Multi-Dimensional Modal Logic

✍ Scribed by Maarten Marx, Yde Venema (auth.)

• Publisher: Springer Netherlands
• Year: 1997
• Tongue: English
• Leaves: 241
• Series: Applied Logic Series 4
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xiii
Multi-Dimensional Modal Logic....Pages 1-9
Two-Dimensional Modal Logics....Pages 11-41
Arrow Logic....Pages 43-91
Modal Logics of Intervals....Pages 93-111
Modal Logics of Relations....Pages 113-167
Multi-Dimensional Semantics for Every Modal Language....Pages 169-179
Back Matter....Pages 181-239

✦ Subjects

Logic; Mathematical Logic and Foundations; Computational Linguistics