A compilation of papers presented at the 1999 European Summer Meeting of the Association for Symbolic Logic, Logic Colloquium '99 includes surveys and research articles from some of the world's preeminent logicians. Two long articles are based on tutorials given at the meeting and present accessible expositions of current research in two active are

The Annual European Meeting of the Association for Symbolic Logic, generally known as the Logic Colloquium, is the most prestigious annual meeting in the field. Many of the papers presented there are invited surveys of developments, and the rest of the papers are chosen to complement the invited talks. This 2007 volume includes surveys, tutorials, and selected research papers from the 2005 meeting. Highlights include three papers on different aspects of connections between model theory and algebra; a survey of major advances in combinatorial set theory; a tutorial on proof theory and modal logic; and a description of Bernay's philosophy of mathematics.

This book constitutes the refereed proceedings of the 10th International Conference on Logic Programming, Artificial Intelligence, and Reasoning, LPAR 2003, held in Almaty, Kazakhstan in September 2003. The 27 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 65 submissions. The papers address all current issues in logic programming, automated reasoning, and AI logics in particular description logics, proof theory, logic calculi, formal verification, model theory, game theory, automata, proof search, constraint systems, model checking, and proof construction.

This book constitutes the refereed proceedings of the 10th European Conference on Logics in Artificial Intelligence, JELIA 2006. The 34 revised full papers and 12 revised tool description papers presented together with 3 invited talks were carefully reviewed and selected from 96 submissions. The papers cover a range of topics within the remit of the Conference, such as logic programming, description logics, non-monotonic reasoning, agent theories, automated reasoning, and machine learning.

"A compilation of papers presented at the 1999 European Summer Meeting of the Association for Symbolic Logic, Logic Colloquium `99 includes surveys and research articles from some of the world's preeminent logicians. Two long articles are based on tutorials given at the meeting and present accessible expositions of current research in two active areas of logic, geometric model theory and descriptive set theory of group actions."

"Over the last 20 years, the theory of Borel equivalence relations and related topics have been very active areas of research in set theory and have important interactions with other fields of mathematics, like ergodic theory and topological dynamics, group theory, combinatorics, functional analysis, and model theory. The book presents, for the first time in mathematical literature, all major aspects of this theory and its applications."--BOOK JACKET.

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the nineteenth publication in the Lecture Notes in Logic series, collects the proceedings of the European Summer Meeting of the Association for Symbolic Logic, held in Paris, France in July 2000. This meeting marked the centennial anniversary of Hilbert's famous lecture and was held in the same hall at La Sorbonne where Hilbert presented his problems. Three long articles, based on tutorials given at the meeting, present accessible expositions of developing research in model theory, computability, and set theory. The eleven subsequent papers present work from the research frontier in all areas of mathematical logic.

Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.

This is this, this ain't something else, this is this -Robert De Niro, Deerhunter his book may to some extent be viewed as the continuation of my T Doctoral thesis Epistemology, Methodology and Reliability. The dissertation was, first of all, a methodological study of the reliable performance of the AGM-axioms (Alchourr6n, Gardenfors and Makin son) of belief revision. Second of all the dissertation included the first steps toward an epistemology for the limiting convergence of knowledge for scientific inquiry methods of both discovery and assessment. The idea of methodological reliability as a desirable property of a scientific method was introduced to me while I was a visiting Ph. D. -student at the Department of Philosophy, Carnegie Mellon University in Pitts burgh, Pennsylvania, USA in 1995-96. Here I became acquainted with formal learning theory. Learning theory provides a variety of formal tools for investigating a number of important issues within epistemology, methodology and the philosophy of science. Especially with respect to the problem of induc tion, but not exclusively. The Convergence of Scientific Knowledge-a view from the limit utilizes a few concepts from formal learning theory to study problems in modal logic and epistemology. It should be duely noted that this book has virtually nothing to do with formal learning theory or inductive learning problems.

This book constitutes the refereed proceedings of the 15th International Workshop on Computer Science Logic, CSL 2001, held as the 10th Annual Conerence of the EACSL in Paris, France in September 2001. The 39 revised full papers presented together with two invited papers were carefully reviewed and selected from 91 submissions. The papers are organized in topical sections on linear logic, descriptive complexity, semantics, higher-order programs, model logics, verification, automata, lambda calculus, induction, equational calculus, and constructive theory of types.