A. Frank: 3839 Linguistically justified ontology
06-Feb-16
A linguistically justified proposal for a spatiotemporal ontology
Andrew U. Frank
Abstract
A consistent ontology for spatio-temporal GIS is urgently needed. Most of the ontology
discussion in philosophy and in information science focuses on a-temporal ontologies, what
Smith aptly called SNAP ontology; they are not easily extended to include time.
The proposal here is radical as it
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starts with a cognitive and linguistic position,
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reduces the number of concepts necessary, and
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clarifies what is assumed initially.
The ontology builds from spatio-temporal regions as the product of space and time; these
have a natural topology and metric. Different kinds of spatio-temporal regions are separated,
constructing locations, times, material entities and events, with the mereology following from
the topological relations, separating topology from mereology. This resolves puzzles like
“Fish are in the water but not part of the water”. The difference between entities and events
reduces to differences in the observation.
The overall structure of the tiered ontology previously described is confirmed. The
account here does not include abstract entities, which must be treated separately. This
proposal is realist, as it assumes a physical world, it is four-dimensionalist, as it starts with
space and time, etc.
A comparison with a list of linguistic primitives demonstrates that this ontology covers
the description of the material world. It leaves out the specific aspects of human beings, their
ability to think in abstract terms and to communicate, which is to be addressed next.
1 Introduction
Most of the ontology discussion concentrates on an a-temporal view and proposes
different methods to classify the entities, which represent the nouns of natural languages or
such instances. Entities are considered a-temporal, existing at every moment in time, in which
they exist, in the same way. This is following the tradition started by Aristotle in his
metaphysics. Much less, discussion addresses questions of events and processes, despite
equally classical roots in Aristotle’s Ethics. For GIS an ontology which includes space and
time, objects and processes is urgently needed (Frank 1998) (Frank 2003). An a-temporal
ontology of objects is sufficient for the construction of database schemata, but is lacking
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when semantics and differences in semantics must be discussed (Kuhn 2000); it is insufficient
to construct a theory of errors and uncertainty (Goodchild 1989; Frank 1998; Goodchild and
Jeansoulin 1998). Ontologies, which should be useful to deal with geography and natural
hazards, must represent geographic space and process; they must include space and time.
Casati has produced an edited volume on Events (Casati and Varzi 1996). Galton has
surveyed temporal logics (Galton 2000). The presentation of a meeting studying the kinds of
changes in socio-economic units contain some interesting example for the issues which a
spatio-temporal ontology had to address (Frank, Raper et al. 2001). Peuquet published
recently a nice, non-conclusive review of the philosophical debate of “Space and Time”
which is mostly about space (Peuquet 2002). A recent meeting put the question of action in
the focus of the discussion [actor meeting]. For this [which one?] article, recent work by
Smith and Bittner [refs to snap and span] and Simons (Simons 2000; Simons 2000; Simons
draft to appear) were influential. Readers interested in the philosophical aspects of the debate
can find further references there.
My problems with reading philosophical debates is the lack of clarity what is assumed as
an ‘ontological commitment’ and what are the consequences following from it. It seems that
some – more or less – practical, common sense question is posed and then tried to see what
ontological commitment would be necessary to prove the point. Philosophical essays do not
convince me that the same set of assumptions is used in all parts and that consistency in the
argumentation is achieved. In this radical approach, here I want therefore to reason strictly
from assumptions forward and to point out exactly what the assumptions are. I cannot see
why frail human logic, using arguments expressed in imprecise natural languages, which are
based on introspection, should reveal much about the ‘way the world is’.
Bennett has addressed the ontology discussion from the point of view of constructing an
‘ontological logic’ structured in two steps: (1) the definition of a vocabulary, an ontology
language, which represents the entities assumed to exist, their properties, and the rules
holding between them and (2) the construction of at least one model which fulfills these rules.
He advocates that well-known mathematical axiom systems are used for the foundation and
other concepts are defined in terms of this vocabulary (Bennett to appear). The proposal here
follows essentially Bennett’s ontological logic O (Bennett 2001) and generalizes it to better
include geographic reality.
What is needed for the construction of spatio-temporal information systems, in particular
Geographic Information systems, is a comprehensive account of space, time, and how objects
and processes are situated in them. This account should agree with Euclidean geometry and
Newtonian physics, because these are the scientific foundations for precise observations and
representations of spatial phenomena.
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The ontology must also agree with human conceptualization of the environment in which
we live (Hayes 1985; Egenhofer and Mark 1995). Human conceptualization is extremely
flexible and by introspection available to each of us; the difficulty is to obtain reliable
descriptions which are not influenced by particular interests, view points etc. In this article, I
use a documented linguistic approach: Wierzbicka has suggested that there are a small
number, exactly 87, fundamental words, occurring in all languages, which are sufficient to
express all other concepts (Wierzbicka 1996). This list of primes can be used to structure the
top of the ontology, the fundamental concepts: SOMETHING, WHERE, WHEN, DO,
HAPPEN, MOVE, INSIDE, PART OF, etc. Wierzbicka’s list of primes is stressing the
fundamental view point, whereas Wordnet is reaching out and collects as many words as
possible, paying less importance to the top-level structure (Fellbaum 1998). This may
overcome a current difficulty with upper-level ontologies which is their arbitrariness of
selecting the roots: different ontology projects start with different upper-level ontologies
(Guarino 1997), which makes it difficult to integrate application ontologies from different
sources, which limits their usefulness to practical ontologies on top of them (Fonseca,
Egenhofer et al.; Frank 1997; Fonseca and Egenhofer 1999).
The article does, to keep a single focus, not cover abstract entities. These are crucial for a
GIS and can be treated using the insight from Searle (Searle 1995) applied for example to
ownership of land (Navratil 2002). Treatment of abstract entities should be covered not as
piecemeal extension, but with a stated theory of mind (Brook and Stainton 2000; Searle
2001). The comparison of the list of linguistic primes from Wierzbicka with this ontology
demonstrates that it covers what is necessary to describe the material world, but excludes all
aspects of communication and thinking, including abstractions, emotions etc. This is left for
future work.
