Formalising a basic hydro-ontology

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Formalising a basic hydro-ontology
School of Computing FACULTY OF ENGINEERING

• David Mallenby
• Knowledge Representation and Reasoning Group

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School of Computing FACULTY OF ENGINEERING

• Vagueness in Geography examples
• Vagueness is ubiquitous in geographical concepts
• Both boundaries and definitions are usually
  vague, as well as resistant to attempts to give
  more precise definitions
• Vagueness is also contextual a large river in
  one country may not be considered large somewhere
  else
• Classical reasoning requires explicit boundaries
  something is or isnt a river

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School of Computing FACULTY OF ENGINEERING

• Vagueness in Geography vague reasoning
  approaches
• A better approach therefore would be to allow
  reasoning of the vague predicates, rather than
  using predefined perspectives and segments
• The principle approaches for vague reasoning are
• Fuzzy Logic
• Supervaluation theory
• Often presented as opposing theories, but this in
  part assumes that vagueness can only take one
  form
• Rather, there are instances suited to each
  approach
• So we must consider what our problem requires,
  then determine which approach is most suitable

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School of Computing FACULTY OF ENGINEERING

• Vagueness in Geography our system
• In our proposed system we wish to segment,
  individuate and label hydrological features
• Crisp boundaries are not suited to fuzzy logic,
  where transitional boundaries would be generated
• Supervaluation theory on the other hand, would
  allow crisp boundaries by using user preferences
  as precisifications
• Therefore, supervaluation theory is preferred
  approach here

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School of Computing FACULTY OF ENGINEERING

• Ontology grounding overview
• Ontology level is usually seen as separate to the
  data level we reason within the ontology and
  return the data that matches our queries
• Thus the data is devoid of context, which has an
  impact on handling vagueness
• An improvement would instead be to ground the
  ontology upon the data
• This means we make an explicit link between the
  ontology and the data, thus allowing reasoning to
  be made within context
• Allows the user to decide the meaning of the
  concepts to some extent

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School of Computing FACULTY OF ENGINEERING

• Ontology grounding usage
• Requires work at both ontology and data level
• At ontology level we consider what attributes we
  require to identify and reason about features
• At data level we consider how to obtain such
  attributes
• For example, linearity is an important
  geographical concept, as the way a feature
  changes shape is often used in classification
• Such an attribute is dependant on the context
• So by identifying linear stretches we have an
  attribute that can be passed to an ontology
  grounded upon the data to facilitate reasoning

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Inland water case study the Hull estuary
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The medial axis of the Hull estuary

• Because only require inland water features,
  medial axis of sea is removed, with only part
  left at river mouth to allow reasoning of mouth

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School of Computing FACULTY OF ENGINEERING

• Data representation linearity
• Calculation of linearity could be performed in a
  variety of ways
• We require a scale invariant approach

• We take a point P on the medial axis, and get the
  maximal inscribed disc at that point (radius R in
  the diagram)
• For all points on medial axis that are inside
  this disc, we get the radius at that point,
  finding the min and max (Rmin and Rmax in the
  diagram)
• If the ratios R-Rmin and R-Rmax fall below a
  certain threshold, the point is labelled linear
• We do this process for all end nodes of arcs in
  the superarc if both nodes of an arc are linear,
  then the arc is marked linear

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• Data representation gaps
• Sometimes arcs we would like to mark as linear
  are not marked as such
• Small inlets at the edge of the river
• Sharp bends
• We could vary our linearity threshold, but this
  may include arcs we do not wish to include
• Instead it is intuitive to have a gap
  precisification, such that we join together
  stretches that are close enough together given
  some threshold

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Results of marking stretches and gaps
Initial result
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School of Computing FACULTY OF ENGINEERING
Results of marking stretches and gaps
Decrease the gap threshold
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Results of marking stretches and gaps
Increase linearity threshold
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School of Computing FACULTY OF ENGINEERING

• From stretch to ontology
• Intention is to build features up from primitives
• In the case study, the main primitive shown is
  that of a stretch
• Initially this stretch was based purely on
  linearity
• Other considerations have arose though
• Linearity measurement may need modifying
• Gaps between linear stretches
• Small inlets at the edges
• So our concept of stretch is itself built up from
  primitive elements

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School of Computing FACULTY OF ENGINEERING

• From stretch to ontology
• System marks and stores polygons with series of
  properties, from which an ontology could build
  upon
• For example, suppose we have the following
  options available to us
• Stretch/non-stretch (can be either just linear
  stretches or major stretches)
• Wide/narrow for stretches
• Large/small area for non-stretches
• We can build simple definitions such as
• ?xriver(x) ? waterfeature(x) ?
  has_property(x,stretch) ? has_property(x,wide)
• ?xlake(x) ? waterfeature(x) ?
  has_property(x,nonstretch) ? has_property(x,large)
  

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• Other basic notions moving to 3D
• Presently only working with 2D data
• This is sufficient for case study, as people are
  able to identify features from 2D maps
• A more complete ontology though would require
  considering the world from a 3D perspective
• Thus an obvious simple property would be depth
• However, also opens up option to consider water
  features from a different perspective the land
  form that contains the water

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School of Computing FACULTY OF ENGINEERING

• Contour surfaces of matter
• Following on from this, we may want to consider
  some primitive matter types, and the interaction
  between them
• 3 simple matter types would be solid, liquid and
  gas
• So building previously mentioned example, a river
  could consist of a contour in a solid surface
  that contains flowing water

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• The reference ellipsoid
• The geoid is a surface that approximates the mean
  ocean surface, and thus approximates the shape of
  the Earth
• The reference ellipsoid approximates the geoid
  (to an accuracy of about 100m)
• Used as basis of co-ordinate system of
  latitude,longitude and height
• Would allow more accurate representation of Earth
  in ontology

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School of Computing FACULTY OF ENGINEERING

• From 3D to 4D
• Final consideration would be the incorporation of
  time
• Geography is full of examples of change through
  time rivers drying up, islands within rivers
  eroding until two rivers join
• Also previously mentioned matters may change over
  time ice to water to vapour