Georgios Christodoulou, Euripides G.M. Petrakis, and Sotirios
Batsakis Department of Electronic and Computer Engineering,
Technical University of Crete (TUC) Chania, Crete, CHOROS: A
Reasoning and Query Engine for Qualitative Spatial Information
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Motivation Qualitative information is expressed without
numerical values using a vocabulary of relationships closer to how
humans represent and reason about commonsense knowledge It it is
possible to deal with incomplete knowledge Reasoning over
qualitative spatial information is the problem this work is dealing
with. Two of the most important aspects of space are topology and
orientation. 2
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Topological Relations Region Connection Calculus (RCC)
abstractly describes regions in a topological space by means of 8
basic relations: disconnected (DC) externally connected (EC) equal
(EQ) partially overlapping (PO) tangential proper part (TPP)
tangential proper part inverse (TPPi) non-tangential proper part
(NTPP) non-tangential proper part inverse (NTPPi) 3
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Directional Relations Cone-shaped Directional (CSD): relative
directional position between two points in space by means of 9
basic relations: north (N) north-east (NE) east (E) south-east (SE)
south (S) south-west (SW) west (W) north-west (NW) identical (O)
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Qualitative Spatial Reasoning Refers to the process of
computing new relations from a set of existing ones and detecting
inconsistencies Using some spatial algebra like CSD-9 and RCC-8
Relies on a Composition table for each calculus Path Consistency
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RCC-8 Composition 6
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Directional Composition 7
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SOWL [Batsakis 2011] SOWL is a framework for handling
spatio-temporal information: An ontology for spatial and temporal
concepts. A reasoner implemented using SWRL rules and OWL 2.0
constructs (e.g., disjoint properties) ensuring path consistency. A
spatio-temporal query language The SOWL spatial representation
supports both RCC and CSD calculi. 8
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PelletSpatial [Stocker 2009] PelletSpatial extends Pellet with
qualitative spatial reasoning over RCC relations. Implements two
RCC reasoners: One implementing translation of RCC relations to
OWL-DL class axioms while preserving their semantics. One operating
on the RCC composition table by implementing a path-consistency
algorithm Doesn't support directional (CSD) algebra 9
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CHOROS Spatial reasoner CHOROS extends PelletSpatial to support
CSD relations in addition to RCC relations. It implements a
path-consistency algorithm based on the composition tables used in
SOWL. query answering Spatial relations are expressed in RDF/OWL
forming an ontology. A relation is represented as a triple. we
represent a region as an OWL individual Spatial relations are
defined as object properties 10
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Spatial Representation CHOROS provides an RDF/OWL vocabulary
for expressing qualitative spatial relations, with both the CSD and
RCC models. One can use his/her own by defining sub-property
axioms. (e.g., "borders" sub-property of "externally ConnectedTo")
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CHOROS Reasoner It is realized by means of a path-consistency
algorithm ensuring that computed and existing relations are
consistent A queue Q keeps track of relations that have to be
processed. The algorithm runs until Q = or an inconsistency is
detected. Q is initialized with all the defined relations Rij N 1.
We process N to infer all the inverse and equals relations. 2. We
compute the compositional inference Tac Rab Sbc (a composition
table lookup) 3. We complete intersections Vac Tac Uac 4. A
relation Rab is path-consistent if the rule Vac Uac Rab Sbc results
in V . 13
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Reasoning Example A spatial configuration is formalized in CSD
as the following constraint network: house1 N house2 house2 NW
house3 house1 NE house4 house4 N house3 Using the CSD composition
table and the path-consistency algorithm, we can refine the network
in the following way: house1 N, NW house3 house1 N, NE house3 That
is, the first house is north of the third which is the intersection
of the above two relations. 14
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CHOROS Variations CHOROS 0.1 applies over all 9 CSD calculus
basic relations. CHOROS 0.2 applies to consistency checking over 8
CSD basic relations ("identical to" is replaced by the owl axiom
"sameAs) Multithreading allows two parts of the same program to run
concurrently. We utilize multithreading by launching each calculi
as a separate thread. In CHOROS as well as in PelletSpatial, path
consistency has O(n 3 ) worst time complexity (with n being the
number of individuals) 15
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Experiments The "TUC spatial ontology" describes the spatial
entities of the campus of Technical University of Crete 16
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TUC Spatial Ontology 17
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Reasoning times 18
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Conclusions & Future Work We presented CHOROS, a
qualitative spatial reasoning and query engine implemented in Java.
CHOROS supports both RCC and CSD models. We evaluated possible
optimizations of CHOROS (CSD-8, multithreading) and compare its
performance with that of a spatial reasoner implemented in SWRL.
Future work includes: extending our implementation to support
qualitative temporal reasoning on basic Allen relations supporting
reasoning beyond the base relations of each calculi (PP as a
disjunction of TPP, NTPP) 19