The structure of the article follows basically the previously proposed ontology in 5 tiers
(Frank 2001; Frank 2001; Frank 2002; Frank to appear). It concentrates on the issues of
material objects: Section 2 discusses what is assumed to exist and what observations are
possible. Section 3 introduces space, time, and space-time regions as elementary building
blocks; the following section discusses projections, snapshots, and geographic projection as
methods to reduced dimensionality. Section 5 introduces regions of uniform values used as
abbreviated description of the world and section 6 the stable reference frames for locations
and times. Material entities are treated in section 8 as a special kind of regions of uniform
values and section 9 shows how the same methods are applied to events. The following
sections cover relations between entities: namely part_of relations between entities and the
involvement of entities in events. Section 12 introduces classification over entities and events,
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2 What exists, and what we know about it
Ontology is about what is, but there are evidently different levels of ‘existence’ assumed in
the debate. For example, Simons (Simons 2000) differentiates between a metaphysical,
fundamental level of existence and an ontological one. Some even accept that abstract
concepts like democracy and prime number exist in the same sense. The radical approach here
starts with clarification what is assumed to exist, namely the physical, material environment
in which we live. The remaining discussion follows from these assumptions; this gives us
assurance that only one and always the same set of assumptions are used.
I assume that a material world exist in space and time. This is the tier 0 of the ontology.
The physical laws of the space-time material world can be described with differential
equations; in the limited world of every-day experience, causation relations give time a
direction. Space and time are assumed as fixed – this Newtonian view is probably sufficient
for all geography and related sciences.
Assumption: A four-dimensional space-time
continuum.
Our knowledge of the world follows (only) from observations; this is tier 1 of the
ontology. Agents – for example humans but also other cognizant beings, like animals – can
observe properties at different points of the four-dimensional spatial continuum that is present
in every moment. Observations are restricted to the time ‘now’, which is moving forward
(Franck to appear). Observations are functions and result in values, which are expressed on
some continuous scale (Stevens 1946) and represent the intensity of the property around this
location at the moment observed: f (x,now) -> v. Observartions average for arbitrary small
regions; Goodchild has pointed out that every process must exhibit positive autocorrelation at
some scale, a world with negative autocorrelation at every scale would be unintelligible and
not inhabitable (Goodchild 2001).
Assumption: Observations for different properties at
time ‘now’ and arbitrary points are possible and yield
values on a continuous scale.
Bennett introduces not point-observable properties but the distribution of matter as the
fundamental aspect of reality modeled (Bennett 2001); this is appropriate to model primarily
table top objects and the model presented here subsumes in this point Bennett’s. Distribution
of matter is not appropriate to cover a geographical perspective, where space is primarily
conceptualized as 2d, with multiple properties observed at points (Goodchild 2001). Remote
sensing is an important source of geographic data and produces exactly such point-like
observations [ref?].
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3 Space-time regions
The assumption of a four-dimensional continuum in space and time implies the existence of
parts of this continuum, which are spatio-temporal, four-dimensional regions; I will use the
terminus 3d-t-regions for such regions. Regions in 3d-t space can be projected to space or
time only; this is an ordinary projection (Walters 1991). For a fixed point in time, snapshots
from a 3d-t-region are possible and give spatial regions. Geographic projection separates two
space coordinates in the plane parallel to the surface of the earth from the height and results in
geographic (2d) spatial regions or geographic space-time (2d-t) regions. All these projections
and the snapshot are topological transformation which preserve topological neighborhood and
some topological relations.
3.1
Metric and topological properties of space-time regions
The space-time continuum is metric, i.e., it is possible to measure distances between points
with the ordinary axioms of distance functions (D1- D3). For most purposes, ordinary
Euclidean distance extended to R**4 is sufficient (for a discussion of Minkoswkian spaces
see (Pigot and Hazelton 1992)). This gives definitions for neighborhoods, and induces a
topology in this space. As a result, regions can be open or closed; the boundaries separate the
interior from the exterior of a closed regions (Jordan’s curve theorem) (Alexandroff 1961) etc.
The representation of points in 3d-t space can use the ordinary vector space and we may use
for calculation coordinates from real number space; i.e. 3d-t space has the structure of R**4.
D1 – D3
Assumption: Space-time is metric.
There are (exist) regions in space-time (3d-t regions)
for which we have topology, separating interior,
boundary and exterior of regions.
For practical purposes, algebraic topology seems sufficient; we assume therefore that regions
have interior, boundary and exterior; the non-intuitive aspects of open and closedness can be
avoided. Topological relations are defined as intersections between interiors, boundaries and
exteriors of the two regions following Egenhofer and Franzosa (Egenhofer 1989) comparable
to the RCC calculus (Cui, Cohn et al. 1993) . It is preferable to use the terminology of
Egenhofer for the relations, because these stress spatial aspects and not the terminology of
RCC, which mix the spatial with the part_of aspects. Linguistic evidence indicates that
‘in/inside’ and ‘part’ are two independent primes, and suggest that both are universal, i.e., are
found in all human languages as separate units (Wierzbicka 1996).
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Egenhofer: disjoint, meet, overlap, covers/covered by,
inside/contains, equal
RCC: disconnected, part, proper part, identical,
overlaps, discrete from, partially overlaps, externally
connected, tangential proper part, non-tangential proper
part.
3.2
Projections
Projection is the operation, which reduces the dimension of a region by leaving away one
of the ‘coordinates’. Projection takes a region of n dimensions and produces a region with m
dimension, where m is strictly less than n. Projection preserves the neighborhood
(topological) structure of regions: a simple connected region projects to a simple connected
region. A projection to space is not a usual operation, but projection from 3d-t space to time is
useful: it gives the timespan in which the region exists (figure 1), some authors use the term
life (Goodchild 2001).
