Preliminaries for an Ontology
of Environment and Habitat
Brandon Bennett
School of Computing
University of Leeds
[email protected]
EnvO, Dagstuhl — 23rd Feb 2010
Overview
These slides overview my prelimary work on constructing an
ontology for environments and habitats, which is described in a
paper which will be presented at FOIS-10.
I cover the following topics:
• Conceptual ambiguity and modes of definition.
• Grounding ontology for geographic and environmental regions.
• Definitions of ‘Environment’.
• Towards defining ‘Habitat’.
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Previous Work
• Grinnell (1917), Idea of Ecological Niche
• Elton (1927), Hutchinson (1957), Vandermeer (1972), development
of informal theory,
• Smith + Varzi (1999), Smith (2002), mereological theory
• Fonseca (2002), requirements of ecological ontologies
• Keet (2005, 2006), Pennington (2006), factors involved in the
niche concept and its representation.
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Conceptual Ambiguity
Ontologists should beware of various kinds of vagueness and
ambiguity — especially deep ambiguity:
• Simple Ambiguity
• Vagueness
– Threshold (or sorites) Vagueness
– Partiality
– Deep Ambiguity
∗ Mode Ambiguity (caused by exemplar clustering)
• Prototype Implication (caused by exemplar clustering and the
etiquette of effective communication)
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Modes of Definitions
Ontologists should be aware that many common terms harbour a
kind of deep indeterminism that I call mode ambiguity.
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Modes of Definitions
Ontologists should be aware that many common terms harbour a
kind of deep indeterminism that I call mode ambiguity.
Eg1: Artifacts may be defined in terms of:
•
physical properties
•
potential use
•
intended use
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Modes of Definitions
Ontologists should be aware that many common terms harbour a
kind of deep indeterminism that I call mode ambiguity.
Eg1: Artifacts may be defined in terms of:
•
physical properties
•
potential use
•
intended use
Eg2: A political party may be identified as either:
•
a set of doctrines,
•
an institutional organisation
•
or a group of people.
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Background Theories
• Space
• Time
• Physical Regions
• Individual Physical Objects
• Matter Types
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Space and Time
I suggest a classical Cartesian model of space and time.
Space is a set of points, with a distance metric d(p1, p2).
I alow a region to be any point set, although we shall typically be
interested in regular 3D regions or regular 2D surfaces, as well as
points and lines.
surf(r) maps any regular 3-dimensional region to its surface.
Time is modelled by a set of time points — linearly ordered and
continuous.
I will also make use of spatio-temporal regions, which are
modelled as sets of space-time pairs hp, ti — meaning that point
p is part of the region at time t.
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Physical Regions
A physical region is a part of the universe considered both
as spatially extended and as possessing material and dynamic
characteristics.
I assume a 1-to-1 correspondence between spatial and physical
regions.
phys(r), maps a spatial region r to a physical region.
ext(ρ), mapping physical region ρ to its purely spatial extension.
I also make use of physical surfaces and in particular oriented
physical surfaces. The latter may be associated with flows of
chemicals, light, heat etc.
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Individual Physical Objects
I use the term individual to refer to an object that persists in time
in accordance with certain identity criteria.
Spatial and physical extensions of an individual depend on a
time parameter. These extensions may be represented using the
functions ext(i, t) and phys(i, t).
The trajectory traj(i) of an individual is a spatio-temporal volume,
whose spatial extension varies continuously over time and is
self-connected at each moment in time. Its spatial extension is
non-empty at every time point within a durative convex temporal
interval span(i), and is empty at every other time point.
The physical region phys(traj(i)) will be abbreviated as life(i).
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Matter Types
I assume that matter types form a lattice structure.
For every pair of matter types there is:
• a union m1 t m2, which refers to the sum of matter of either
type (e.g. fluid = liquid t gas,
• an intersection m1 u m2 (e.g. liquid u metal), which refers to
matter that manifests the characteristics of both matter types.
(If m1 and m2 are incompatible, m1 u m2 will refer to the empty
(or non-existent) matter type m⊥.)
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Totalities
I use the word totality in a technical sense.
Let φ(r) be a property of regions — i.e. a formula with a free region
variable r. Then the term totalityr [φ(r)] denotes the largest region
r∗ satisfying φ(r∗). More precisely:
r∗ = totalityr [φ(r)] ≡ def
(φ(r∗) ∧ ∀r0[(φ(r0) ∧ Part(r∗, r0)) → r∗ = r0])
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Geographic Regions
Rigorous specification of geographic/environmental ontologies
requires clarity about what kind of entity is a geographic region.
We may consider a geographic region to be a ‘part of the Earth’s
surface’ but several complications arise:
• One problem is the presence of non-rigid substances such as
water, mud or sand.
• Further ambiguity arises due to the presence of overhangs and
cavities.
• Another complication is that, in many contexts, a geographic
region is not treated as a mathematical surface of zero
thickness but more like a 3-dimensional volume that can contain
material objects such as trees or buildings.
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GeoRegs
I introduce GeoRegs as a set-theoretic model for geographic
regions.
I take the surface of the Earth’s reference ellipsoid as a primitive
entity, by res. We write
cres refers to the point at the centre of res.
We can use res to define identity criteria for geographic regions.
Let resProj(ρ), map each geo-reg to a regular closed subsurface
of res — i.e. all those points on res that lie above or below or
are coincident with some point that is considered to be within the
physical region ρ, along a line passing through the centre of the
reference ellipsoid.
