Gilles Dowek is a Professor at École Polytechnique. He is also a Researcher at the Laboratoire d'Informatique de l'École Polytechnique and the Institut National de Recherche en Informatique et en Automatique (INRIA). His research concerns the formalization of mathematics and the mechanization of reasoning. His main contribution is a reformulation of the axiomatic method which provides a central role to the notion of computation.

Proofs and Algorithms: An Introduction to Logic and Computability

Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation.
Proofs and Algorithms: An Introduction to Logic and Computability is an introduction to the fundamental concepts of contemporary logic - those of a proof, a computable function, a model and a set. It presents a series of results, both positive and negative, - Church's undecidability theorem, Gödel's incompleteness theorem, the theorem asserting the semi-decidability of provability - that have profoundly changed our vision of reasoning, computation, and finally truth itself.
Designed for undergraduate students, this book presents all that philosophers, mathematicians and computer scientists should know about logic.

Proofs.-Predictive Logic.-Models.-Algorithms.-Computable Functions.-Computation as a Sequence of Small Steps.-Proofs and Algorithms.-Church's Theorem.-Automated Theorem Proving.-Decidable Theories.-Constructivity.-Epilogie.-Index.-Bibliography