Figure 1: Category diagram
Figure 2: timespan and projection of a region, depicted following
Hagerstrands Time Geography (Tom bycicles from S to T)
[hagerstrand ref fehlt]
Applying projections and then constructing the product from the results gives the Minimal
Bounding Box, which is the 4d generalization of the well-known Minimal Bounding
Rectangle.
Figure 3: Minimial bounding box from projections in 2 spatial and 1
temporal dimension
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3.3
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Snapshots:
Snapshots are an alternative method to convert a 3d-t region to a region with fewer
dimensions, by fixing the value for one or more dimension and determine the region for the
remaining dimensions (figure 3). As the name indicates, snapshots are typically a projection
from 3d-t regions for a fixed time point t to a spatial 3d region. The term will be used here
usually in this restricted sense.
Figure 4: snapshot
Pigot and Hazelton (Pigot and Hazelton 1992) have described the construction of 4d
regions from 1d and 3d regions, i.e., snapshots. They represent the snapshots as cell
complexes and connect identical boundary elements from both snapshots; this results in a 4d
cell complex; under some restrictions. They have generally shown how from 3d (or 2d)
topological space and bounded regions in these spaces and 1d time line a 4d space results as a
product and that desirable topological properties transfer between the projections and the
product.
3.4
Geographical projections
Geography and related sciences and technologies consider often the surface of the planet earth
as a 2d surface (Goodchild 2001); it is therefore useful to introduce a geographical
projection, which separates the height from the other coordinates. Geographic projection
applied to 3d-t space-time regions, give 2d-space-time regions (2d-t) and height regions.
Geographic projection applied to snapshots (3d regions) gives 2d regions.
3.5
Topological Relations between regions, projections and snapshots
Projection and snapshot operations are topological mappings and preserve neighborhood.
Regions (in particular simple connected regions) map to (simple connected) regions. Do they
preserve topological relations? The answer is unfortunately, only partial.
Interior points project to interior points and boundary points of projections are boundary
points of the original, but not all boundary points project to boundary points (fig 5). For
snapshots, boundary points map to boundary points and interior points map to interior points.
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Fig 5 The boundary points of a 3d volume do not all project to
boundary points of a 2d projection
Fig 6 Snapshots map boundary to boundary and interior to interior
Topological relations as defined by Egenhofer (Egenhofer 1989) are not preserved, but some
relations are maintained: for example, if a snapshot of a region A is inside of the snapshot of
another region B, then region A is inside, covered or overlapping region B. A systematic
account how projection and snapshot transform topological relations would be very useful.
3.6
Stable Reference Frames: Locations and Times
To make sense of the world, we construct stable reference frames against which changes can
be observed, reported and discussed. Locations are fixed regions in space, which do not move
(at least not relative to some larger frame of reference) and occupy therefore peculiar spacetime regions. Similarly, fixed regions in time are used as references independent of spatial
location; their space-time regions are across all space. Bittner has in his PhD. thesis
investigated how the location of arbitrary objects can be described with respect to a fixed
frame of spatial subdivisions (Bittner 1999); the results extend naturally to temporal relations.
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Figure 6 Location
Figure 7 Time
Locations are very often named: England, USA, Gascogne. Not all the named locations
have well defined boundaries (Burrough 1996; Burrough and Frank 1996); sometimes human
actions construct exact boundaries(Smith 1995; Smith and Varzi 1997), but these should be
discussed together with socially constructed reality (Searle 1995) and are not covered here.
Fixed regions in time – here dubbed “times” in analogy to location – have conventional
names, using references to the calendar: March 15, 2003, the year 2000. Boundaries are often
not well defined as for “spring 2003”; times have seldom proper names.
Locations and times are with reference to a fixed frame – the part of the environment,
which does seemingly not change. Change of the ‘frame of reference’ may be too slow to be
noticeable – continental drift between Europe and America is for most human activities
negligible – or the frame of reference is large enough that all meaningful activities are inside.
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This applies equally to the use of the earth as a frame of reference, ignoring the earth rotation
and orbit around the sun etc., but applies also to the use of say an airplane as the local frame
of reference to describe the activities inside the plane, ignoring the planes movement in an
outer reference frame.
We use two sets of tokens L and T and functions location and time to map to the
particular 3d-t regions, which are interpreted as locations and times. These cover the concepts
of WHERE and WHEN.
Locations: Assume a set L of tokens l, which map to
spatio-temporal (3d-t) regions, which have the same
snapshot for any t.
Times: Assume a set of T of tokens t which map to
spatio-temporal (3d-t) regions, which have the same
snapshot for any t.
4 Regions of uniform values
Regions with uniform values for some properties are cognitively important; they help us to
reduce the enormous variety in the world to a smaller number of entities which we can keep
track of (Miller 1956). Regions of uniform value are important to identify material entities,
geographic units but also – when considering change in the observations – to identify events.
4.1
Uniform values for observed properties
For each point in time, a very large number of observations are possible. A TV camera
observation of a limited field of vision produces about 200,000 observations of light intensity
in 3 band about 15 times a second. Most of these observations are redundant, because most
aspects of the environment are strongly spatial autocorrelated. Observations near to a given
observation are most likely similar, both for observation spatial near or temporal near
(Goodchild 2001). Most of the world remains the same and only few things in the world are
changing, and these require our attention – both in our cognition as in a geographic
information system.
In snapshots – for example the snapshots our eyes deliver – regions of uniform values are
identified, for example the regions which have the same color, the same material properties
deduced from the visual system, observing color, specula, texture etc on the surface.
Uniformity is always with respect to some threshold; there is, for example, considerable
variation in the color of the leaves of my apple tree (picture 1), but we cognize usually the
leave-mass, not the individual leaves of a tree, similarly for a wooden surface etc.