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Identity of GeoRegs
A necessary and sufficient identity criterion for geo-regs is that
two geo-regs are identical if and only if they have the same
projection onto the reference ellipsoid:
∀ρρ0[GeoReg(ρ) → ((ρ = ρ0) ↔ resProj(ρ) = resProj(ρ0))
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Geographic Surfaces
We shall often want to refer to certain types of surface that occur
within the extension of a geo-reg.
Surfaces of interest can often be described in terms of the vertical
ordering of matter types within a geo-reg. Hence we define:
• GeoAbove(p1, p2) ≡ def (d(p1, cres) > d(p2, cres))
• GeoBelow(p1, p2) ≡ def (d(p1, cres) < d(p2, cres))
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Global Upper Surfaces
We can now define the global upper surface of a given matter type
m to be the surface of those points furthest from the centre of the
Earth that have points of matter type m immediately below them:
globalUpperSurface(m) = def
{p | p ∈ ext(maxGeoReg) ∧ ∀q[GeoAbove(q, p) → ¬(q ∈ m)] ∧
∃p0[GeoBelow(p0, p) ∧
∀q[GeoAbove(q, p0) ∧ GeoBelow(q, p) → (q ∈ m)]]}
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Cartographic Surfaces
The cartographic surface of the Earth, incorporates the surfaces
of both water bodies and (non-submerged) land-forms.
I define:
cartSurf = def globalUpperSurface(solid t liquid)
The cartographic surface of a given geographic region ρ is then
simply given by cartSurf(ρ) = ρ ∩ cartSurf.
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Deriving Regions from Surface Point Properties
RSSPP means ‘region satisfies surface point property’.
RSSPPp[ρ, φ(p)] ≡ def ∀p[(p ∈ cartSurf(ρ)) → φ(p)]]
tsspp is the ‘totality’ satisfying a given surface point property:
tssppp(φ(p)) = def totalityρ[RSSPPp(ρ, φ(p))]
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Four Modes of ‘Environment’
• Immediate Environment: the factors that affect a particular
subject by directly impacting the subject’s outer surface,
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Four Modes of ‘Environment’
• Immediate Environment: the factors that affect a particular
subject by directly impacting the subject’s outer surface,
• Affective Environment: collection of objects and/or quantities of
substance contributing to and jointly determining the immediate
environment of the subject,
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Four Modes of ‘Environment’
• Immediate Environment: the factors that affect a particular
subject by directly impacting the subject’s outer surface,
• Affective Environment: collection of objects and/or quantities of
substance contributing to and jointly determining the immediate
environment of the subject,
• Local Environment: the physical region proximal to the subject
(this is vague as the degree of proximity is unspecified — the
local environment of an organism could be related to the range
over which it can move during one day),
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Four Modes of ‘Environment’
• Immediate Environment: the factors that affect a particular
subject by directly impacting the subject’s outer surface,
• Affective Environment: collection of objects and/or quantities of
substance contributing to and jointly determining the immediate
environment of the subject,
• Local Environment: the physical region proximal to the subject
(this is vague as the degree of proximity is unspecified — the
local environment of an organism could be related to the range
over which it can move during one day),
• Global Environment: a physical totality characterised in terms
of physical characteristics that determine a range of immediate
environments that are possible within the region of that totality.
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Illustration
Four Modes of Environment: Immediate, Affective, Local, Global.
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Types of Affective Entities
The affective environment consists of a wide variety of entities that
have some impact on the subject:
• the atmosphere or fluid in which the subject exists,
• the sun,
• objects and matter constituting the surface upon which the
subject resides,
• objects and their surfaces contributing to the visual perception
of the subject,
• gravitational force (or material objects contributing to gravity
local to the subject).
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Representing Global Enviroments
I propose to represent global environments as being of the same
logical category as matter types (albeit ones that can refer to
rather heterogeneous portions of matter).
Hence, in their global sense terms such as ‘rainforest’ and
‘desert’, though structurally more complex, will be treated as of
the same logical type as ‘wood’ and ‘desert’.
desert = tssppp[(avTemp(p) > 15◦C)
∧ (avPrecip(p) < 20mm per month))]
(Note vagueness and standpoint.)
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Interactions Among the Modes
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Mode Ambiguities of ‘Habitat’
• ‘Habitat’ may be interpreted either as a kind of global
environment (as per the formal specification given above), or in
terms of an organism’s affective environment (i.e. a collection
of objects which have some effect on the organism). (It seems
less natural to conceive of a habitat in terms of a local or
immediate environment).
• ‘Habitat’ may be applied to an individual organism or to a
species. (It is also possible that one considers an individual
in relation to the habitat of its species — e.g. ‘This caged polarbear is not in its natural habitat’.)
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• ‘Habitat’ may refer to the actual environment where an
individual or species occurs (its geographic range), or to
environments that are typical of a species, or to possible
environments that are survivable by an organism/species
(potential habitat), or perhaps to environments in which an
organism/species is likely to thrive.
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Formal Specification of ‘Potential Habitat’
Suppose the environmental niche constraints for species s are
specified by a geographic point predicate Niche preds(p).
We can define:
potential habitat(s) = tssppp(Niche preds(p)) .
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More Detailed Analysis of Organisms and Habitat
• Internal State Parameters — these describe the intrinsic
physical condition of the organism.
• Metabolism — organism’s metabolism can be modelled by a
function mapping its environment inputs into outputs.
• Shielding — the capability to block or reflect environmental
inputs.
• Tolerance — the range of values internal compatible with the
functioning and survival of the organism.
• Mobility — movement capability of the organism.
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