1. 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)

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...

4. 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...

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

6. Qualitative Spatial Representations DC EC PO TPP NTPP EQ TPPi NTPPi l1l1 l2l2 l3l3 +-- ++- +++ -++ --+ --- +-+

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

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

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

12. 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

13. 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

14. 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

15. Represent RCC relation by two sets of constraints: “model constraints”“entailment constraints” DC (x,y)~x  y ~x  y EC (x,y) ~(x  y) ~x  y, ~x  y PO (x,y)--- ~x  y, ~x  y, y  x, ~x  y TPP (x,y)x  y ~x  y, ~x  y, y  x NTPP (x,y) ~x  y ~x  y, y  x EQ (x,y) x  y ~x  y Decidable, tractable representation

16. 9-intersection+DEM DEM: when entry is ‘¬’, replace with dimension of intersection: 0,1,2 81+ region-region relations

17.  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

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