Picture 1 apple tree
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4.2
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Uniform change between observations of properties
Consecutive observations are filtered for temporal autocorrelation – values, which remain the
same, have no novelty – and regions of uniform changes are investigated. It may be useful to
introduce the notion of a ‘difference observation’, i.e., the value resulting as the difference
of two observation close in time and refine it to the notion of ‘differential observation’ with
the usual sense of dv/dt, the rate of change of the observed value in time at the same location.
Regions with no change have for all observed properties the differential of zero, areas of
change have differential observations different to zero. The most important example for such
a ‘differential observations’ is the speed and direction of movement of points, which is
uniform for a moving, non-rotating, object. There is evidence for neural structures in our
visual system that change is necessary for observation and movement, as difference between
consecutive time points, is detected early in the processing of visual signals (Gibson 1979;
Marr 1982).
Formulae: f (x, t1) /= f (x, t2) t1 /= t2
4.3
Material Entities
Material objects are salient; SOMETHING is suggested as a linguistic prime. Our conceptual
world is populated by material objects, which will be called entities. The concept of material
entity is limited to spatially located, material objects (Frank 2003) , abstract objects are not to
be dealt with here. Examples for material objects are given in photos x, showing a rock, a cat,
and a banana. The material entities here correspond roughly to the chunks of matter, which
are maximal interior-connected regions of the region occupied by one kind of matter (Bennett
2001).
For entities, we have internal names – this cat, that fork, the banana on the table –, which
are representing the observed entities in our brains. For some important objects, we have
proper names “Punkti” (the name of the cat in photo x), Andrew Frank (the name of the
author of this paper) etc. This does not suggest that the brain uses anything like a compact
identifier – but all the observable behavior of the brain as an information-processing unit
seems to be structurally compatible with a model, in which such ‘internal names’ exist.
The general properties of material objects restrict the space-time regions they can
occupy. Different kinds of material objects have different space-time regions and the
properties of the space-time regions can be used for a classification of the material entities:
rigid bodies, liquids, gas etc. Note however, that from limited observations of a space-time
regions it is not possible to deduce with certainty that what we observe is a material object;
the object could be exchanged against another object in an interval too brief to be observed.
Tricks of magicians are possible and rely on our very strong experience to deduce from few
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observations that some region in space is one and the same material object, with many other
entailments.
From the properties assumed for material objects, follows that their space-time regions
are simple connected. Material objects remain at one location or move continuously in space,
but cannot disappear at one place and reappear at another.
For present purposes, we posit a set of tokens e.g., names of material entities, which map
to spatio-temporal regions, which we interpret as material objects (Thomas Bittner 2003
(draft)). Material entities are conceptual and correspond to 3d-t regions, which have
approximately the corresponding properties; not all 3d-t regions, which have the right
properties, are adorned with a name. The function from tokens to spatio-temporal regions is
not bijective i.e., one-to-one, and it is possible that at one and the same location, more than
one entity exist (Casati and Varzi 1999). The specific properties of material entities are
typically the integral of observable properties over the spatio-temporal region; many
properties for material entities are invariant in time, i.e., the integral over any snapshot of the
entity gives the same result.
Material entities: Assume a set M of tokens m, which
map to spatio-temporal (3d-t) regions, with properties
X
Physical entities are often constructed from areas of the same solid material and their
boundaries become apparent by moving. Material type is a classification of a number of
observable properties e.g., color, specula, weight; and material objects have a property
‘material’, but we do not claim, that the material is ‘part-of’ the object. Bennett introduces
matter and its distribution as fundamental and constructs regions, which describe the current
distribution of matter (Bennett 2001). Such regions of material are subsumed in this model as
a particular kind of regions with uniform properties.
4.4
Physical Events
Events are changing some of the observable properties of the space continuum over time. A
property observed at a location x at time t1 and t2 differ. Events result in space-time regions
of differential observations with some specific properties. The uniform movement of a rigid
body material entity results in space-time region with a uniform vector of movement; other
properties may change non-uniformly. Again, a classification of events results from observing
which properties the corresponding space-time regions of differential observations have.
We posit a set of tokens which are names for events that map to spatio-temporal regions,
which we interpret as physical events. Physical events are conceptual and correspond to 3d-t
regions, which approximate the predicted properties. Not all of the 3d-t regions which have
the right properties are adorned with an event name.
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Events: Assume a set V of tokens v, which map to
spatio-temporal (3d-t) regions, with some differential
properties.
The difference between entities and events – endurants perdurants (Thomas Bittner 2003
(draft)) or continuants and occurants (Simons 2000) – is not found in the space-time region
and its properties, but in the more fundamental observation of a property respective to the
observation of a change in a property. Everyday experience tells that from a single
observation, a snapshot made photographically, we cannot identify the events, only the
objects; common experience allows often to deduce the occurring event, but it is not possible
to differentiate between a picture showing a car to say if it is in movement or not (photo), nor
from a picture of a group of persons to see if one is punching the other or they just hold such a
pose (photos).
Objects do not change unless involved in a process,
processes change observable properties.
4.5 Topological Relations between regions map to relations between
tokens
Between spatio-temporal regions, exist topological relations. It is customary to map these
relations to relations between tokens. For example, we say France and Germany are neighbors
now, meaning that the two spatial regions which are the snapshots ‘now’ from the two spatiotemporal regions which the tokens “France” and “Germany’ map to are in the relation
‘neighbor’ (Egenhofer 1989). The topological relation between two objects represented by the
tokens e1 and e2 at time t is determined as the topological relation between the snapshots at t
of the spatio-temporal regions associated with e1 and e2 (figure x).
