as remarkable growth in two-way interactions between classical computability theory and areas of applications. There is also a great deal of work on algorithmic randomness, reverse mathematics, computable analysis, and in computable structure theory/computable model theory. The goal of this workshop is to bring together researchers representing different aspects of computability theory to discuss recent advances, and to stimulate future work

Classical Theorems in Reverse Mathematics and Higher Recursion Theory

Ph.DDOCTOR OF PHILOSOPH

Variants of Partial Learning in Inductive Inference

Master'sMASTER OF SCIENC

Aspects Topologiques des Représentations en Analyse Calculable

Computable analysis provides a formalization of algorithmic computations over infinite mathematical objects. The central notion of this theory is the symbolic representation of objects, which determines the computation power of the machine, and has a direct impact on the difficulty to solve any given problem. The friction between the discrete nature of computations and the continuous nature of mathematical objects is captured by topology, which expresses the idea of finite approximations of infinite objects.We thoroughly study the multiple interactions between computations and topology, analysing the information that can be algorithmically extracted from a representation. In particular, we focus on the comparison between two representations of a single family of objects, on the precise relationship between algorithmic and topological complexity of problems, and on the relationship between finite and infinite representations.L’analyse calculable permet de formaliser le traitement algorithmique d’objets mathématiques infinis. La théorie repose sur une représentation symbolique des objets, dont le choix détermine les capacités de calcul de la machine, notamment sa difficulté à résoudre chaque problème donné. La friction entre le caractère discret du calcul et la nature continue des objets est capturée par la topologie, qui exprime l’idée d’approximation finie d’objets infinis.Nous étudions en profondeur les multiples interactions entre calcul et topologie, cherchant à analyser l’information qui peut être extraite algorithmiquement d’une représentation. Je me penche plus particulièrement sur la comparaison entre deux représentations d’une même famille d’objets, sur les liens détaillés entre complexité algorithmique et topologique des problèmes, ainsi que sur les relations entre représentations finies et infinies

The Nature of Law and Legality in the Byzantine Canonical Collections 381-883

The present work seeks to explore the nature of law and legality in the Byzantine canonical tradition through a careful reading of the central texts of the Byzantine canonical corpus. The principal topics to be considered include the shape and growth of the corpus as a whole, the content and themes of the traditional prologues, the language, genre and style of the canons themselves, and the traditional thematic rearrangements of the canonical corpus. As a cultural-historical exploration of law, this work has as its goal throughout to trace the fundamental contours of how the tradition conceives, frames and "imagines" itself as a legal system: central themes and concepts, basic presuppositions, recurring patterns, and prominent contextualizations. Drawing on categories of modern legal theory and legal anthropology, this work is particularly interested in the nature of legal norms and their relationship to other normative systems, the place and role of technical rule-discourse, and mechanisms of change, development and interpretation. The relationship of the canons to the secular law will also be taken into account. The central argument of this work is that the picture of law that emerges from the Byzantine material is fundamentally at odds with many formalist/positivist expectations of modern western legal culture. This dissonance had traditionally made it very easy to dismiss Byzantine canon law as "primitive" or "decadent". If approached more sympathetically, however, this strange legal world can be read as constituting a surprisingly coherent and rich legal system that is characterized by 1) a deep investment in embedding itself in broader value-narratives; 2) the centrality of the idea of law as a sacred (and relatively inviolable) tradition; and 3) a strong orientation towards the realization of substantive justice, not formal consistency. If taken seriously, this picture of law has a number of important implications for contemporary Orthodox canonical legal theory, the broader history of church law, and the study of late antique and Byzantine law generally