AR

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ARA in Temporal Spatial ReasoningSARA 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)

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ARA in Temporal and Spatial Reasoning.

• the role of ARA in ST reasoning
• the types of abstraction and approximations that
  are useful for ST reasoning
• the differences in the use of abstraction and
  approximation in ST reasoning
• wish list for work on ARA in ST
• ...

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Abstraction in Spatial ReasoningWhy?

• 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
• ...

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Kinds of spatial abstraction

• Regions rather than points (aggregation)
• granularity shifts (eg pixel size)
• dimension changing
• qualitative relations
• relevant abstractions
• ...

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Qualitative Spatial Representations
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Changing scale Baarle-Nassau/ Baarle-Hertog (tha
nks to Barry Smith for the example)
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Approximation

• Qualitative relations
• (eg sector orientations)
• Regions, and regions with indeterminate
  boundaries
• the egg/yolk calculus
• X is crisper than Y

...
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Conceptal neighbourhoods approximation

• Conceptual neighbourhoods give next relation
• Uncertainty of relation gives connected sub-graph
• e.g. composition table entries

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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 Nebels analysis of Allen

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Reformulation

• RCC 1st order theory ? Zero order formulation
• 9-intersectionDEM (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

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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. Ú is sum
• e.g. Þ is P
• Spatial logic rather than logical theory of space

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Decidable, tractable representation

• Represent RCC relation by two sets of
  constraints
• model constraints entailment
  constraints
• DC(x,y) xÚy x, y
• EC(x,y) (xÙy) x, y, xÚy
• PO(x,y) --- x, y, xÚy, yÞx, xÚy
• TPP(x,y) xÞy x, y, xÚy, yÞx
• NTPP(x,y) xÚy x, y , yÞx
• EQ(x,y) xÛy x, y

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9-intersectionDEM

• DEM when entry is , replace with dimension
  of intersection 0,1,2
• 81 region-region relations

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? CMB (5 polymorphic relations)

• disjoint x Ç y Æ
• touch (a/a, l/l, l/a, p/a, p/l) x Ç y Í b(x) È
  b(y)
• in x Ç y Í y
• overlap (a/a, l/l) dim(x)dim(y)dim(x Ç y) Ù
  x Ç y ¹ Æ Ù y ¹ x Ç y ¹ x
• cross (l/l, l/a) dim(int(x))Çint(y))max(int(x)),
  int(y)) Ù x Ç y ¹ Æ Ù y ¹ x Ç y ¹ x
• EG touch(L,A) Ù cross(L,b(A)) Ù
• disjoint(f(L),A) Ù
  disjoint(t(L),A)

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Research issues

• Moving between abstraction levels
• Qualitative/quantitative integration
• Choosing abstraction level
• Expressiveness/efficiency tradeoff
• Cognitive Evaluation
• Ambiguity
• ...