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Figure 8
5 Mereology, Part_of relation
Wierzbicka has pointed out that the ‘part’ relation is a semantic prime and universal; it is
found in all human languages (Wierzbicka 1996); the word ‘part’ is polysemous and has 3
meanings: 1) an identifiable part, 2) a part which is separated from a whole, but was not
identified before the separation, 3) some objects of a group. Only the first meaning is the
prime concept - the other two meanings are expressed with the prime ‘some of’- and is the
meaning intended here for a strict ‘part_of’ relation. The core properties of the part relation is
a partial order, which is reflexive, antisymmetric and transitive; this is the strict subset
relation of mathematics. Additional axioms are discussed by Simons (Simons 1987).
Casati and Varzi (Casati and Varzi 1999) explore the relation between topology and
mereology; the INSIDE relation for spatial regions has very similar properties to the PART
OF relation, but it seems impossible to find a coherent and simple set of axioms covering both
[Casati and cohn 2001]. “An account …involves mereological as well as topological aspects,
and neither can be reduced to the other.” (Casati and Varzi 1999) p. 197. I suggest here to
separate the two and restrict topological relations to regions and mereological relations to
relations between material entities. This is reversing Husserl’s intent to use ‘part-of’ in the
widest sense (Husserl “Logical investigations” quoted in (Casati and Varzi 1999).
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For material objects inside can be derived from part_of, but not the reverse: if A is part
of B then A is inside B, but one must not conclude from A inside B that A is part of B: an
ring is not part of the box (figure) nor are people inside a building part of the building (photo).
Part_of requires more than just a spatial situation; the parts together must form a whole
(meaning 1 of part above).
Casati and Varzi list four justifications of wholeness:

causally unitary, i.e., operations performed on some parts have effects for the
whole;

functionally unitary, i.e., the parts contribute to an overall function;

teleologically unitary, i.e., the parts contribute to an overall goal;
unitary by dependence meaning that a part is dependent on some other parts, but there are
others (Casati and Varzi 1999); I do not believe that there are simple criteria to determine
wholeness and in consequence it seems advisable to separate part_of and inside as two
separate relations; there are, for example, complex legal rules to determine when equipment
in a building is part of the building, and is mortgaged with the building, and when it is not
[Swiss code](Black 1996).
I suggest that the part_of relation obtains only between two locations, two times, two
material entities or two events, but not mixed: an a location is not part of a times, etc., and
then implies ‘inside’. This is best-expressed as a parameterized relation: part_of is a relation
from a x a to Boolean, where a can be a token from L, T, M or V.
part_of :: a x a -> Bool
a element of {L, T, M, V}
There are no mereological relations between the space-time regions, only between specific
interpretations of these. This limits part_of relations to meaningful cases and avoids nonsense
as:
*Vienna part of spring of 2000.
*The liver is part of his walking home.
*Peter is part of Vienna.
For material entities, in general topological relations in (inside) can be interpreted as part_of,
with the exception that some material entities are interpreted as containers and for these, an
inside relation does not count as part_of: the ring is in the box, but it is not part of the box;
there is no wholeness concept for the ring and the box, the box is just the container.
5.1
Involvement of entities in events
I use the term ‘involve’ to describe the relation between an event and the entities it relates to,
since the entities involved in an event are certainly not part of the event. Many entities can be
involved in an event and they can be involved in different ways. Different types of
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involvement are possible and rely on specific relations between the space-time regions.
Processes can involve locations and times, i.e., spatial snapshots and temporal projections.
For example, assuming that the individuals are all completely determined, “Punkti
moved from my house to my garden today at 12:15”
Move (t1215, punkti, house, garden)
H = snapshot 1215 – dt, house
G = snapshot 1215 + dt, garden
P1 = snapshot 1215- dt punkti
P2 = snapshot 1215 + dt punkti
Inside H p1, inside g p2, notInside H p2, notInside G p1
House and garden are spatial locations and only the cat Punkti moves. This is the general
pattern for moving events and leads to the classification of events to processes and a
discussion of the kinds of entities that can be involved. In general, the space-time region of a
process is of little interest – the entities involved are sufficient indication of the locus of the
process. Specificly spatial processes list the involved regions as locations.
6 Classification of entities and events to kinds and processes
It is a universal concept to form classes of like things; the notion of ‘kind’ is an universal
prime (Wierzbicka 1996). For example, different types of entities result in different spacetime regions: solid bodies give space-time regions, which have congruent snapshots. Noncompressible liquids give space-time regions where the volume of the snapshot is constant
etc. The same goes for events: an event of dissipation of heat gives a space-time region, which
has the form of a cone.
Figure 9 Classificaiton of material objects
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Figure 10 Heat dissipation in space-time diagram
6.1
Classification of properties to materials
Bennett has proposed tokens for materials; I consider materials’ classification of observed
properties which occur often: a certain combination of physical properties is encountered
wherever water, or gold, etc is. It is often sufficient to have a value for one of the properties to
determine the others, based on previous experience.
6.2
Classification of entities
The invariants of space-time regions are useful to classify entities in kinds, classes. Above we
have seen that material objects can be classified in non-compressible and compressible ones,
mostly gases. The non-compressible ones are then separated into liquids and rigid bodies.
We assume a set of tokens k and a function kind, which
maps each entity to a kind (token):
kind :: entity -> kind
Assigning a kind to an entity is an ontological commitment: an entity has the same kind for all
its life. If it changes the kind, it also changes the entity identity. An ontology where material
quantities are considered, which are sometimes liquid, sometimes solid, must use ‘material
quantity’ as a kind and have an attribute ‘phase’ with the values solid, liquid, gaseous. In the
same ontology, objects, which are solid and remain solid can have kind ‘solid’ ,e.g., the tubes
in which the liquids or gases are transported.
6.3
Classification of relations and entity attributes
Relations between entities like the topological relations and attributes of entites, e.g., the
weight or volume are classified.
6.4
Classification of events to processes
Similar to the classification of entities to kinds, events can be classified to processes; different
types of movement by people using their feet slowly can be described as the process of
‘walk’.
