© 1997

Multi-Dimensional Modal Logic


Part of the Applied Logic Series book series (APLS, volume 4)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Maarten Marx, Yde Venema
    Pages 1-9
  3. Maarten Marx, Yde Venema
    Pages 11-41
  4. Maarten Marx, Yde Venema
    Pages 43-91
  5. Maarten Marx, Yde Venema
    Pages 93-111
  6. Maarten Marx, Yde Venema
    Pages 113-167
  7. Maarten Marx, Yde Venema
    Pages 169-179
  8. Back Matter
    Pages 181-239

About this book


Modal Logic is a branch of logic with applications in many related disciplines such as computer science, philosophy, linguistics and artificial intelligence. Over the last twenty years, in all of these neighbouring fields, modal systems have been developed that we call multi-dimensional. (Our definition of multi-dimensionality in modal logic is a technical one: we call a modal formalism multi-dimensional if, in its intended semantics, the universe of a model consists of states that are tuples over some more basic set.)
This book treats such multi-dimensional modal logics in a uniform way, linking their mathematical theory to the research tradition in algebraic logic. We will define and discuss a number of systems in detail, focusing on such aspects as expressiveness, definability, axiomatics, decidability and interpolation. Although the book will be mathematical in spirit, we take care to give motivations from the disciplines mentioned earlier on.


Tuple artificial intelligence bibliography computer formalism linguistics logic modal logic model philosophy predicate logic semantic semantics tradition will

Authors and affiliations

  1. 1.Department of ComputingImperial CollegeLondonUK
  2. 2.CISFree UniversityAmsterdamThe Netherlands

Bibliographic information

  • Book Title Multi-Dimensional Modal Logic
  • Authors Maarten Marx
    Yde Venema
  • Series Title Applied Logic Series
  • DOI
  • Copyright Information Springer Science+Business Media Dordrecht 1997
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-7923-4345-5
  • Softcover ISBN 978-94-010-6401-9
  • eBook ISBN 978-94-011-5694-3
  • Series ISSN 1386-2790
  • Edition Number 1
  • Number of Pages XIII, 239
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Logic
    Mathematical Logic and Foundations
    Computational Linguistics
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