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REASONING WITH TOPOLOGICAL AND DIRECTIONAL SPATIAL INFORMATION
Author(s) -
Li Sanjiang,
Cohn Anthony G.
Publication year - 2012
Publication title -
computational intelligence
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.353
H-Index - 52
eISSN - 1467-8640
pISSN - 0824-7935
DOI - 10.1111/j.1467-8640.2012.00431.x
Subject(s) - local consistency , mathematics , consistency (knowledge bases) , constraint satisfaction problem , topological space , representation (politics) , set (abstract data type) , constraint satisfaction , topology (electrical circuits) , constraint (computer aided design) , computer science , discrete mathematics , combinatorics , statistics , geometry , politics , probabilistic logic , political science , law , programming language
Current research on qualitative spatial representation and reasoning mainly focuses on one single aspect of space. In real‐world applications, however, multiple spatial aspects are often involved simultaneously. This paper investigates problems arising in reasoning with combined topological and directional information. We use the RCC8 algebra and the rectangle algebra (RA) for expressing topological and directional information, respectively. We give examples to show that the bipath‐consistency algorithm Bipath‐Consistency is incomplete for solving even basic RCC8 and RA constraints. If topological constraints are taken from some maximal tractable subclasses of RCC8, and directional constraints are taken from a subalgebra, termed DIR49, of RA, then we show that Bipath‐Consistency is able to separate topological constraints from directional ones. This means, given a set of hybrid topological and directional constraints from the above subclasses of RCC8 and RA, we can transfer the joint satisfaction problem in polynomial time to two independent satisfaction problems in RCC8 and RA. For general RA constraints, we give a method to compute solutions that satisfy all topological constraints and approximately satisfy each RA constraint to any prescribed precision.