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We assume a set of tokens p and a function process,
which maps each event to a process (token). Process ::
event -> process
An event cannot change its classification, its process; if an event changes its characteristics
sufficiently [, insofar?] that its signature changes then we also have a new event. Different
processes result in different space-time region. Figure x gives a sketch of the space-time
region occupied by a movement and a diffusion process; the difference is crucial for the
classification.
6.5
Signature as classification of involvement
Processes are described by what kind of entities are involved and the classification of entities
relates these to the processes they can be involved in. Algebra describes these relations as
‘signatures’ and uses a notation, where the process name is followed by an ordered list of the
kinds of entities involved.
Move :: Time -> Material Object -> Location -> Location
The types of involvement can be classified (causation, resistance, time, location, agent….),
suggestions by linguists are either the schemata of Lakoff (Lakoff 1987) or Universal Primes
(Wierzbicka 1996). Most fundamental verbs, as to be, to go, to do etc., can be used to identify
the basic relations of involvement which are encoded in natural language grammar, often the
case system (Langacker 1987; Langacker 1991; Langacker 1991). For example, Latin uses
case markers to indicate the time, the location at which an event occurred or the destination of
a movement, etc.
A description of an event must complete the schema, provided by the signature. For
example, above we had
Move (t1215, punkti, house, garden)
which is only well formed if t215 is a time, Punkti is a material object, and house and garden
are locations. We say that a formula is correctly typed, if for an event all the entities involved
have the appropriate types. Formulae which are not properly typed are meaningless; there is
no discussion what it means to state move (house, t1200, Punkti, garden), which would
translate to: “at the time ‘house’, noon moved from Punkti into garden”.
7 Formalizing the ontology
Following Bennett’s example (Bennett 2001) it is necessary to identify what foundational
theories with axioms are used here and what definitions are used to extend them. The
foundation is an algebra with equality. From set theory we include element of and subset
relations and restrict the sets to finite sets given by extension. [Subject verb missing] Integers
with the regular arithmetics. Topology can be dealt with the methods of algebraic,
combinatoric topology (Henle 1994) with interior, boundary, and exterior, which is sufficient
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to define the topological relations. Time is based on an order relation. Space and time are
combined using product and projections from category theory.
Unlike Bennett, we intend to combine these mathematical foundational theories in a
categorical setting (Barr and Wells 1990; Asperti and Longo 1991; Walters 1991) and use an
algebraic approach (Loeckx, Ehrich et al. 1996). The functional programming language
Haskell (Peyton Jones, Hughes et al. 1999) which separates – as Bennett desires – the
axiomatic small theory from definitional extensions and the model. The algebraic approach
does not make the proof of completeness of an axiomatization simpler, but gives good
guidelines to find the axioms necessary for completeness.
8 Correspondence with Linguistic Results
Wierzbicka has listed a small set of words, which she considers to be primes – i.e., all other
human concepts expressible in language can be expressed in these – and universal – i.e., they
occur in all human languages (Wierzbicka 1996). The onotology constructed, when
considered as a language (Bennett 2001), covers – with some stretching – all the linguistic
primitives Wierzbicka lists as necessary to describe the environment of humans (Wierzbicka
1996). Not included are all the expressions of mental states, of communication etc, but this
was not intended.
Some of the primes are included in the algebra used to describe the ontology: NOT,
THIS, THE SAME, OTHER follow from equality, ONE, TWO, from integers, ALL, SOME,
MORE are constructed as second order functions.
The ontology proper covers entities: SOMETHNG, events and processes: DO, HAPPEN,
time: WHEN, BEFORE, AFTER, A LONG TIME, A SHORT TIME, NOW, space: WHERE,
FAR/NEAR, SIDE, INSIDE, HERE, (and for geographic space: UNDER, ABOVE),
partononomy: PART OF and taxonomy KIND OF, movement and existence: MOVE, THERE
IS.
What is not included? The following primes are neglected: I, YOU, SOMEONE,
PEOPLE; mental predicates: THINK, KNOW, WANT, FEEL, SEE, HEAR, speech: SAY,
WORD; life: LIFE; evaluators: GOOD, BAD, imagination: IF...WOULD, CAN, MAYBE;
interclausal linkers: IF, BECAUSE, LIKE. It is very obvious that the completion of the
ontology to include abstract concepts will have to start with these ‘left-overs’.
9 Conclusion
The current discussion of spatio-temporal ontologies is very tentative and confusing. Different
authors explore different lines of thought without coming to simple conclusions; terminology
is abundant, often without definitions and no reasons for the introduction of new terminology
is given (Bennett to appear). I – and seemingly others – am confused by the attempt to
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differentiate between entities and events by the statement that events have property temporal
parts and entities have not (Simons 2000; Smith 2002 (draft)) [smith what?]. The proposal
here does not rely on such fine arguments but accepts the current view of physics as the
starting point and attempts to reconcile this point with cognition, in particular linguistics
(Egenhofer and Mark 1995).
What I seem to assume as fundamental is the existence of a physical world in which the
property values are connected, as expressed in physical differential equations. Our experience
interacting with the world results in the observation of regular patterns, which permit
predictions and are useful to exploit to improve our lives. The account given here does not
require that our explanation of the world is correct and allows for errors: if we see the empty
glass of wine in the evening on the table and see it again in the morning at the same place, we
may infer that we see the very same glass and that it was not involved in a process during the
night; this may be true or not, from the given observation it cannot be deduced with certainty
– but practically, it is sufficient to act on prima facie evidence and put the glass in the dish
washer!
This proposal is applying Occam’s razor to some of the proposals debated and shown to
be defective to deal with spatio-temporal entities (Casati and Varzi 1994; Casati and Varzi
1999); it introduces separation where they are necessary. For example: material entities

occupy spatio-temporal regions (they are not these),

consist of material, the material is not part of them,

are in various ways involved in events (as agent, as object, as location), they are
not part of these,

relate topologically and mereologically to other entities.
