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  3. Cambridge Tracts in Theoretical Computer Science

This series offers books on theoretical computer science, that part of computer science concerned with fundamental mathematical questions about computers, programs, algorithms, data, and information processing systems in general. Computers and programs are inherently mathematical objects, and an understanding of their mathematical basis is essential to the appreciation of the foundations of computer science.The series covers the complete field of theoretical computer science, including mathematical foundations of computer science, formal methods of reasoning about programs and data, and formal semantics of programs and data, including formal semantics for natural language, pictures, and sound.

  • Associate Editors: S. Abramsky, Oxford University
  • Editorial Boards: P. H. Aczel, University of Manchester, Y. Gurevich, Microsoft Research, J. V. Tucker, Swansea University

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43 results in Cambridge Tracts in Theoretical Computer Science

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Belief Revision
  • Edited by Peter Gärdenfors
  • Published online:
    21 September 2009
    Print publication:
    21 May 1992
  • Belief revision is a topic of much interest in theoretical computer science and logic, and it forms a central problem in research into artificial intelligence. In simple terms: how do you update a database of knowledge in the light of new information? What if the new information is in conflict with something that was previously held to be true? An intelligent system should be able to accommodate all such cases. This book contains a collection of research articles on belief revision that are completely up to date and an introductory chapter that presents a survey of current research in the area and the fundamentals of the theory. Thus this volume will be useful as a textbook on belief revision.

Logic and Computation
  • Interactive Proof with Cambridge LCF
  • Lawrence C. Paulson
  • Published online:
    17 September 2009
    Print publication:
    15 October 1987
  • This book is concerned with techniques for formal theorem-proving, with particular reference to Cambridge LCF (Logic for Computable Functions). Cambridge LCF is a computer program for reasoning about computation. It combines the methods of mathematical logic with domain theory, the basis of the denotational approach to specifying the meaning of program statements. Cambridge LCF is based on an earlier theorem-proving system, Edinburgh LCF, which introduced a design that gives the user flexibility to use and extend the system. A goal of this book is to explain the design, which has been adopted in several other systems. The book consists of two parts. Part I outlines the mathematical preliminaries, elementary logic and domain theory, and explains them at an intuitive level, giving reference to more advanced reading; Part II provides sufficient detail to serve as a reference manual for Cambridge LCF. It will also be a useful guide for implementors of other programs based on the LCF approach.

Rippling: Meta-Level Guidance for Mathematical Reasoning
  • Alan Bundy, David Basin, Dieter Hutter, Andrew Ireland
  • Published online:
    13 August 2009
    Print publication:
    30 June 2005
  • Rippling is a radically new technique for the automation of mathematical reasoning. It is widely applicable whenever a goal is to be proved from one or more syntactically similar givens. It was originally developed for inductive proofs, where the goal was the induction conclusion and the givens were the induction hypotheses. It has proved to be applicable to a much wider class of tasks, from summing series via analysis to general equational reasoning. The application to induction has especially important practical implications in the building of dependable IT systems, and provides solutions to issues such as the problem of combinatorial explosion. Rippling is the first of many new search control techniques based on formula annotation; some additional annotated reasoning techniques are also described here. This systematic and comprehensive introduction to rippling, and to the wider subject of automated inductive theorem proving, will be welcomed by researchers and graduate students alike.

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