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Analogical Representation of RCC-8 for Neighborhood-Based Qualitative Spatial Reasoning Diedrich Wolter [email protected] Arne Kreutzmann [email protected]
• qualitative spatial reasoning is a subfield of knowledge representationinvolved with common-sense spatial understanding
• spatio-temporal reasoning is concerned with possible changes over time, • conceptual neighborhoods capture possible basic changes ➡ development of configurations described topologically by RCC-8 can be
determined in polynomial time – we present a practical algorithm get digital!
Spatio-temporal representation and reasoning using RCC-8 !
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• RCC-8 (Randell, Cui, and Cohn; 1992) defines eight base relations among regions • deciding joint satisfiability of RCC-8 statements is NPc, but O(n3) for e.g. base relations (Renz; 1999) • conceptual neighborhoods (Freksa; 1991) capture changes possible:
two relations are neighbored if in the domain a direct continuous transformation exists • neighorhood-based reasoning considers potential changes, e.g., for similarity assessment, planning, …
base relations of RCC-8 organized according to possible neighborhood transitions
C. Freksa (1992). Conceptual neighborhood and its role in temporal and spatial reasoning.In:Singh, M., Travé-Massuyès, L. (eds.), Decision Support Systems and Qualitative Reasoning, pp. 181 – 187. North Holland S. Palmer (1978). Fundamental aspects of cognitive representation.In: Rosch,E.,Lloyd,B.(eds.) Cognition and Categorization, pp. 259–303. Erlbaum D. A. Randell, Z. Cui, and A. G. Cohn (1992). A spatial logic based on regions and “connection”. In Proc. of KR 1992. Morgan Kaufmann, 165–176.J. Renz (1999). Maximal tractable fragments of the region connection calculus: a complete analysis. In: Proc. of IJCAI, 448–455, Morgan Kaufmann J. G. Stell (2000). Boolean connection algebras: a new approach to the region-connection calculus. Artificial Intelligence 122(1), 111–136
References
How can conceptual neighborhoods be applied to configurations? • complexity not studied so far, naive algorithm in ExpTime • would yield good basis for spatio-temproal reasoning
if possible in an efficient way • several applications already identified, e.g., in AI robotics,
smart environments, semantic data fusion
relation changeovers may occur simultaneously in configurations as relations are interdependent
“I wonder how the future can look like…”
photo: Vivien Mast
Idea • develop an analogical representation (Palmer; 1978) to
retain topological structure of domain: the inclusion graph • unlike logic an analogical representation is always satisfiable • model neighborhood transitions as graph transformations
(can be flexibly applied for different tasks)
Results • performing neighborhood transitions is O(n2) • enumerating all neighborhood transitions possible in O(n4) • constructing inclusion graph is O(n4) (consistency checking
would alone be O(n3) – little extra effort) ➡ good basis for spatio-temporal reasoning!
n2
not just a theoretical result – good scaling of implementation
disconnectedDC
externally connectedEC
partially overlappingPO
equalEQ
tangential proper part-1TPPi
non-tangential proper part-1NTPPi
tangential proper partTPP
non-tangential proper partNTPPi
B EQ CA DC BA DC C
B EQ CA EC BA EC C
A rAB BA rAC CA rBC D …Y rYZ Z
?3 objects n objects
universeregion containmentclosure of sub-region sub-region belonging to B and U
axioms and operations of inclusion graphs make it a Boolean connection algebra, these are models for RCC-8 (Stell; 2000)
n: number of regions in configuration
n2
