Optimization methods for logical inference

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Jean-Yves Girard, Yves Lafont, Laurent Regnier

Linear logic, introduced in 1986 by J.-Y. Girard, is based upon a fine grain analysis of the main proof-theoretical notions of logic. The subject develops along the lines of denotational semantics, proof nets and the geometry of interaction. Its basic dynamical nature has attracted computer scientists, and various promising connections have been made in the areas of optimal program execution, interaction nets and knowledge representation. This book is the refereed proceedings of the first international meeting on linear logic held at Cornell University, in June 1993. Survey papers devoted to specific areas of linear logic, as well as an extensive general introduction to the subject by J.-Y. Girard, have been added, so as to make this book a valuable tool both for the beginner and for the advanced researcher.

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J.M. Larrazabal, D. Lascar, G. Mints (eds

This volume contains eleven contributions by invited speakers at the annual Logic Colloquium which was held in San Sebastian, Spain, in July 1996. They cover model theory, proof theory, recursion and complexity theory, logic for artificial intelligence and formal semantics of natural languages, and include both recent results and survey articles on the central topics in logic written by specialists for a wide audience.

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Lars Gårding, Torbjörn Tambour

The aim of this book is to teach the reader the topics in algebra which are useful in the study of computer science. In a clear, concise style, the author present the basic algebraic structures, and their applications to such topics as the finite Fourier transform, coding, complexity, and automata theory. The book can also be read profitably as a course in applied algebra for mathematics students.

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Areski Nait Abdallah

This book presents the foundations of reasoning with partial information and a theory of common sense reasoning based on monotonic logic and partial structures. This theory was designed specifically for the needs of practicing computer scientists and provides easily implementable algorithms. Starting from first principles, following the logic of discovery of Karl Popper and Imre Lakatos, and the semantics of programming languages, the book develops a system of reasoning with partial information, and applies it to a comprehensive study of the problem examples from the literature of common sense reasoning. Proof-theoretic and model-theoretic views are considered in the applications, as well as logical problems of theoretical physics, such as issues related to Heisenberg's uncertainty principle. The book points out that customary expositions of common-sense reasoning are based on a flawed non-monotonic reasoning paradigm and that the resulting solutions proposed for major problems, such as the frame problem, are either ad hoc or inadequate. It is shown that non-monotonicity results from hiding information that should not be hidden. The essential research in common-sense reasoning has been developed in isolation from the disciplines of theoretical computer science and classical logic. This work breaks the isolation and establishes deep links. The book will be of interest to computer scientists, mathematicians, logicians, and philosophers interested in the foundations and applications of reasoning with partial information.