1. Faculty of Environmental Sciences, Department of Geosciences, Professorship of GIS Reasoning on conceptual schemas of spatial data Stephan Ms Dagstuhl Seminar on Automated Reasoning on Conceptual Schemas 20th May 2013

2. Overview 1. Specifics of Spatial Data Schemas 2. Reasoning on Spatial Semantic Integrity Constraints Reasoning on conceptual schemas of spatial data Stephan Ms 2

3. http://wetterstationen.meteomedia.de/ Reasoning on conceptual schemas of spatial data Stephan Ms 3

4. Peculiarities of Spatial Data Schemas Combination of spatial, temporal and thematic components Basic datatypes for spatial concepts Fields Geometry types for object data Topology Representation of different scale, granularity and levels of abstraction Spatial reference systems Units of measure Source: Bartelme 1995 Reasoning on conceptual schemas of spatial data Stephan Ms 4

5. Integrity rules in spatial data schemas On geometries e.g. closed polygons, self intersecting lines Semantic integrity constraints on (implicit) spatial relations partonomic relations e.g. between administrative regions non-overlapping and covering regions Topological relations Metric relations Direction relations Combinations with thematic constraints Source: Plmer et al. 1997 Constraints between different scales / LoD Transaction rules Reasoning on conceptual schemas of spatial data Formalization is still an issue Stephan Ms 5

6. Examples of Spatial Semantic Integrity Constraints Topological Restrictions Contour lines don't intersect with lakes An alluvial forest is inside of a floodplain Orientation / directional restrictions The backyard must be at the rear of a house Road signs have to face the direction opposite of the driving lane they are attached to Metric restrictions Petrol stations must be in at least 300m distance from schools Reasoning on conceptual schemas of spatial data Stephan Ms 6

7. Reasoning on spatial semantic integrity constraints Each alluvial forest is inside of exactly one floodplain All floodplains are disjoint from all nuclear power stations All alluvial forests are disjoint from all nuclear power stations All alluvial forests contain a nuclear power station Reasoning on conceptual schemas of spatial data Stephan Ms 7

8. Reasoning on spatial relations Composition of spatial relations Finite set of spatial relations with defined logics For example b a c Inheritance of Class Relations explicit knowledge: - a inside b and b disjoint c implicit knowledge: - a is disjoint from c Stephan Ms 8

9. Compositions of spatial relations Egenhofer, M. (1994): Deriving the Composition of Binary Topological Relations. Reasoning on conceptual schemas of spatial data Stephan Ms 9

10. Constraint Satisfaction Problems Nodes represent objects Edges represent (spatial) relations Reasoning on conceptual schemas of spatial data Stephan Ms 10

11. Reasoning on spatial sem. integrity constraints two level reasoning approach: Class Level separate the compositions of the cardinality restrictions from those of the spatial relations Composition Table of the Cardinality Restrictions Instance Level Composition Table of the Instance Relations Reasoning on conceptual schemas of spatial data Combined Composition of Integrity Constraints / Class Relations Stephan Ms 11

12. Other things to consider Restrictions of the number of instances #countries = #capitals Symmetry Infinity Problems Reasoning on conceptual schemas of spatial data Stephan Ms 12

13. Recent work: Inheritance of Sem. Integrity Constraints Subclasses inherit properties of the superclass in the hierarchy dependencies between the cardinality restrictions of a relation at different hierarchy levels The relation between the superclass and the class outside the hierarchy subsumes the relations between the subclasses and the class outside the hierarchy. Reasoning on conceptual schemas of spatial data Stephan Ms 13

14. Reasoning on Spatial Semantic Integrity Constraints Ms, Stephan (2013): Reasoning on Class Relations: an Overview. In: Raubal, Martin; Mark, David M.; Frank, Andrew U. (Eds.), Cognitive and Linguistic Aspects of Geographic Space New Perspectives on Geographic Information Research. Springer Lecture Notes in Geoinformation and Cartography Ms, Stephan (2008): Reasoning on Spatial Relations between Entity Classes. GIScience 2008 Lecture Notes in Computer Science 5266 Ms, Stephan (2007): Reasoning on Spatial Semantic Integrity Constraints. COSIT 2007 Lecture Notes in Computer Science 4736 Reasoning on conceptual schemas of spatial data Stephan Ms 14

15. Fakultt Forst, Geo- und Hydrowissenschaften, Fachrichtung Geowissenschaften, Professur Geoinformationssysteme Thanks ! Stephan Ms www.stephanmaes.de