Transcript No Slide Title

AR&A in Temporal & Spatial
Reasoning
SARA 2000
Tony Cohn (University of Leeds) chair
Claudio Bettini (Università degli Studi di Milano)
Ben Kuipers (University of Texas at Austin)
Ivan Ordonez (Ohio State University)
AR&A in Temporal and Spatial
Reasoning.
• the role of AR&A in S&T reasoning
• the types of abstraction and approximations
that are useful for S&T reasoning
• the differences in the use of abstraction and
approximation in S&T reasoning
• wish list for work on AR&A in S&T
• ...
Abstraction in Spatial Reasoning
Why?
• Efficiency
– eg: quad trees for very large spatial DBs
• Data integration
– DBs may contain data at different scales
• HCI:
– eg: Cartographic generalisation
– eg: high level queries (incl. NL)
• Spatial planning (eg navigation)
• High level vision
• ...
Kinds of spatial abstraction
•
•
•
•
Regions rather than points (aggregation)
granularity shifts (eg pixel size)
dimension changing
qualitative relations
– relevant abstractions
• ...
Qualitative Spatial
Representations
DC
EC
PO
l1
---
TPP NTPP
l2
EQ TPPi NTPPi
+-+++-+
l3
--+
+++
-++
Changing scale:
Baarle-Nassau/
Baarle-Hertog
(thanks to Barry Smith for the example)
Approximation
• Qualitative relations
– (eg sector orientations)
• Regions, and regions with indeterminate
boundaries
– the “egg/yolk” calculus
...
– X is crisper than Y
Conceptal neighbourhoods &
approximation
• Conceptual neighbourhoods give “next”
relation
• Uncertainty of relation gives connected
sub-graph
– e.g. composition table entries
Finer grained representations
can be more efficient
• Constraint satisfaction in CYCORD is NP
complete
– 24 relation calculus is polynomial on base
relations
• Similarly: tractable subsets of RCC8,
RCC5,..
– Cf Buerkert & Nebel’s analysis of Allen
Reformulation
• RCC: 1st order theory  Zero order
formulation
• 9-intersection+DEM (81+ relations) 
CMB (5 polymorphic relations)
• spatial analogies: reformulating other
domains as a spatial problem
– eg: view database class integration as a spatial
problem using egg/yolk theory
• global orientation  local orientation
• Vector  raster
Intuitionistic Encoding of RCC8:
(Bennett 94)
• Motivated by problem of generating
composition tables
• Zero order logic
– “Propositional letters” denote (open) regions
– logical connectives denote spatial operations
• e.g. is sum
• e.g. is P
• Spatial logic rather than logical theory of
space
Decidable, tractable
representation
• Represent RCC relation by two sets of constraints:
“model constraints”
DC(x,y)
EC(x,y)
PO(x,y)
TPP(x,y)
NTPP(x,y)
EQ(x,y)
~xy
~(xy)
--xy
~xy
xy
“entailment constraints”
~x,y
~x,y, ~xy
~x,y, ~xy, yx, ~xy
~x,y, ~xy, yx
~x,y , yx
~x,y
9-intersection+DEM

boundary(y) interior(y) exterior(x)
¬
boundary(x) ¬

interior(x)



exterior(x)
¬

¬
• DEM: when entry is ‘¬’, replace with
dimension of intersection: 0,1,2
• 81+ region-region relations
 CMB (5 polymorphic relations)
disjoint: x y = 
touch (a/a, l/l, l/a, p/a, p/l): x y b(x) b(y)
in: x y y
overlap (a/a, l/l): dim(x)=dim(y)=dim(x y) 
x y  y x y x
• cross (l/l, l/a):
dim(int(x))int(y))=max(int(x)),int(y))
 x y  y x y x
•
•
•
•
• EG:
touch(L,A) cross(L,b(A)) 
disjoint(f(L),A)  disjoint(t(L),A)
L
Research issues
• Moving between abstraction levels
– Qualitative/quantitative integration
• Choosing abstraction level
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Expressiveness/efficiency tradeoff
Cognitive Evaluation
Ambiguity
...