A Modal Walk Through Space

We investigate the major mathematical theories of space from a modal standpoint: topology, affine geometry, metric geometry, and vector algebra. This allows us to see new fine-structure in spatial patterns which suggests analogies across these mathematical theories in terms of modal, temporal, and conditional logics. Throughout the modal walk through space, expressive power is analyzed in terms of language design, bisimulations, and correspondence phenomena. The result is both unification across the areas visited, and the uncovering of interesting new questions. Technical Report PP-2001-23 University of Amsterdam http://www.illc.uva.nl/Publications/ Also, Intelligent Sensory Information Systems, University of Amsterdam 1 

• Type: Journal
• Year: 2002
• Where: JANCL
• Authors: Marco Aiello, Johan van Benthem
• Keywords: JANCL 2002, Major Mathematical Theories, Mathematical Theories, Modal Standpoint