Reasoning on Spatial Semantic Integrity Constraints
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Reasoning on conceptual schemas of spatial data
Faculty of Environmental Sciences, Department of Geosciences, Professorship of GIS
Stephan Mäs
Dagstuhl Seminar on Automated Reasoning on Conceptual Schemas20th May 2013
Overview
1. Specifics of Spatial Data Schemas
2. Reasoning on Spatial Semantic Integrity Constraints
Reasoning on conceptual schemas of spatial data Stephan Mäs 2
Reasoning on conceptual schemas of spatial data Stephan Mäs 3
http://wetterstationen.meteomedia.de/
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
…
Reasoning on conceptual schemas of spatial data Stephan Mäs 4
Source: Bartelme 1995
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
Constraints between different scales / LoD
Transaction rules
…
Reasoning on conceptual schemas of spatial data Stephan Mäs 5
Source: Plümer et al. 1997
Formalization is still an issue
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 Mäs 6
Reasoning on spatial semantic integrity constraints
Reasoning on conceptual schemas of spatial data Stephan Mäs 7
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 spatial relations
Inheritance of Class Relations Stephan Mäs 8
Composition of spatial relations
ab
c
explicit knowledge: - a inside b and b disjoint c
implicit knowledge:
- a is disjoint from c
Finite set of spatial relations
with defined logics
For example
Compositions of spatial relations
Reasoning on conceptual schemas of spatial data Stephan Mäs 9
Egenhofer, M. (1994): Deriving the Composition of Binary Topological Relations.
Constraint Satisfaction Problems
Nodes represent objects
Edges represent (spatial) relations
Reasoning on conceptual schemas of spatial data Stephan Mäs 10
Reasoning on spatial sem. integrity constraints
Reasoning on conceptual schemas of spatial data Stephan Mäs 11
two level reasoning approach:
separate the compositions of
the cardinality restrictions from
those of the spatial relations
Combined Composition of
Integrity Constraints /
Class Relations
Composition Table of the Cardinality Restrictions
Class Level
Composition Table of the Instance Relations
Instance Level
Other things to consider
Restrictions of the number of instances
Symmetry
Infinity Problems
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#countries = #capitals
Recent work: Inheritance of Sem. Integrity Constraints
Reasoning on conceptual schemas of spatial data Stephan Mäs 13
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 Spatial Semantic Integrity Constraints
Reasoning on conceptual schemas of spatial data Stephan Mäs 14
Mäs, 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
Mäs, Stephan (2008): Reasoning on Spatial Relations between Entity Classes. GIScience 2008 Lecture Notes in Computer Science 5266
Mäs, Stephan (2007): Reasoning on Spatial Semantic Integrity Constraints. COSIT 2007 Lecture Notes in Computer Science 4736
Fakultät Forst, Geo- und Hydrowissenschaften, Fachrichtung Geowissenschaften, Professur Geoinformationssysteme
Stephan Mäswww.stephanmaes.de
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