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

Qualitative Spatial Information Qualitative 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 2.0ICTAI 2014, Limassol, Cyprus2

Topological Relations RCC-8 Describes the spatial arrangement of regions in space using 8 basic relations CHOROS 2.0ICTAI 2014, Limassol, Cyprus3

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) CHOROS 2.0ICTAI 2014, Limassol, Cyprus4

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, C ObjectProperties: East, West ObjectPropertyExpression: (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) CHOROS 2.0ICTAI 2014, Limassol, Cyprus5

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. CHOROS 2.0ICTAI 2014, Limassol, Cyprus6

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) CHOROS 2.0ICTAI 2014, Limassol, Cyprus7

Compositions of RCC-8 relations CHOROS 2.0ICTAI 2014, Limassol, Cyprus8

Compositions of CSD-9 Relations CHOROS 2.0ICTAI 2014, Limassol, Cyprus9

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 axioms PelletSpatial (M. Stocker, E. Sirin, 2009): Extends Pellet to support reasoning over RCC-8 relations Implemented in Java Reasoning on CSD-9 relations is not supported CHOROS 1.0 (Christodoulou, Petrakis, Batsakis 2012): Extends PelletSpatial to support CSD-9 relations CHOROS 2.0ICTAI 2014, Limassol, Cyprus10

CHOROS 2.0 Improves 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 2.0ICTAI 2014, Limassol, Cyprus11

CHOROS Architecture CHOROS 2.0ICTAI 2014, Limassol, Cyprus12

Implementation Parser: 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 inference Re-constructor: updates ontology with new spatial inferences CHOROS 2.0ICTAI 2014, Limassol, Cyprus13

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 2 9 x2 9 space for CSD and 2 8 x2 8 space for RCC-8 relations Compositions are computed "on the fly" using simple look- up operations on CSD and RCC composition tables CHOROS 2.0ICTAI 2014, Limassol, Cyprus14

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 CHOROS 2.0ICTAI 2014, Limassol, Cyprus15

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 CHOROS 2.0ICTAI 2014, Limassol, Cyprus16

De(Re) Composition Rules CHOROS 2.0ICTAI 2014, Limassol, Cyprus17

EW and NS Composition Tables CHOROS 2.0ICTAI 2014, Limassol, Cyprus18

Evaluation Path Consistency when applied on a set of assertions containing only basic relations guarantees tractable, sound and complete reasoning Path consistency is O(N 3 ) in the worst case ◦ When exactly N 2 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(N 2 ) in the average case ◦ When less than N 2 relations are produced from N input relations e.g., N objects with random relations CHOROS 2.0ICTAI 2014, Limassol, Cyprus19

Experimental Set-up Compare CHRONOS 2 with SOWL and CHOROS 1 in the average and worst case Measure 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 CHOROS 2.0ICTAI 2014, Limassol, Cyprus20

Overall Performance (avg. case) CHOROS 2.0ICTAI 2014, Limassol, Cyprus21

Overall Performance (worst case) CHOROS 2.0ICTAI 2014, Limassol, Cyprus22

Case study: TUC Campus CHOROS 2.0ICTAI 2014, Limassol, Cyprus23 Reasoning Engine Response time (msecs) SOWL (SWRL)8,313 CHOROS 12,312 CHOROS 2407

Conclusions CHOROS 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) CHOROS 2.0ICTAI 2014, Limassol, Cyprus24

THANK YOU CHOROS 2.0ICTAI 2014, Limassol, Cyprus25

Decomposition (average case) CHOROS 2.0ICTAI 2014, Limassol, Cyprus26

Decomposition (worst case) CHOROS 2.0ICTAI 2014, Limassol, Cyprus27

CSD-9 (average case) CHOROS 2.0ICTAI 2014, Limassol, Cyprus28

CSD-9 (worst case) CHOROS 2.0ICTAI 2014, Limassol, Cyprus29

RCC-8 (average case) CHOROS 2.0ICTAI 2014, Limassol, Cyprus30

RCC-8 (worst case) CHOROS 2.0ICTAI 2014, Limassol, Cyprus31