1. Presentation to Networking Geospatial Information Technology for Interoperability and Spatial Ontology School of Computing University of Leeds
Tony Cohn

2. My/Leeds interests Knowledge representation and reasoning
Qualitative and “common sense” reasoning
Qualitative spatial and spatio-temporal representation and reasoning
Spatial ontologies
Vagueness, uncertainty, granularity
Applications
Cognitive Vision
Mapping the Underworld”

3. Qualitative Spatial Reasoning
Motivation
Efficiency
Cognitive arguments
Abstraction
Applications (GIS, Vision, Natural Language,…)
Challenge
Expressive and efficient
Expressive calculi
Mereotopology, geometry, orientation
Efficient reasoning
Propositional (modal, intuitionistic, constraint)

4. E.g. RCC-8 (cf Egenhofer) DC EC PO TPP NTPP
8 provably jointly exhaustive pairwise disjoint relations (JEPD)
DC EC PO TPP NTPP
EQ TPPi NTPPi
Implemented in: CYC, Foundational Anatomy,…

5. Reasoning Techniques Tension between expressivity and efficiency
E.g. First order logic formulation of mereotopology is not decidable
Dispense with full first order theory and find decidable subset, e.g. constraint language of RCC8
In fact, constraint language of RCC8 is tractable
Various tractable disjunctive languages
Variety of special purpose reasoning techniques, e.g.:
Composition tables
Spatial logics

6. Existential import of Composition Tables
Weak reading:
8 x,y,z [[R1(x,y) Æ R2(y,z)] ! [R31(x,z) Ç … Ç R3n(x,z)]]
or (extensional reading):
8 x,z [9 y[R1(x,y) Æ R2(y,z)] $ [R31(x,z) Ç … Ç R3n(x,z)]]
E.g. consider the TPP x TPP entry
8 x,z [9 y[TPP(x,y) Æ TPP(y,z)] $ [TPP(x,z) Ç NTPP(x,z)]] Ã

7. Qualitative shape Beyond mereotopology Orientation calculi
Convexity: conv(x) (+RCC)
Affine geometry

8. RBG: Region Based Calculus
Primitives: P(x,y), CG(x,y)/Sphere(x)
Categorical
Complete geometry with coordinates
Constraint sublanguages:
MC6: CG, CGTPP, CGNTPP, CNO
RCC8+MC6+relative size
Important research direction: combining calculi

9. Continuity Networks/ Conceptual Neighbourhoods
What are next qualitative relations if entities transform/translate continuously?
E.g. RCC-8
Basis of qualitative simulator

10. Space time and continuity
4D spatio temporal histories
Mereotopological theory
Definition of continuity
Continuous histories
Allows proof of non existence of missing links in conceptual neighbourhood diagram
E.g. DC – PO is impossible

11. Continuity of Multiple Component Histories
Allowing multiple component histories gives rise to many possible weaker notions of qualitative continuity.
Identity criteria via continuity?

12. Modal spatio-temporal logics (joint with Zakharyashev et al)
Decidable combinations of RCC+temporal logic
PTL (Propositional Temporal Logic)
temporal operators: Since, Until
X Until Y, Z Since W
Can define:
Next: O
Always in the future ¤F (similarly for past)
Sometime in the future ¦F (similarly for past)
Eg ¬ ¤F P(Kosovo,Yugoslavia)
Kosovo will not always be part of Yugoslavia

13. Extensions
allow the other temporal operators to apply to region variables (iteratively)
E.g. DC(Russia S Russian_empire, Russia S Germany)
“The part of Russia that has been Russian since the Russian empire is DC from the part of Germany that became Russian after WW2 (Koenigsberg)”
BRCC8
can add Boolean operators to region terms and the constraint lanuage of RCC-8 remains decidable (NP complete)
E.g. P(Alps,France+Germany+Italy+Switzerland+Austria)

14. A Qualitative Representation of Trajectory Pairs
The movement or transition between two objects at an instant can be qualitatively represented using three functions:
movement of the 1st object wrt the 2nd object’s position
movement of the 2nd object wrt the 1st object’s position
relative speed of the 1st object wrt the 2nd object
Since we are interested in a qualitative calculus, we can represent the values of each of these functions by “+”, “0” or “”.
For the first two functions, we take “” to mean motion towards the other object, “+” to mean motion away, and “0” to mean an absence of motion to/from the other object. In the 3rd case, “+/0/ ” mean a greater/same/lower speed respectively. This triple forms the basis of our Qualitative Trajectory Calculus (QTC).

