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Georgios Christodoulou, Euripides G.M. Petrakis, and Sotirios BatsakisDepartment of Electronic and Computer Engineering,Technical University of Crete (TUC) Chania, Crete,CHOROS: A Reasoning and Query Engine for Qualitative Spatial Information11MotivationQualitative information is expressed without numerical values using a vocabulary of relationshipscloser to how humans represent and reason about commonsense knowledgeIt it is possible to deal with incomplete knowledgeReasoning over qualitative spatial information is the problem this work is dealing with.Two of the most important aspects of space are topology and orientation.22Topological RelationsRegion 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)

33Directional RelationsCone-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)

44Qualitative Spatial ReasoningRefers 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-8Relies on a Composition table for each calculusPath Consistency 5RCC-8 Composition

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Directional Composition77SOWL [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 languageThe SOWL spatial representation supports both RCC and CSD calculi.88PelletSpatial [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 algorithmDoesn't support directional (CSD) algebra

9CHOROS Spatial reasonerCHOROS 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 answeringSpatial relations are expressed in RDF/OWL forming an ontology. A relation is represented as a triple. we represent a region as an OWL individualSpatial relations are defined as object properties 1010Spatial RepresentationCHOROS 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 - ComponentsParser: loading ontologies, queries Reasoner: consistency checkingQuery Engine: answering queriesCHOROS separates spatial reasoning from semantic OWL-DL reasoning.1212CHOROS ReasonerIt 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

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 UacA relation Rab is path-consistent if the rule Vac Uac Rab Sbc results in V .1313Reasoning Example A spatial configuration is formalized in CSD as the following constraint network: house1 N house2 house2 NW house3 house1 NE house4 house4 N house3Using 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 house3That is, the first house is north of the third which is the intersection of the above two relations.1414CHOROS VariationsCHOROS 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)1515ExperimentsThe "TUC spatial ontology" describes the spatial entities of the campus of Technical University of Crete

1616TUC Spatial Ontology17

Reasoning times

1818Conclusions & Future WorkWe 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)1919Thank YouQuestions?2020