Research On Some Problems Of Complex Spatial Relations Models And Spatial Description Logic

Most of the knowledge of the people’s daily life is space-related and spatialinformation processing has been the research focus of artificial intelligence.Qualitative spatial reasoning studies basic characteristics of the space objects (such asshape, size, etc.) or the spatial relations between spatial objects (such as topologicalrelations, distance relations, orientation relations, etc.) by qualitative description andreasoning. The spatial relation means relations with spatial characteristics betweenthe spatial targets, including topological relations, distance relations, orientationrelations, etc. It has a wide range of applications in the field of computer vision,geographic information systems (GIS) and spatial database.In recent years, spatial information processing has been made a number of researchresults. But there are also some problems. Existing spatial information processing ismostly under idealized conditions, which makes its findings can only be applied to asimple spatial environment. The practical spatial information is complex, andcomplex spatial information processing is widely concerned. In this paper, two issuesof complex spatial relations and fuzzy spatial information are studied. The world welived in is three-dimensional and spatial objects always show various complexities(for example, holes, more than one part). Moreover, a variety of spatial relations (suchas point/line, line/region, region/region, region/body) coexist in the actual spacescene. The various complex phenomena mentioned above are called complex spatialrelations. In practical applications, improper modeling of these complex phenomenawill often lead to a deviation of the spatial information extracting and directly affectthe effectiveness of spatial queries and spatial analysis.The existing methods forprocessing spatial relations are mostly conducted on a single type of spatial relationsbetween simple objects in two-dimensional space and apparently are not suitable fordealing with complex spatial relations. Admittedly, the complex spatial relationmodeling is more significant. But the research is still at a preliminary stage and needto be strengthened. In addition, the spatial description logic is a powerful tool to deal with spatial information. Due to the limitations of human language, cognition,Information collection and other factors, spatial information is often fuzzy. In manypractical applications, the membership degree of objects is often difficult todetermine, and the interval-valued membership is relatively easier to obtain.Reasoning with interval-value is more in line with the fuzziness and uncertainties ofhuman cognition. Therefore, the interval-valued fuzzy spatial description logicbecomes a research direction.To solve these problems, this paper has done the following two aspects of work.(1)In the aspect of complex spatial relation model:①For topological relations betweenspatial regions with holes, D9-intersection model is proposed which refines the9-intersection model and is more expressive;②For spatial reasoning on thedirectional relations between heterogeneous objects in3dimensional space, wepresent a new orientation algebra3D-SOA which initially realized orientationreasoning for heterogeneous objects in3D space;③To express the relativeorientation relations in3D space, we get a new model3DTPCC by extending theclassical model TPCC, and improves the two-dimensional model TPCC and candescribe relative orientation relations in3D space.(2) For interval-valued fuzzyinformation we presente the interval-valued fuzzy description logic IF-ALCN andIF-ALCRP(D), which improve the expressiveness of dealing with fuzzy spatialinformation, and lays theoretical foundation for representation and reasoning ofinterval-valued fuzzy information on the spatial semantic web.The main research results are as follows:(1) This thesis surveys and analyzes the research status of the existing qualitativespatial relation models including the topological models such as the RCC model,4-intersection model, and9-intersection model, the orientation models such ascone-based and projection-based frames, cardinal directional relation matrix and thedouble cross. Finally the open problems and future research directions are pointed out.(2) In order to describe topological relations between regions with holes, a newmodel the D9-intersection model is proposed by extending9-intersection model.Compared with9-intersection model, the D9-intersection model is more expressive.To support spatial query and analysis, we give an algorithm to decide the validity ofthe D9-intersection matrixes. To assess the similarity of topological relations formally,an algorithm based on D9-intersection model was presented. At the end the reasoningproblem of the D9-intersection model is discussed. (3) A model for orientation relations between heterogeneous objects in3dimensional space3D-SOA. The space scenes are in3D space, and there are varioustypes of spatial objects (point, line, surface and block). The existing studies mostlyconsider2D Euclidean space and targeted spatial relations between single-typeobjects. Based on Point Algebra and Interval Algebra, this thesis proposes a newrelational algebra for spatial orientation relations between heterogeneous objects in3D space. Relations are described and the basic operations of relations (inverse,intersection, and composition) are defined. Moreover, the satisfiability of the3D-SOAconstraint networks is researched. Benefitting from the tractability of the pointalgebra, we characterized a tractable fragment of our language saturated-pointisablerelations and presented an algorithm to decide its consistency. Moreover, theconsistency problem of general networks on3D-SOA can be solved by a backtrackingalgorithm optimized by firstly using Path-Consistency algorithm.(4) The model of relative orientation relations in3D space—3DTPCCThe relative orientation relation is a very important aspect of the spatial relation.Most of the current models are two-dimensional and they work by modeling allspatial objects on some plane and can only express relations in2D space. But the realworld is three-dimensional, and modeling all objects on the same plane does notcomply with people s cognitive habits. Furthermore, the orientation relations betweenspatial objects are not limited to what the current model express. Considering pointobjects, the classical model TPCC is extended to a new model3DTPCC for therelative orientation relations in3D space.3DTPCC can express both distance andorientation, and can distinguish125kinds of relations. Then these relations areformally defined and the inversion table is presented. In the final, the application ofthe model is illustrated through examples.(5) Interval-valued fuzzy spatial description logic IF-ALCN and IF-ALCRP (D)Spatial description logic is the logical and theoretical basis of spatial ontologies andspatial semantic web. To deal with the interval-valued fuzzy spatial information on thespatial semantic web, firstly an extension of the description logic ALCN withinterval-valued fuzzy set theory is presented and then a detailed reasoning algorithmfor deciding fuzzy ABox consistency. Furthermore, the algorithm is proved to besound and complete and the consistency of IF-ALCN ABoxes is PSpace-complete.Using the idea of IF-ALCN, the spatial description logic ALCRP (D) is extended toIF-ALCRP (D) which can deal with interval-valued fuzzy spatial information. Its syntax and semantics are given. Finally, the reasoning problem is discussed and therules of inference are presented.