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Near & FarNear & FarStefan Hahmann
Alexander PadbergChristian MayerAneta Florczyk
Ontology and VaguenessTutor: Brandon Bennet
IFGI Spring School, 21-31 March 2010, Muenster, Germany
Natural Language Definition Natural Language Definition “Near”“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“
Natural Language Definition Natural Language Definition “Far”“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“
Modes of ClassificationModes 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)
GoalGoal
Nearness
Farness
Nearness and Farness are interpretations of distance
Light green: area reachable by car in five minutes
Parameters of VariabilityParameters of Variability
1. Effort1. Spatial gap2. Time3. Financial cost
2. Context1. Scale2. Size3. Significance
EffortEffortSpatial gapSpatial gap
ContextContextScaleScale
ContextContextSizeSize
Predication criteriaPredication 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
ApproachApproach
Human farness = f(context, effort)nearness = f(context, effort)
Geometric farness = f(context)nearness = f(context)
Temporal farness = f(context)nearness = f(context)
DefinitionsDefinitions
farness ~ [f(effort) * scale] / [size * significance]
nearness ~ 1 / farness
AxiomsAxioms
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))
ConclusionConclusion
VAGUE!!!