||Till Mossakowski, Reinhard Moratz, Dominik Lücke
||Relations Between Spatial Calculi About Directions and Orientations
||Journal of Artificial Intelligence Research
Qualitative spatial descriptions characterize essential properties of spatial
objects or configurations by typically relying on relative comparisons
rather than measuring.
Typically, in qualitative approaches only relatively coarse distinctions
between configurations are made.
Qualitative spatial knowledge can be used to represent incomplete and
underdetermined knowledge in a systematic way. This is especially
useful if the task is to
describe features of classes of configurations rather than individual
Relative directions play a key role in human spatial descriptions
and there are several approaches how to represent them using qualitative methods.
In these approaches
directions between spatial locations can be expressed as
constraints over infinite domains, e.g. the Euclidean plane.
The theory of relation algebras has been successfully applied to this field.
Viewing relation algebras as universal algebras and
applying standard tools from universal algebra in this work, we
(re)define notions of qualitative constraint calculus, of
homomorphism between these, and of quotient of these.
Based on this method we derive important properties for spatial calculi
from corresponding properties of related calculi.
From a conceptual point of view these formal mappings between calculi are a means
to translate between different granularities.
Qualitative Spatial Reasoning Universal Algebra
09. 02. 2015