Multi-Dimensional Modal Logic
by Maarten Marx
2020-07-22 13:41:22
Multi-Dimensional Modal Logic
by Maarten Marx
2020-07-22 13:41:22
Modal Logic is a branch of logic with applications in many related disciplines like computer science, philosophy, linguistics or artificial intelligence. Over the last twenty years, in all of these neighboring fields, modal systems have been develope...
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Modal Logic is a branch of logic with applications in many related disciplines like computer science, philosophy, linguistics or artificial intelligence. Over the last twenty years, in all of these neighboring 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.). It is the aim of this book to treat 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, focussing 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.
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