This book constitutes the refereed proceedings of the Third International Conference on Computability in Europe, CiE 2007, held in Sienna, Italy, in June 2007. The 50 revised full papers presented together with 36 invited papers were carefully reviewed and selected from 167 submissions.

In the 21st century, digitalization is a global challenge of mankind. Even for the public, it is obvious that our world is increasingly dominated by powerful algorithms and big data. But, how computable is our world? Some people believe that successful problem solving in science, technology, and economies only depends on fast algorithms and data mining. Chances and risks are often not understood, because the foundations of algorithms and information systems are not studied rigorously. Actually, they are deeply rooted in logics, mathematics, computer science and philosophy.Therefore, this book studies the foundations of mathematics, computer science, and philosophy, in order to guarantee security and reliability of the knowledge by constructive proofs, proof mining and program extraction. We start with the basics of computability theory, proof theory, and information theory. In a second step, we introduce new concepts of information and computing systems, in order to overcome the gap between the digital world of logical programming and the analog world of real computing in mathematics and science. The book also considers consequences for digital and analog physics, computational neuroscience, financial mathematics, and the Internet of Things (IoT).

Computational Intelligence (CI) has emerged as a novel and highly diversified paradigm supporting the design, analysis and deployment of intelligent systems. This book presents a careful selection of the field that very well reflects the breadth of the discipline. It covers a range of highly relevant and practical design principles governing the development of intelligent systems in data mining, robotics, bioinformatics, and intelligent tutoring systems. The lucid presentations, coherent organization, breadth and the authoritative coverage of the area make the book highly attractive for everybody interested in the design and analysis of intelligent systems.

The general problem addressed in this book is a large and important one: how to usefully deal with huge storehouses of complex information about real-world situations. Every one of the major modes of interacting with such storehouses – querying, data mining, data analysis – is addressed by current technologies only in very limited and unsatisfactory ways. The impact of a solution to this problem would be huge and pervasive, as the domains of human pursuit to which such storehouses are acutely relevant is numerous and rapidly growing. Finally, we give a more detailed treatment of one potential solution with this class, based on our prior work with the Probabilistic Logic Networks (PLN) formalism. We show how PLN can be used to carry out realworld reasoning, by means of a number of practical examples of reasoning regarding human activities inreal-world situations.

We all learn - in schools, factories, bars and streets. We gather, store, process and transmit information in society. Molecular systems involved in our senses and within our brains allow all this to happen and molecular systems allow living things of all kinds to handle information for the purpose of survival and growth. Nevertheless, the vital link between molecules and computation was not generally appreciated until a few decades ago. Semiconductor-based information technology had penetrated society at many levels and the interest in maintaining momentum of this revolution led to the consideration of molecules, among others, as possible information handlers. Such an overlap between the recent engineering-oriented revolution with the ancient biology-oriented success story is very interesting and George Boole's times in Ireland 150 years ago produced the logic ideas that provide the foundations of computation to this day. Molecular logic and computation is a field which is 17 years young, has had a healthy growth and is a story which deserves to be told. It is a growing branch of chemical science which highlights the connection between information technology (engineering and biological) and chemistry. The author and co-workers of this publication launched molecular logic as an experimental field by publishing the first research in the primary literature in 1993 and are uniquely placed to recount how the field has grown. There is no other book at present on molecular logic and computation and is more comprehensive than that found in any review available so far. It shows how designed molecules can play the role of information processors in a wide variety of situations, once we are educated by those information processors already available in the semiconductor electronics business and in the natural world. Following a short history of the field, is a set of primers on logic, computing and photochemical principles which are an essential basis in this field. The book covers all of the Boolean logic gates driven by a single input and all of those with double inputs and the wide range of designs which lie beneath these gates is a particular highlight. The easily-available diversity of chemical systems is another highlight, especially when it leads to reconfigurable logic gates. Further on in the book, molecular arithmetic and other more complex logic operations, including those with a memory and those which stray beyond binary are covered. Then follows molecular computing approaches which lie outside the Boolean blueprint, including quantum phenomena and finally, the book catalogues the useful real-life applications of molecular logic and computation which are already available. This book is an authoritative, state of the art, reference and a 'one-stop-shop' concerning the current state of the field for scientists, academics and postgraduate students.

This Festschrift volume, published in honor of Yuri Gurevich on the occasion of his 70th birthday, contains contributions, written by his colleagues. The collection of articles herein begins with an academic biography, an annotated list of Yuri's publications and reports, and a personal tribute by Jan Van den Bussche. These are followed by 28 technical contributions. These articles - though they cover a broad range of topics - represent only a fraction of Yuri Gurevich’s multiple areas of interest.

`Intellectics' seeks to understand the functions, structure and operation of the human intellect and to test artificial systems to see the extent to which they can substitute or complement such functions. The word itself was introduced in the early 1980s by Wolfgang Bibel to describe the united fields of artificial intelligence and cognitive science. The book collects papers by distinguished researchers, colleagues and former students of Bibel's, all of whom have worked together with him, and who present their work to him here to mark his 60th birthday. The papers discuss significant issues in intellectics and computational logic, ranging across automated deduction, logic programming, the logic-based approach to intellectics, cognitive robotics, knowledge representation and reasoning. Each paper contains new, previously unpublished, reviewed results. The collection is a state of the art account of the current capabilities and limitations of a computational-logic-based approach to intellectics. Readership: Researchers who are convinced that the intelligent behaviour of machines should be based on a rigid formal treatment of knowledge representation and reasoning.