Near & Far

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!!!