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Full Description
A spatial logic is a formal language interpreted over any class of structures featuring geometrical entities and relations, broadly construed. In the past decade, spatial logics have attracted much attention in response to developments in such diverse fields as Artificial Intelligence, Database Theory, Physics, and Philosophy. The aim of this handbook is to create, for the first time, a systematic account of the field of spatial logic. The book comprises a general introduction, followed by fourteen chapters by invited authors. Each chapter provides a self-contained overview of its topic, describing the principal results obtained to date, explaining the methods used to obtain them, and listing the most important open problems. Jointly, these contributions constitute a comprehensive survey of this rapidly expanding subject.
Contents
What is Spatial Logic?.- First-Order Mereotopology.- Axioms, Algebras and Topology.- Qualitative Spatial Reasoning Using Constraint Calculi.- Modal Logics of Space.- Topology and Epistemic Logic.- Logical Theories for Fragments of Elementary Geometry.- Locales and Toposes as Spaces.- Spatial Logic + Temporal Logic = ?.- Dynamic Topological Logic.- Logic of Space-Time and Relativity Theory.- Discrete Spatial Models.- Real Algebraic Geometry and Constraint Databases.- Mathematical Morphology.- Spatial Reasoning and Ontology: Parts, Wholes, and Locations.
