1. Synthetic Experiments for Spatial Reference Systems Engineering Approaches to Cognitive Science –Andrew U. Frank –Geoinformation –TU Vienna –frank@geoinfo.tuwien.ac.at

2. Overview Methodology in general Spatial Reference Frames

3. Geographic Information Systems Need to understand cognition of space to make progress in multi-scale, map series hierarchies temporal data imprecise and incomplete data Nothing is more practical than a good theory! (Ludwig Boltzmann)

4. Tools in Science: The tool influences –the research question and –the approach To further advance we have to sharpen our tools.

5. Formalization Axiomatic - Forming Theories –a new theory for the form of human knowledge –capture high levels of abstraction: e.g., –eq, notEq = not.eq, –transitivity –idempotency

6. Formalization Typed formal system - object classes –avoids Russel’s paradox –build layered models e.g., Kuipers’ level of control for a robot

7. Formalization Algebraic - Objects and operations –Definition of Operations in terms of observations of results of other operations –potential to capture semantics, important for cooperation between systems and data exchange

8. Formalization Constructive (computational) - Models –avoid solutions which cannot be implemented e.g., raster model for RCC 8 alternative goals: small number of concepts (Habel, Cohn) traditional geometry

9. Synthetic experiments e.g., Kuipers’ simulated robot Hypothesis: a formal model a of process Determine the performance Compare with the observed behavior Confirm or reject hypothesis

10. Synthetic experiments model can predict –response time, –error level, –error characteristics asymmetry front, side, back types of error (Steven & Coupe, Tversky) This is the “It can’t be otherwise“ argument (Kuipers)

11. Formal Models Models should replace Metaphors –e.g., ‘Mental Image’ (Kosslyn) For a formal model decide on –Representation and –Operation

12. Formal Models and Isomoprhism In algebra, a representation is determined only ‘up to isomorphisms’ –e.g.: roman numerals or Arabic - isomorphic –needed: a theory of relaxed isomorphism which allows for errors

13. The Case: Description of Reference Frames Confusion in the terminology Unclear (incomplete) definitions ‘at best sufficient for European languages’

14. A confusing case

15. Left: The Ball is on my left. The Ball is to the left of the tree

16. Cognitive Model used: from visual observation of the world to speech: –world -> –visual observation -> image –discretization -> propositions –perspective taking -> proto-sentences –(language production -> speech)

17. interest: world -> proto-sentences specifically perspective taking novel: –model of formal processes, –differentiate process and representation –start with a model of the world (which is external to cognition)

18. World consists of Objects limited for the usual reference frame discussion This representation is not part of the cognitive model!

19. 2D objects with coordinates in a fixed frame with a single reference point (no extension) orientation/heading direction of the major axis –in the allocentric reference frame (cardinal directions here) some objects do not have an orientation

20. The World

21. Observation of the World EGO -> sees -> World -> imagistic model of the world observations are –distance –directions –heading from the EGO and relative to the body axis, Klatzky’s egocentric coordinates

22. Representation of the view representation of objects, with –distance and direction from EGO and –heading additional observation: EGO’s orientation in the world (EGO’s heading in the allocentric frame) –either from visual perception or from the vestibular system

23. Discretization: Translation of Imagistic to Propositional 8 cones of directions (front, front-left, left,..) 4 distance values (here, near, far, very far) use of distances and directions jointly

24. Representation of discretized view distance direction heading –all in the EGOs reference frame

25. Propositional Representation = Egocentric Perspective Paul says: –Der Ball liegt rechts vor mir. –Der Stuhl ist vor mir.

26. Perspective Taking perspective taking is necessary to understand another person simplest case: how does the speaker see the world –Peter speaking to Paul: Der Ball liegt direkt vor Simon. requires: path completion (or vector subtraction)

27. The World

28. Invariant of Perspective Taking The result of perspective taking must be the same than the observation of the other person (up to errors) persp b a (persp a b (rep)) = rep

29. How is perspective taking computed? Two hypothesis: Perspective taking is done –in imagistic representation –or –in propositional representation

30. Synthetic experiment: What would be the difference? How precise could a propositional computation be: – (8 directions, 4 distances) Result: on average 3% error (of maximal dimension) Comparing with human performance does not allow to confirm/reject the hypothesis.

31. Absolute frame of reference e.g., cardinal directions needs orientation (heading) of EGO in space –Klatzky’s ‘local view’ operation is just a rotation of directions. two variants: –egocentric: Paris is to the west –relative: Paris is south of London

32. Definition of a frame of reference origin orientation/heading (direction of the axes) handedness (or distribution of axes over the horizon) –a simple determination of figure and ground is not sufficient –orientation is not necessarily taken from ground

33. Frames of References in English/German: Terms: Front, Left, Back, Right egocentric –ground=speaker, orienation=speaker, right-handed intrinsic (person) –ground=person, orientation=person, right-handed

34. Frames of References II intrinsic (thing) –ground=thing, orientation=thing, left-handed retinal –ground=object, orientation=towards speaker, left-handed

35. Deictic usual description: ground = observer, orientation = observer not likely in English/German –in English or German, the orientation is taken from the arrow from observer to the ground

36. Haussa - ball in front of the tree description: the reference system in an deictic reference frame in Haussa is facing the same direction as the speaker.

37. Ball in front of the tree:

38. Conclusions Formalization has demonstrated what is necessary for a complete description of a reference frame: ground, orientation, handedness

39. Conclusions 2 a model with processes and representation is possible using an algebraic, constructive and theory/model approach

40. Conclusions 3 performance can be tested errors in performance can be included to compare different hypothesis –requires detailed reporting of error characteristics in experiments

41. Practical conclusion “Topology is important” –(Egenhofer relations are patented!) comming issue for industry: “Semantics”