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13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 1.0 Qualitative representations of the geospatial world Tony Cohn School of Computing The University of Leeds [email protected] http://www.comp.leeds.ac.uk/ rticular thanks to: EPSRC, EU, Leeds QSR group and ...
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Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

Mar 28, 2015

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Page 1: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 1.0

Qualitative representations of the geospatial world

Tony CohnSchool of Computing

The University of [email protected]

http://www.comp.leeds.ac.uk/

Particular thanks to: EPSRC, EU, Leeds QSR group and ...

Page 2: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 2.0

Contents

Brief survey of qualitative spatial/spatio-temporal representations and reasoningMotivationSome qualitative spatial representationsSpatial Change

Challenges

Page 3: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 3.0

The geospatial world

Huge amounts of metric and symbolic data Very diverse ontologically

Natural and man made objectsProcesses at many different time scalesMany different kinds of objectsDifferent spatial scales

Different representations, languages, standards,… Abstraction, analysis, mining, comparison, querying,

integration…

Page 4: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 4.0

Qualitative spatial/spatio-temporal representations

Naturally provides abstraction Well developed calculi, languages, (often) semantics Complementary to metric representations Provide foundation for geospatial ontologies and

reasoning

Page 5: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 5.0

Some Challenges (Summary)Some Challenges (Summary)

Vagueness and uncertainty Space and time Efficiency/expressiveness Combining calculi for different spatial aspects Choosing/designing appropriate representations and

ontologies, at the appropriate level of granularity, and moving between these

Integrating ontologies Combining qualitative and quantative representations Interfacing with the human user; “cognitive semantics” Modelling is hard

Page 6: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 6.0

What is QR? (1)

QR (about physical systems)symbolic, not analogicalcontinuous scalar quantities mapped to finite discrete

space (qualitative quantity space)e.g... , 0, +

model situation by relationships between these quantities

relative size; arithmetical relationships, ...

de Kleer, Kuipers, Forbus,…

Page 7: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 7.0

Not a replacement for Quantitative reasoning

What is QR? (2)

relevant distinctions only e.g. empty/full ... - 0 +

Ambiguity

+ + 0 - + + + ? 0 + 0 -

- ? - -

* + 0 - + + 0 - 0 0 0 0

- - 0 +

Page 8: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 8.0

Develop QR representations specifically for space Richness of QSR derives from multi-dimensionality

Consider trying to apply temporal interval calculus in 2D:

What is QSR? (1)

=<m

o

d

f

s

Can work well for particular domains -- e.g.

envelope/address recognition (Walischewski 97)

Page 9: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 9.0

What is QSR? (2) Many aspects:

ontology, topology, orientation, distance, shape...

spatial changeVagueness and uncertaintyreasoning mechanismspure space v. domain dependent

Page 10: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 10.0

“Poverty Conjecture” (Forbus et al, 86)

“There is no purely qualitative, general purpose kinematics”

Of course QSR is more than just kinematics, but... 3rd (and strongest) argument for the conjecture:

“No total order: Quantity spaces don’t work in more than one dimension, leaving little hope for concluding much about combining weak information about spatial properties''

Page 11: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 11.0

“Poverty Conjecture” (2)

transitivity: key feature of qualitative quantity space can this be exploited much in higher dimensions ?? “we suspect the space of representations in higher

dimensions is sparse; that for spatial reasoning almost nothing weaker than numbers will do”.

Challenge: to provide calculi which allow a Challenge: to provide calculi which allow a machine to represent and reason qualitatively with machine to represent and reason qualitatively with spatial entities of higher dimension, without spatial entities of higher dimension, without resorting to the traditional quantitative techniques.resorting to the traditional quantitative techniques.

Page 12: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 12.0

Why QSR? Traditional QR spatially very inexpressive Potential applications of QSR in:

Natural Language UnderstandingGIS/GIScienceVisual LanguagesBiological systemsRoboticsMulti Modal interfacesEvent recognition from video inputSpatial analogies...

Page 13: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 13.0

Ontology of Space extended entities (regions)? points, lines, boundaries? mixed dimension entities? Open/closed/regular/non regular regions? Multi-piece (disconnected)? Interior connected? What is the embedding space?

connected? discrete? dense? dimension? Euclidean?... What entities and relations do we take as primitive,

and what are defined from these primitives?

Challenge 2: the diversity of spatial Challenge 2: the diversity of spatial ontologyontology

Page 14: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 14.0

Mereology

Theory of parthood (Simons 87) In fact, many theories What principles should hold? E.g. Weak supplementation principle:

If x is a proper part of y, then there should be some other proper part z of y not identical with x.