15. Indeterminate boundaries/vague regions: egg-yolk calculus
...
Using RCC8: 601 jointly exhaustive, pairwise disjoint relations
40 natural clusters
Can specify that hill and valley are vague regions which touch, without specifying the boundary
Can also be used to represent locational uncertainty as well as boundary indeterminacy
More Leeds work on vagueness (Bennett)
Supervaluation techniques / “in some sense”
Built environment, hydrology ontologies

16. VISTA & Mapping the Underworld

18. State of the Art Each utility has their own asset record
Sometimes digital
Varying degrees of data quality
Often mapped wrt no longer existing reference points
Sensing technology
GPR, “Cat and Genny”
Problems with soil types, dampness, plastic pipes…
Location technology
GNSS, eg GPS
Problem in urban canyons, even with trees in leaf

19. VISTA Consortium Stakeholders Contractors and Equipment Manufacturers
Severn Trent Water Thames Water Transport for London
Ordnance Survey Yorks Water BT
United Utils Anglian Water Transco
Three Valleys Water
Contractors and Equipment Manufacturers
Leica Ewan Group Adien
Scott Wilson Jacobs
Umbrella organisations and Professional Bodies
UKWIR (Lead partner)
NJUG Pipeline Industries Guild Inst. Civil Engineers
Universities
Leeds Nottingham
21 so far and still growing …

20. Enabling Swift, Safe, Cost Effective Streetworks.
A SYSTEM VISION / IDEA
ASSET REPAIR & MAINTENANCE
Enabling Swift, Safe, Cost Effective Streetworks.
RTK GPS
TPS
3G Comms 3D
GIS data
OS Maps
Sensing
and
Locating
Find it and
dig it up
All above Merged into 1 Unit
Centrally
controlled
Solution Output
3D Data & Aug Reality
Small
Simple to use
Big buttons
Highly accurate
Real-time Data capture & supply
Web Service
GML / VRML
Data Server

21. Some Research Challenges
Virtual integration of disparate asset records
Varying data quality
Varying spatial alignment
spatial and non spatial properties: joint ontology
Conversion of legacy raster records
Integration with real-time GNSS data points of street furniture/sensor information
Visualization of integrated information
Taking account of residual uncertainty
Augmented reality?

22. Cognitive Vision: Two paradigms from 1960’s Pattern recognition
continuous feature spaces
Very successful, huge progress in pattern recognition but relatively little progress on “cognitive vision”
Relational models
qualitative relations between image regions (e.g. touching, part of, inside, near, approaching)
graph matching, symbolic reasoning
Potentially useful, but too little interaction/integration with pattern recognition/quantitive approaches
The Challenge: integration

23. approach Point and learn – any scene!
Integration of quantitative and qualitative modes of representation, learning and reasoning:
quantitative visual processing for tracking & motion analysis
qualitative spatio-temporal representations abstract away:
from unnecessary details
error and uncertainty
commonsense knowledge as constraints on interpretations
Learn as much as possible
Autonomously (unsupervised)
Point and learn – any scene!

24. (Some) Research Issues
What background theory and how to learn it?
How to integrate low level (quantitative) reasoning/representations with higher level symbolic (qualitative)?
How to select preferred abduced explanations of sensor input?
What qualitative representations?
Dealing with noise. …

25. Progress to date System which learned traffic behaviours
Qualitative spatio-temporal models
Learning of qualitative spatial relationships
Allows domain specific distinctions to be learned
Reasoning about classification
Reasoning about commonsense knowledge of continuity to refine ambiguous classifications
Learning symbolic descriptions of intentional behaviours
Use ILP to induce rules to describe simple games
… learning the ontology of the game…