CHOROS: IMPROVING THE PERFORMANCE OF QUALITATIVE SPATIAL REASONING IN OWL Nikolaos Mainas, Euripides G.M. Petrakis Technical University Of Crete (TUC),

CHOROS: IMPROVING THE PERFORMANCE OF QUALITATIVE SPATIAL REASONING IN OWL

Nikolaos Mainas, Euripides G.M. Petrakis

Technical University Of Crete (TUC), GreeceIntelligent Systems Laboratorywww.intelligence.tuc.gr

Qualitative Spatial InformationQualitative information is

expressed without numerical values using a vocabulary of relationships◦Example: “TUC is located north of the port of Souda”

Spatial information can be described using the topology and orientation of spatial entities (e.g., objects or regions)

CHOROS 2.0 ICTAI 2014, Limassol, Cyprus 2

Topological Relations RCC-8Describes the spatial arrangement of regions in space using 8 basic relations


Cone-Shaped Directional CSD-9

Describes the relative orientation between two regions using 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)


Why Spatial Reasoning ? In ontologies, spatial information is

expressed in OWL: concepts (Classes) and the relationships between them (Properties)

OWL cannot fully encode the semantics of spatial relations

Individuals: A, B, CObjectProperties: East, WestObjectPropertyExpression: (East inverse West)Assertions: (A East B), (B South C)An OWL DL reasoner (Pellet) can infer (B West A) but cannot infer (A {East, South, SouthEast C)


Spatial Representation

CHOROS 2.0 defines an RDF/OWL vocabulary for expressing qualitative spatial relations with both CSD and RCC models.

Spatial terms are defined as simple OWL object properties.

Spatial relations between entities are represented as an OWL object property assertion.


Qualitative Spatial Reasoning Given a set of N spatial entities and their

RCC-8 and CSD-9 relations, new relations are inferred using compositions of existing relations

◦ (A South B) ͦ (B SouthWest C) → (A {South, SouthWest} C)

◦ (A TPP B) ͦ (B EC C) → (A {DC, EC} C) Path-consistency (Nijel et.al. 2013): The

inferred relations are checked with existing ones for consistency until no new relations are added or an inconsistency is detected (the composition is rejected)


Compositions of RCC-8 relations


Compositions of CSD-9 Relations


Previous Work

SOWL (Batsakis, Petrakis 2012): An ontology for spatial CSD-9 and RCC-8 relations and temporal information A reasoner is implemented using SWRL rules

and OWL 2.0 property axiomsPelletSpatial (M. Stocker, E. Sirin, 2009): Extends Pellet to support reasoning over RCC-8 relations Implemented in Java Reasoning on CSD-9 relations is not supportedCHOROS 1.0 (Christodoulou, Petrakis, Batsakis 2012): Extends PelletSpatial to support CSD-9 relations


CHOROS 2.0Improves CHOROS 1.0 in several ways:compositions are computed on the fly

rather than stored in memory Speeds-up reasoning by decomposing

CSD-9 relations into two relation sets with 4 relations, each one

Similarly to CHOROS 1.0 separates spatial reasoning from semantic OWL-DL reasoning (also CSD-9 is separated from RCC-8 reasoning)

Updates the ontology with the results of reasoning


CHOROS Architecture


ImplementationParser: loads ontologies and extracts their spatial relations Quantitative parser: computes CSD-9, RCC-8 relations

from Qualitative parser: CSD-9, RCC-8, OWL triples are

stored in their respective CN Constraint Network (CN): stores spatial and non-

spatial information One CN for each relation type Non-spatial relations are stored in Pellet’s Knowledge

Base Assertion Box (assertions about individuals) Terminological Box (axioms about classes)Reasoner: applies consistency checking and logical inferenceRe-constructor: updates ontology with new spatial inferences


Optimizations: Computing Disjunctions Not all compositions yield a unique relation as a

result(A North B) (B NorthWest C)→(A {North, ͦNorthWest} C)

CHOROS 1 stores all possible compositions of basic CSD and RCC relations in tables

This requires 29x29 space for CSD and 28x28 space for RCC-8 relations

Compositions are computed "on the fly" using simple look-up operations on CSD and RCC composition tables


Optimizations: Reduction of Basic Relations CSD relation identicalTo is replaced with

OWL axiom sameAs RCC relation EQ with OWL axiom sameAs Less relations for the spatial reasoners Identical relations are asserted into

Pellet’s KB and are treated as standard OWL axioms


Decomposition of CSD-9 relations Are decomposed using two coordinate axes Reasoning on these axes infers less relations

than the CSD-9 model

East-West axis North-South axis


De(Re) Composition Rules


EW and NS Composition Tables


Evaluation Path Consistency when applied on a set of

assertions containing only basic relations guarantees tractable, sound and complete reasoning

Path consistency is O(N3) in the worst case ◦ When exactly N2 relations are produced from N

input relations e.g., when N objects are each one North of another

◦ Inconsistencies may terminate reasoning earlier

Complexity less than O(N2) in the average case ◦ When less than N2 relations are produced from N

input relations e.g., N objects with random relations


Experimental Set-upCompare CHRONOS 2 with SOWL and

CHOROS 1 in the average and worst caseMeasure running time as a function of the

size of input data set (number or relations in an ontology)

10 ontologies comprising between 10 and 100 assertions

All measurements are averages over 10 runs


Overall Performance (avg. case)


Overall Performance (worst case)


Case study: TUC Campus


Reasoning Engine Response time (msecs)

SOWL (SWRL) 8,313

CHOROS 1 2,312

CHOROS 2 407

ConclusionsCHOROS 2 is a qualitative spatial reasoner

for both CSD-9 and RCC-8 calculi Implements several optimizations and runs

faster than its SWRL counterpart Future work

Investigate on more effective reasoning methods e.g., small sets of basic relations for CSD and RCC

Support OWL 2 restrictions on spatial relations Extent for spatio-temporal information Performance on real applications (expedition of

Alexander the Great into Asia)


THANK YOU


Decomposition (average case)


Decomposition (worst case)


CSD-9 (average case)


CSD-9 (worst case)


RCC-8 (average case)


RCC-8 (worst case)


Documents

CHOROS: IMPROVING THE PERFORMANCE OF QUALITATIVE SPATIAL REASONING IN OWL Nikolaos Mainas, Euripides G.M. Petrakis Technical University Of Crete (TUC),