(not all mereologies obey this principle)

Page 15: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 15.0

Mereotopology

Combining mereology and topological notions Usually built from a primitive binary conection

relation, C(x,y)Reflexive and symmetricSeveral different interpretations in the literature

Can define many relations from C(x,y)

Page 16: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 16.0

Defining relations using C(x,y) (1)

DC(x,y) df ¬C(x,y)

x and y are disconnected

P(x,y) df z [C(x,z) C(y,z)]

x is a part of y

PP(x,y) df P(x,y) ¬P(y,xx)

x is a proper part of y

EQ(x,y) df P(x,y) P(y,x)

x and y are equalalternatively, an axiom if equality built in

Page 17: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 17.0

Defining relations using C(x,y) (2)

O(x,y) df 9z[P(z,x) P(z,y)]x and y overlap

DR(x,y) df ¬O(x,y)x and y are discrete

PO(x,y) df O(x,y) ¬P(x,y) ¬P(y,x)x and y partially overlap

Page 18: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 18.0

Defining relations using C(x,y) (3)

EC(x,y) df C(x,y) ¬O(x,y) x and y externally connect

TPP(x,y) df PP(x,y) 9z[EC(zz,y) EC(zz,xx)]x is a tangential proper part of y

NTPP(x,y) df PP(x,y) ¬TPP(x,y)x is a non tangential proper part of y

Page 19: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 19.0

RCC-8

DC EC PO TPP NTPP

EQ TPPi NTPPi

8 provably jointly exhaustive pairwise disjoint relations (JEPD)

Page 20: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 20.0

C(x,y) is very expressive

Can also define: Holes, dimension, one pieceness Topological functions Boolean functions (sum, complement, intersection) …

Page 21: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 21.0

An alternative basis: 9-intersection model (9IM)

boundary(y) interior(y) exterior(y)

boundary(x) ¬ ¬

interior(x)

exterior(x) ¬ ¬

29 = 512 combinations8 relations assuming planar regular point sets

potentially more expressiveconsiders relationship between region and

embedding spaceVariant models discrete space (16 relations)

(Egenhofer & Sharma, 93)

Page 22: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 22.0

“Dimension extended” method (DEM)

In the case where array entry is ‘¬’, replace with dimension of intersection: 0,1,2

256 combinations for 4-intersection Consider 0,1,2 dimensional spatial entities

52 realisable possibilities (ignoring converses)(Clementini et al 93, Clementini & di Felice 95)

Page 23: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 23.0

The 17 different L/A relations of the DEM

Page 24: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 24.0

Mereology and Topology

Which is primal? (Varzi 96) Mereology is insufficient by itself

can’t define connection or 1-pieceness from parthood

1. generalise mereology by adding topological primitive

2. topology is primal and mereology is sub theory

3. topology is specialised domain specific sub theory

Challenge: choosing primitives and inter-relatingChallenge: choosing primitives and inter-relatingprimitives in different theoriesprimitives in different theories

Page 25: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 25.0

 Baarle-Nassau/Baarle-Hertog

Page 26: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 26.0

Between Topology andMetric representations

What QSR calculi are there “in the middle”? Orientation, convexity, shape abstractions… Some early calculi integrated these

we will separate out components as far as possible Some example calculi in next few slides Mostly defined using algebraic techniques rather

than logics, or only semi-formally.

Challenge: finding expressive but efficientChallenge: finding expressive but efficient““semi-metric” calculi.semi-metric” calculi.

Page 27: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 27.0

Orientation Naturally qualitative: clockwise/anticlockwise

orientation Need reference frame

deictic: x is to the left of y (viewed from observer)intrinsic: x is in front of y

(depends on objects having fronts)

absolute: x is to the north of y Most work 2D Most work considers orientation between points or

wrt directed linesChallenge: combining region based mereotopologyChallenge: combining region based mereotopologywith point based orientation calculi.with point based orientation calculi.

Page 28: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 28.0

Qualitative Positions wrt oriented lines

pos(p,li) = + iff p lies to left of li

pos(p,li) = 0 iff p lies on li

pos(p,li) = - iff p lies to right of lil1 l2

l3

+--

++-

+++

-++

--+

---

+-+

Note: 19 positions (7 named) -- 8 not possible

Page 29: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 29.0

Star Calculus (Renz and Ligozat)

If more than 2 intersecting lines used for defining sectors, then easy todefine a coordinate system and thus a geometry.