This reduces many conundrums in current discussions, e.g. an island is inside the lake,
but it is not part of the lake (Casati and Varzi 1999) [Eschenbach.. where?] (Donnelly 2003).
This proposal balances between the requirements of an ontology of small manipulable
material entities as they populate tables top space (Montello 1993) but reconciles it with the
requirements of geography, where the same space is divided in many different, overlapping
ways (Goodchild 2001). Bennett has pointed out “The vast majority of sort terms used in
natural languages refer to either human artifacts, biological organism and organs, and
geographic features”. I hope that I have achieved the necessary balance.
Acknowledgements
Revigis; FWF project;
References
Alexandroff, P. (1961). Elementary Concepts of Topology. New York, USA, Dover Publications.
20
A. Frank: 3839 Linguistically justified ontology
06-Feb-16
Asperti, A. and G. Longo (1991). Categories, Types and Structures - An Introduction to Category Theory for the
Working Computer Scientist. Cambridge, Mass., The MIT Press.
Barr, M. and C. Wells (1990). Category Theory for Computing Science. New York, Prentice Hall.
Bennett, B. (2001). Sapce, Time, Matter and Things. FOIS'01.
Bennett, B. (to appear). The Role of Definitions in Construction and Analysis of Formal Ontologies. School of
Computing. Leeds, University of Leeds: pp.8.
Bittner, T. (1999). Rough Location. Institute of Geoinformation. Vienna, Austria, Technical University: 196.
Black, H. C. (1996). Black's Law Dictionary, West Publishing.
Brook, A. and R. J. Stainton (2000). Knowledge and Mind. Cambridge, Mass., The MIT Press.
Bruegger, B. P. (1994). Spatial theory for the integration of resolution-limited data. Orono, Maine, University of
Maine.
Burrough, P. A. (1996). Natural Objects with Indeterminate Boundaries. Geographic Objects with Indeterminate
Boundaries. P. A. Burrough and A. U. Frank. London, Taylor and Francis: 3-28.
Burrough, P. A. and A. U. Frank, Eds. (1996). Geographic Objects with Indeterminate Boundaries. GISDATA
Series. London, Taylor & Francis.
Casati, R. and Varzi, Eds. (1996). Events. International Research Library of Philosophy, Dartmouth Publ. Co.
Casati, R. and A. C. Varzi (1994). Holes and Other Superficialities. Cambridge, Mass., MIT Press.
Casati, R. and A. C. Varzi (1999). Parts and Places. Cambridge, Mass., The MIT Press.
Cui, Z., A. G. Cohn, et al. (1993). Qualitative and Topological Relationships in Spatial Databases. Advances in
Spatial Databases (Third Symposium on Large Spatial Databases, SSD '93, Singapore). D. Abel and B.
C. Ooi. Berlin, Springer-Verlag. 692: 296-315.
Donnelly, M. (2003). Layered Mereotopology. Leipzig: pp.6.
Egenhofer, M. J. (1989). Spatial Query Languages, University of Maine.
Egenhofer, M. J. and D. M. Mark (1995). Naive Geography. Spatial Information Theory - A Theoretical Basis for
GIS. A. U. Frank and W. Kuhn. Berlin, Springer-Verlag. 988: 1-15.
Fellbaum, C., Ed. (1998). WordNet: An Electronic Lexical Database. Language, Speech, and Communication.
Cambridge, Mass., The MIT Press.
Fonseca, F., M. Egenhofer, et al. Semantic Granularity in Ontology-Driven Geographic Information Systems.
Fonseca, F. T. and M. J. Egenhofer (1999). Ontology-driven geographic information systems. 7th ACM
Symposium on Advances in Geographic Information Systems, Kansas City, MO.
Franck, G. (to appear). The Hard Problem of Time.
Frank, A. U. (1997). Spatial Ontology: A Geographical Information Point of View. Spatial and Temporal
Reasoning. O. Stock. Dordrecht, Kluwer: 135-153.
Frank, A. U. (1998). GIS for Politics. GIS Planet'98, Lisbon, Portugal (September 9-11, 1998), IMERSIV.
Frank, A. U. (1998). Metamodels for Data Quality Description. Data quality in Geographic Information - From
Error to Uncertainty. R. Jeansoulin and M. Goodchild. Paris, Editions Hermès: 15-29.
Frank, A. U. (2001). The rationality of epistemology and the rationality of ontology. Rationality and Irrrationality,
Proceedings of the 23rd International Ludwig Wittgenstein Symposium, Kirchberg am Wechsel, August
2000. B. Smith and B. Brogaard. Vienna, Hölder-Pichler-Tempsky. 29.
Frank, A. U. (2001). "Tiers of ontology and consistency constraints in geographic information systems."
International Journal of Geographical Information Science 75(5 (Special Issue on Ontology of
Geographic Information)): 667-678.
Frank, A. U. (2002). An Ontology in Connected Tiers.
Frank, A. u. (2003). Put verbs into the ontology! A formal ontology with processes. Institute for Geoinformation.
Vienna, Technical University Vienna: pp.18.
Frank, A. U. (to appear). Ontology for spatio-temporal databases. Spatiotemporal Databases: The Chorochronos
Approach. T. Sellis. Berlin, Springer-Verlag.
Frank, A. U., J. Raper, et al., Eds. (2001). Life and Motion of Socio-Economic Units. GISDATA Series. London,
Taylor & Francis.
Freksa, C. (1991). Qualitative Spatial Reasoning. Cognitive and Linguistic Aspects of Geographic Space. D. M.
Mark and A. U. Frank. Dordrecht, The Netherlands, Kluwer Academic Press: 361-372.
Galton, A. (2000). Qualitative Spatial Change. Oxford, Oxford University Press.
Gibson, J. (1979). The Ecological Approach to Visual Perception. Hillsdale, NJ, Erlbaum.
