Transcript Διαφάνεια 1
CHOROS: A Reasoning and Query Engine
for Qualitative Spatial Information
Georgios Christodoulou, Euripides G.M. Petrakis, and Sotirios
Batsakis
Department of Electronic and Computer Engineering,
Technical University of Crete (TUC) Chania, Crete,
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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.
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Topological Relations
Region Connection Calculus (RCC) abstractly describes regions in a topological space
by means of 8 basic relations:
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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)
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
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Directional Composition
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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.
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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
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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
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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 Architecture - Components
Parser: loading ontologies, queries
Reasoner: consistency checking
Query Engine: answering queries
CHOROS separates spatial reasoning from
semantic OWL-DL reasoning.
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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.
2.
3.
4.
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We process N to infer all the inverse and equals relations.
We compute the compositional inference Tac ⟵ Rab ⃘ Sbc (a
composition table lookup)
We complete intersections Vac ⟵ Tac ⋂Uac
A relation Rab is path-consistent if the rule Vac ⟵ Uac ⋂ Rab ∘ Sbc
results in V ≠ ∅.
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.
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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(n3)
worst time complexity (with n being the number of individuals)
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Experiments
The "TUC spatial ontology" describes the spatial entities of
the campus of Technical University of Crete
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TUC Spatial Ontology
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Reasoning times
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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)
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Thank You
Questions?
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