Page 30: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 30.0

boundary representations axial representations shape abstractions synthetic: set of primitive shapes

Boolean algebra to generate complex shapes

Qualitative Shape Descriptions

Challenge: finding useful qualitative shape calculiChallenge: finding useful qualitative shape calculi

Page 31: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 31.0

Hoffman & Richards (82): label boundary segments:curving out curving in straight angle outward >angle inward <cusp outward Âcusp inward Á

Meathrel & Galton (2001) provide a hierarchical, unbounded representation calculusGeneralises all previous approaches

boundary representations

>

>

>

<>

|

>

Page 32: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 32.0

conv(x) + C(x,y) topological insidegeometrical inside“scattered inside” “containable inside”...

Using Convex Hull to describe shape

Page 33: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 33.0

Expressiveness of conv(x)

Constraint language of EC(x) + PP(x) + Conv(x) can distinguish any two bounded regular regions not

related by an affine transformationDavis et al (97)

intractable (at least as hard as determining whether set of algebraic constraints over reals is consistentDavis et al (97)

Page 34: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 34.0

Mereogeometries

Region Based Geometry (RBG)2nd order axiomatisation P(x,y) + Sphere(x)Categorical(Region based version of Tarski’s geometry)

Borgo and Masolo (06)Analysis of several other systems (eg de Laguna)Four shown to be strongly semantically equivalent

Some work on on constraint systemsLess expressive but more tractable

Page 35: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 35.0

Qualitative Spatio-temporal representations

Many temporal calculiTemporal modal logics, Allen’s calculus…

How to combine?Ontology of space-time (3+1D v. 4D)Computational issues

Capturing interactions between time and spacecontinuity

Challenge: finding useful qualitative spatio-temporal calculiChallenge: finding useful qualitative spatio-temporal calculi

Page 36: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 36.0

Decidable Spatiotemporal modal logics(Wolter & Zakharyashev)

Combine point based temporal logic with RCC8temporal operators: Since, Untilcan define: Next (O), Always in the future ¤ +,

Sometime in the future ¦+

ST0: allow temporal operators on spatial formulaesatisfiability is PSPACE completeEg ¬ ¤+P(Kosovo,Yugoslavia)

Kosovo will not always be part of Yugoslaviacan express continuity of change (conceptual

neighbourhood) Can add Boolean operators to region terms

E.g. EQ(UK,GB+N.Ireland)

Page 37: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 37.0

Spatiotemporal modal logic (contd) ST1: allow O to apply to region variables

(iteratively) Eg ¤+P(O EU,EU)

The EU will never contractsatisfiability decidable and NP complete

ST2: allow the other temporal operators to apply to region variables (iteratively)finite change/state assumptionsatisfiability decidable in EXPSPACEP(Russia, ¦+ EU)

all points in Russia will be part of EU (but not necessarily at the same time)

Page 38: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 38.0

Metatheoretic results: decidability Topology not decidable (Grzegorczyk, 51):

Boolean algebra is decidable add: closure operation or EC results in undecidability

can encode arbitrary statements of arithmetic

Decidable subsystems? Constraint language of “RCC8” (Bennett 94)

Modal/intuitionistic encoding

Other decidable languages? Constraint language of RCC8 + Conv(x) (Davis et al, 97) Modal logics of place

P: “P is true somewhere else” (von Wright 79)

Some spatio-temporal logics (See below)

Page 39: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 39.0

Reasoning by Relation Composition R1(a,b), R2(b,c)

R3(a,c)?

In general R3 is a disjunction

Ambiguity

Page 40: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 40.0

Composition tables are quite sparse

•cf poverty conjecture

DC EC PO TPP NTPP TPPi NTPPi EQ DC ? DR,PO,

PP DR,PO,PP

DR,PO,PP

DR, PO, PP

DC DC DC

EC DR,PO,PPi

DR,PO, TPP,TPi

DR,PO,PP

EC,PO,PP

PO, PP

DR DC DC

PO DR,PO,PPi

DR, PO, PPi

? PO,PP PO, PP

DR, PO, PPi

DR, PO, PPi

PO

TPP DC DR DR,PO,PP

PP NTPP DR,PO,TPP,TPi

DR, PO, PPi

TPP

NTPP DC DC DR,PO,PP

NTPP NTPP DR,PO,PP

? NTPP

TPPi DR,PO, PPi

EC,PO, PPi

PO,PPi PO,TPP,TPi

PO, PP

PPi NTPPi TPPi

NTPPi DR,PO, PPi

PO,PPi PO,PPi PO,PPi O NTPPi NTPPi NTPPi

EQ DC EC PO TPP NTPP TPPi NTPPi EQ

Page 41: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 41.0

Composition Tables and Constraints

Reasoning using composition tables is a constraint based approach to reasoningFinite set of JEPD relations (e.g. RCC-8)Composition table gives constraints amongst these

