Multi-Dimensional Modal Logic

1. Front Matter

   Pages i-xiii

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2. Multi-Dimensional Modal Logic

   • Maarten Marx, Yde Venema

   Pages 1-9

3. Two-Dimensional Modal Logics

   • Maarten Marx, Yde Venema

   Pages 11-41

4. Arrow Logic

   • Maarten Marx, Yde Venema

   Pages 43-91

5. Modal Logics of Intervals

   • Maarten Marx, Yde Venema

   Pages 93-111

6. Modal Logics of Relations

   • Maarten Marx, Yde Venema

   Pages 113-167

7. Multi-Dimensional Semantics for Every Modal Language

   • Maarten Marx, Yde Venema

   Pages 169-179

8. Back Matter

   Pages 181-239

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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

• Department of Computing, Imperial College, London, UK

  Maarten Marx

• CIS, Free University, Amsterdam, The Netherlands

  Yde Venema

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