Handbook of Spatial Logics

by Aiello, Marco; Pratt-Hartmann, Ian. E; Van Benthem, Johan

• ISBN13: 9781402055867
• ISBN10: 1402055862
• Edition: 1st
• Format: Hardcover
• Copyright: 2007-08-03
• Publisher: Springer Verlag

Summary

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.

Table of Contents

What is Spatial Logic?	p. 1
First-Order Mereotopology	p. 13
Axioms, Algebras and Topology	p. 99
Qualitative Spatial Reasoning Using Constraint Calculi	p. 161
Modal Logics of Space	p. 217
Topology and Epistemic Logic	p. 299
Logical Theories for Fragments of Elementary Geometry	p. 343
Locales and Toposes as Spaces	p. 429
Spatial Logic + Temporal Logic = ?	p. 497
Dynamic Topological Logic	p. 565
Logic of Space-Time and Relativity Theory	p. 604
Discrete Spatial Models	p. 713
Real Algebraic Geometry and Constraint Databases	p. 799
Mathematical Morphology	p. 857
Spatial Reasoning and Ontology: Parts, Wholes, and Locations	p. 945
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