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AR&A in Temporal & Spatial Reasoning SARA 2000

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.

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AR&A in Temporal & Spatial Reasoning SARA 2000

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  1. AR&A 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)

  2. 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 • ...

  3. 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 • ...

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

  5. l1 l2 DC EC PO TPP NTPP +-- --- ++- +-+ l3 --+ +++ -++ EQ TPPi NTPPi Qualitative Spatial Representations

  6. Changing scale: Baarle-Nassau/ Baarle-Hertog(thanks to Barry Smith for the example)

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

  8. Conceptal neighbourhoods & approximation • Conceptual neighbourhoods give “next” relation • Uncertainty of relation gives connected sub-graph • e.g. composition table entries

  9. 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

  10. 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

  11. 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

  12. Decidable, tractable representation • Represent RCC relation by two sets of constraints: “model constraints” “entailment constraints” DC(x,y) ~xÚ~y ~x, ~y EC(x,y) ~(xÙy) ~x, ~y, ~xÚ~y PO(x,y) --- ~x, ~y, ~xÚy, yÞx, ~xÚ~y TPP(x,y) xÞy ~x, ~y, ~xÚy, yÞx NTPP(x,y) ~xÚy ~x, ~y , yÞx EQ(x,y) xÛy ~x, ~y

  13. 9-intersection+DEM • DEM: when entry is ‘¬’, replace with dimension of intersection: 0,1,2 • 81+ region-region relations

  14. L  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)Ùdisjoint(t(L),A)

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

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