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This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these emerging topics, it includes proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences.Suitable for researchers and graduate students in mathematical, computational and philosophical logic, and in theoretical computer science and artificial intelligence, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (2nd Edition), Dov M. Gabbay, Mark A. Reynolds, and Marcelo Finger's Temporal Logic Mathematical Foundations and Computational Aspects , J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning , and P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2 .
David J. Pym hold a Royal Society Industry Fellowship at Hewlett-Packard Laboratories, Bristol and the University of Bath.
Preface ; Foreword by Lincoln Wallen ; 1. Deductive Logic, Reductive Logic, and Proof-search ; 2. Lambda-calculi for Intuitionistic and Classical Proofs ; 3. The Semantics of Intuitionistic and Classical Proofs ; 4. Proof Theory for Reductive Logic ; 5. Semantics for Reductive Logic ; 6. Intuitionistic and Classical Proof-search and Their Semantics ; References ; Index
Alex Citkin, Alexei Muravitsky, New York) Citkin, Alex (CIO, CIO, Metropolitan Telecommunications, Louisiana Scholars' College at Northwestern State University of Louisiana) Muravitsky, Alexei (Professor of Mathematics, Professor of Mathematics
Ian Pratt-Hartmann, University of Opole) Pratt-Hartmann, Ian (Senior Lecturer, University of Manchester Professor of Mathematical Sciences, University of Opole, Senior Lecturer, University of Manchester Professor of Mathematical Sciences
Giovanni Sambin, Jan M. Smith, Italy) Sambin, Giovanni (Professor of Mathematical Logic, Professor of Mathematical Logic, University of Padua, Sweden) Smith, Jan M. (Professor, Department of Computing Science, Professor, Department of Computing Science, Chalmers University of Technology, Jan Smith
Dov M. Gabbay, Larisa Maksimova, King's College London) Gabbay, Dov M. (, Department of Computer Science, Russia) Maksimova, Larisa (, Institute of Mathematics, Siberian Branch of Russian Academy of Science, Novosibirsk
Erik Sandewall, Sweden) Sandewall, Erik (Professor, Department of Computer and Information Science, Professor, Department of Computer and Information Science, Linkoping University
Giovanni Sambin, Jan M. Smith, Italy) Sambin, Giovanni (Professor of Mathematical Logic, Professor of Mathematical Logic, University of Padua, Sweden) Smith, Jan M. (Professor, Department of Computing Science, Professor, Department of Computing Science, Chalmers University of Technology, Jan Smith