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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 1

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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) 4

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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 5

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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") 11

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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. 12

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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

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Thank You Questions? 20