1. Near & Far Stefan Hahmann Alexander Padberg Christian Mayer Aneta Florczyk Ontology and Vagueness Tutor: Brandon Bennet IFGI Spring School, 21-31 March 2010, Muenster, Germany

2. Natural Language Definition Near NEAR not far distant in time or space or degree or circumstances Simple Ambiguity Almost Examples of ambiguity "near neighbors" "a near hit by the bomb" "in the near future" "they are near equals" "a very near thing" "she was near tears" "his nearest approach to success

3. Natural Language Definition Far FAR located at a great distance in time or space or degree Examples of ambiguity "we come from a far country" "far corners of the earth" "the far future" "a far journey" "the far side of the road" "far from the truth" "far in the future

4. Modes of Classification Physical Geometric Distance - relative (context) and subjective interpretation Historical Changed due to the changes of the way of traveling Functional Common way of describing distances Legal/Conventional Restriction (law or regulation) E.g. German case: reimbursement for commuters (if distance to work is more than 20 km)

5. Goal Nearness Farness Nearness and Farness are interpretations of distance

6. Light green: area reachable by car in five minutes

7. Parameters of Variability 1. Effort 1. Spatial gap 2. Time 3. Financial cost 2. Context 1. Scale 2. Size 3. Significance

8. Effort Spatial gap

9. ContextScale

10. ContextSize

11. Predication criteria Individuation take all possible objects and arrange them in pairs of two Demarcation whether a pair of objects is considered far apart or near to each other is determined via a threshold Identity whether a distance is conceived as far or near might change if context or effort change over time

12. Approach Human farness = f(context, effort) nearness = f(context, effort) Geometric farness = f(context) nearness = f(context) Temporal farness = f(context) nearness = f(context )

13. Definitions farness ~ [f(effort) * scale] / [size * significance] nearness ~ 1 / farness

14. Axioms Precondition: context = CONSTANT Axiom1: all x1 all y1 all x2 all y2 ( effort( near(x1,y1) ) < effort( far(x2,y2) ) ) Axiom2: all x all y all z ( near(x,y) & near(y,z) -> ¬far(x,z) )

15. Conclusion VAGUE!!!