relationsGiven a set of ground, possibly disjunctive facts

For each triple of objects, check if constraints are satisfied

If all combinations of triples are consistent wrt the composition table, then path consistent

Page 42: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 42.0

Spatial Change

Challenge: Want to be able to reason over time Challenge: Want to be able to reason over time about spatial entitiesabout spatial entitiescontinuous deformation, motion

c.f.. traditional Qualitative simulation (e.g. QSIM: Kuipers, QPE: Forbus,…)

Equality change lawtransitions from time point instantaneoustransitions to time point non instantaneous

0 +

Page 43: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 43.0

Kinds of spatial change (1)

Topological changes in ‘single’ spatial entity:change in dimension

usually by abstraction/granularity shifte.g. road: 1D2D 3D

change in number of topological components e.g. breaking a cup, fusing blobs of mercury

change in number of tunnels e.g. drilling through a block of wood

change in number of interior cavities e.g. putting lid on container

Page 44: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 44.0

Kinds of spatial change (2)

Topological changes between spatial entities:e.g. change of RCC/4IM/9IM/… relation

change in position, size, shape, orientation, granularitymay cause topological change

Page 45: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 45.0

Continuity Networks/Conceptual Neighbourhoods

If uncertain about the relation what are the next most likely possibilities?Uncertainty of precise relation will result in connected subgraph

(Freksa 91)

Can be used as basis of a qualitative simulation algorithm

What are next qualitative relations if entities transform/translate continuously?E.g. RCC-8

Page 46: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 46.0

What exactly is qualitative continuity?

No spatial leaps No pinching No temporal gaps

Can we formally prove the non existence of the missing links in the conceptual neighbourhood from a formal definition of qualitative continuity?

Page 47: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 47.0

Continuity of Multiple Component Histories

Page 48: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 48.0

Conceptual Neighbourhoods for other calculi Virtually every calculus with a set of JEPD relations

has presented a CN. E.g.

Page 49: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 49.0

Vagueness

Ubiquitous in geographic phenomena Hills, valleys, forests, rivers, lakes … Even man made artifacts (walls, roofs,…)

Can’t avoid, must develop techniques to handle Eg:

The tree is near the summit of the mountain. The mountain is far from the sea. ² The tree is not near to the sea.

Challenge: representing vagueness in a useful way (we can Challenge: representing vagueness in a useful way (we can still make inferences)still make inferences)

Page 50: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 50.0

Modal Supervaluation Logic

We can define modal operators which take account of how the truth of propositions may vary according to different senses of the concepts that it contains.

U — is unequivocally true. S — is true in some sense.

U¬(Near(x,y) Æ Far(x,y)) (Pond(x) ! S(Lake(x)))

Applications in ontology e.g. current geo-ontology projects Reified approach with key parameters (e.g. width, depth,

flow for river/lake)

Page 51: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 51.0

Indeterminate boundaries/vague regions:egg-yolk calculus

Using RCC8: 601 jointly exhaustive, pairwise disjoint relations 40 natural clustersCan 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

...

Page 52: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 52.0

Recap

Surprisingly rich languages for qualitative spatial representationsymbolic representationsTopology, orientation, distance, ...hundreds of distinctions easily made

Static reasoning: composition, constraints, 0-order logic

Dynamic reasoning: continuity networks/conceptual neighbourhood diagrams

Page 53: Tony Cohn, The University of Leeds 2007 NESC-3-07 0.0 13:35 Qualitative representations of the geospatial world Tony Cohn School of Computing The University.

13:35 Tony Cohn, The University of Leeds 2007 NESC-3-07 53.0

Discussion Topics Modelling

Choice of language/representation(s) Granularity of representation How best to handle vagueness and uncertainty Space and time Integration of representations (incl. semantics) Do we need new/more languages?

Inference and Computation What kinds of tasks? (prediction, simulation, consistency

checking, ontology integration, change of granularity/abstraction…)

Integration with quantitative representations/computation Bridging the research/application gap