Authors:
Kazuko Takahashi
;
Mizuki Goto
and
Hiroyoshi Miwa
Affiliation:
Kwansei Gakuin University, Japan
Keyword(s):
Qualitative Spatial Reasoning, Formalization, PLCA, Planarity.
Related
Ontology
Subjects/Areas/Topics:
Artificial Intelligence
;
Knowledge Representation and Reasoning
;
Knowledge-Based Systems
;
Symbolic Systems
Abstract:
PLCA is a framework for qualitative spatial reasoning. It provides a symbolic expression of spatial entities
and allows reasoning on this expression. A figure is represented using the objects used to construct it, that is,
points, lines, circuits and areas, as well as the relationships between them without numerical data. The figure
is identified by the patterns of connection between the objects. For a given PLCA expression, the conditions
for planarity, that is, an existence of the corresponding figure on a two-dimensional plane, have been shown;
however, the construction of such a PLCA expression has not been discussed. In this paper, we describe a
method of constructing such expressions inductively, and prove that the resulting class coincides with that of
the planar PCLA. The part of the proof is implemented using a proof assistant Coq.