School of something FACULTY OF OTHER School of Computing FACULTY OF ENGINEERING Formalising a basic hydro-ontology David Mallenby Knowledge Representation

School of somethingFACULTY OF OTHER

School of ComputingFACULTY OF ENGINEERING

Formalising a basic hydro-ontology

David Mallenby

Knowledge Representation and Reasoning Group

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 isn’t a river


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


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


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


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



Inland water case study: the Hull estuary


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

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

R

P

Rmax

Rmin

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



Results of marking stretches and gapsInitial result


Results of marking stretches and gapsDecrease the gap threshold


Results of marking stretches and gapsIncrease linearity threshold

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


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:

• ∀x:[river(x) ↔ waterfeature(x) ∧ has_property(x,stretch) ∧ has_property(x,wide)]

• ∀x:[lake(x) ↔ waterfeature(x) ∧ has_property(x,nonstretch) ∧ has_property(x,large)]


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


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


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


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


Documents

School of something FACULTY OF OTHER School of Computing FACULTY OF ENGINEERING Formalising a basic hydro-ontology David Mallenby Knowledge Representation