Goodchild, M. (2001). A Geographer looks at Spatial Information Theory. COSIT'01.
Goodchild, M. and R. Jeansoulin, Eds. (1998). Data Quality in Geographic Information - From Error to
Uncertainty. Paris, Hermes.
Goodchild, M. F. (1989). Modelling error in objects and fields. Accuracy of Spatial Databases. M. F. Goodchild
and S. Gopal. London, Taylor & Francis: 107-113.
Guarino, N. (1997). Some organizing principles for a unified top-level ontology. AAAI Spring Symposium on
Ontological Engineering.
Hayes, P. J. (1985). The Second Naive Physics Manifesto. Formal Theories of the Commonsense World. J. R.
Hobbs and R. C. Moore. Norwood, N.J., Ablex Publishing Corp.: 1-36.
Henle, M. (1994). A Combinatorial Introduction to Topology. New York, Dover Publications.
Kuhn, W. (2000). How to produce ontologies: an approach grounded in texts. Geographical Domain and
Geographical Information Systems (EuroConference on Ontology and Epistemology for Spatial Data
Standards, La-Londe-les-Maures, France). S. Winter. Vienna, Institute for Geoinformation. 19: 63-71.
21
A. Frank: 3839 Linguistically justified ontology
06-Feb-16
Lakoff, G. (1987). Women, Fire, and Dangerous Things: What Categories Reveal About the Mind. Chicago, IL,
University of Chicago Press.
Langacker, R. W. (1987). Foundations of Cognitive Grammar. Stanford, CA., Stanford University Press.
Langacker, R. W. (1991). Foundations of Cognitive Grammar - Descriptive Applications. Stanford, CA, Stanford
University Press.
Langacker, R. W. (1991). Foundations of Cognitive Grammar - Theoretical Prerequisites. Stanford, CA, Stanford
University Press.
Loeckx, J., H.-D. Ehrich, et al. (1996). Specification of Abstract Data Types. Chichester, UK and Stuttgart, John
Wiley and B.G. Teubner.
Marr, D. (1982). Vision. New York, NY, W.H. Freeman.
Miller, G. A. (1956). "The magic number seven, plus or minus two; some limits on our capacity for processing
information." Psychological Review 63: 81-97.
Montello, D. R. (1993). Scale and Multiple Psychologies of Space. Spatial Information Theory: A Theoretical
Basis for GIS. A. U. Frank and I. Campari. Heidelberg-Berlin, Springer Verlag. 716: 312-321.
Navratil, G. (2002). Formalisierung von Gesetzen - Am Beispiel des Österreichischen Allgemeinen
Grundbuchsgesetzes. Vienna, Institute for Geoinformation.
Peuquet, D. (2002). Representations of Time and Space. New York, Guilford.
Peyton Jones, S., J. Hughes, et al. (1999). Haskell 98: A Non-strict, Purely Functional Language.
Pigot, S. and B. Hazelton (1992). The Fundamentals of a Topological Model for A Four-Dimensional GIS.
Proceedings of the 5th International Symposium on Spatial Data Handling, Charleston, IGU Commission
of GIS.
Rigaux, P. and M. Scholl (1995). Multi-Scale Partitions: Application to Spatial and Statistical Databases. Fourth
International Symposium on Large Spatial Databases-SSD95, Portland, ME, Springer Verlag,
Heidelberg.
Searle, J. R. (1995). The Construction of Social Reality. New York, The Free Press.
Searle, J. R. (2001). Rationality in action, MIT Press.
Simons, P. (1987). Parts - A Study in Ontology. Oxford, Clarendon Press.
Simons, P. (2000). "Continuants and Occurrents." The Aristotalian Society Supplementary Vol. LXXIV: pp. 12.
Simons, P. (2000). "How to Exist at a Time When You Have No Temporal Parts." The Monist 83: pp. 419-436.
Simons, P. (draft to appear). Events. Leeds: pp.37.
Smith, B. (1995). On drawing lines on a map. Spatial Information Theory - A Theoretical Basis for GIS (Int.
Conference COSIT'95). A. U. Frank and W. Kuhn. Berlin Heidelberg, Springer-Verlag. 988: 475-484.
Smith, B. (2001). Objects and their Environments: from Aristotle to Ecological Ontology. Life and Motion of
Socio-Economic Units, London, Taylor & Francis.
Smith, B. (2002 (draft)). Aristoteles 2002. Kann man heute noch etwas anfangen mit Aristoteles? H. F. Thomas
Buchheim, Richard A.H. King. Hamburg, Felix Meiner Verlag: pp. 3-38.
Smith, B. and A. C. Varzi (1997). Fiat and Bona Fide Boundaries: Towards an Ontology of Spatially Extended
Objects. Spatial Information Theory - A Theoretical Basis for GIS (International Conference COSIT'97.
S. C. Hirtle and A. U. Frank. Berlin, Springer-Verlag. 1329: 103-119.
Stevens, A. and P. Coupe (1978). "Distortions in judged spatial relations." Cognitive Psychology 10: 422 - 437.
Stevens, S. S. (1946). "On the theory of scales of measurement." Science 103(2684): 677-680.
Thomas Bittner, B. S. (2003 (draft)). Formal ontologies for space and time. IFOMIS, Department of Philosophy.
Leipzig, Buffalo, University of Leipzig, University at Buffalo and NCGIA: pp.17.
Timpf, S. (1992). Conceptual Modeling of Highway Navigation. Department of Surveying Engineering. Orono,
Maine (U.S.A), University of Maine: 75.
Timpf, S. (1998). Hierarchical Structures in Map Series. Faculty of Science and Technology. Vienna, Technical
University Vienna: 124.
Walters, R. F. C. (1991). Categories and computer science. Cambridge, UK, Carslaw Publications.
Wierzbicka, A. (1996). Semantics - Primes and Universals. Oxford, Oxford University Press.
22