Processes as
Continuants
Antony Galton
School of Engineering, Computer Science and
Mathematics,
University of Exeter, UK
Processes and Events
• Mourelatos: Process and Event are disjoint
subcategories of Occurrence.
• Sowa: Event is a subcategory of Process.
• Moens and Steedman: Process is a
subcategory of Event.
PART ONE
Continuants and Occurrents:
A fundamental ontological
distinction
Continuants I
• Continuants endure through time; hence,
they are also called endurants.
• A continuant exists as a whole at each
moment of its existence.
• A continuant can undergo change: i.e., its
properties may be different at different
times, although its identity remains fixed.
• It may have spatial, but not temporal parts.
Occurrents
• Occurrents occur in time; they are also
called perdurants.
• An occurrent is not wholly present at any
time less than its entire duration.
• Rather, it has temporal parts, which may
have different properties.
• But the occurrent itself does not undergo
change.
Examples
CONTINUANTS
OCCURRENTS
•
•
•
•
•
•
•
•
•
•
A person
An aircraft
An orchestra
A volcano
A heart
A life
A flight
A performance
An eruption
A heartbeat
Time-dependence
• The properties of a continuant can vary with
time; hence continuants are time-dependent
entities.
• The properties of an occurrent are possessed
timelessly; hence occurrents are timeindependent entities.
Example: An Occurrent
• The first solo flight across the Atlantic.
• This is an occurrent (specifically: an event)
• It occurred over a 33-hour period in May
1927.
• Its temporal parts include the beginning (in
New York) and the end (in Paris).
• These properties are timeless: they cannot
change.
Example: A Continuant
• The Spirit of St Louis
• This is the aircraft in which Charles
Lindbergh completed the first solo flight
across the Atlantic.
• At each moment of the flight, the aircraft
was present – not just a part of it!
• At different moments, it had different
properties – e.g., its position, speed,
altitude. So, it underwent change.
But do events really not change?
• ‘My life is becoming
harder’
• ‘Their lives moved
apart’
• ‘The battle grew
fiercer’
• ‘The protest became
violent’
In these cases what
changes is not an
event but a process
associated with an
event.
This solves nothing if
processes are, like
events, occurrents …
PART TWO
Processes
What is a process?
• Examples of processes, as I am using the
term, include:
– Human activities such as walking, swimming,
eating, drinking, driving a car, playing the
piano, pushing a barrow, peeling potatoes,
writing.
– Natural phenomena such as rainfall, ebb and
flow of the tide, photosynthesis, circulation of
the blood, flowing of a river, erosion and
deposition, rotation of the earth.
Some non-processes
• I do not include such things as the ‘process’
of making a pot of tea, making a cake,
preparing the index to a book, refuelling a
motor-car, or checking in at the airport.
• These are closed routines consisting of a
definite sequence of actions or activities
leading to a specific end result.
• I shall call them structured actions.
Key properties of processes
• They are dissective: a period of time
occupied by a process can be divided into
subperiods each of which is occupied by
that process.
• They are open-ended: a process does not
have an intrinsic termination beyond which
it cannot continue.
Dissectivity
• The flow of the Thames through London: it
flowed throughout the twentieth century; it
flowed throughout 1988; it flowed
throughout March 1988; …
• If I walk for an hour, then the walking
process goes on during each subinterval of
that hour [subject to a granularity caveat
which is often misunderstood …]
Events are not dissective
• The conference takes place over the period
15th-17th June.
• So it doesn’t take place on the 15th June, or
during the hour 2pm-3pm on 15th June.
• Parts of the conference took place on those
intervals, but not the whole conference.
• (Compare: ‘part/whole of the flow of the
river’ – these are spatial, not temporal!)
Open-endedness
Processes are open-ended:
• If I am walking, I can continue walking.
• If the river is flowing it can continue
flowing.
But events are not:
• If I run a mile, I cannot continue running it
(though I can start another one).
Can processes change?
• The flow of the river increases when the
snow melts.
• The heartbeat speeds up during exercise.
• The work became more diligent when the
supervisor arrived.
• The music became faster/louder/more
dissonant
• The protest became violent.
Can processes change?
• The grazing of the savannah became more
intense.
• The growth of the tree speeds up during
summer.
• The resurfacing work progressed from north
to south along the road.
• As the day continued, his driving became
more erratic.
Processes can change!
• In all these cases, we seem to have an
example of a process undergoing change.
• Occurrents, as described earlier, cannot
undergo change.
• So if we take the examples at face value,
processes are not occurrents.
• Which contradicts the universal assertion
that processes are occurrents.
PART THREE
EXP and HIST
A fresh start
• I propose to set aside the distinction
between continuants and occurrents for
now.
• In its place, I want to put a distinction
which more accurately reflects the essential
distinctions to be drawn.
• This is not a new distinction, but I shall use
it in a new way.
John Lyons (Semantics, 1977)
“The term … ‘historical’ is intended to suggest the
narration of events ordered in terms of successivity and
presented dispassionately with the minimum of subjective
involvement; and this mode of description clearly relates to
the static, non-deictic, objective conception of time. The
term ‘experiential’, on the other hand, is suggestive of the
kind of description that might be given by someone who is
personally involved in what he is describing; and this
mode is no less clearly related to the dynamic, deictic,
subjective conception of time.”
The Experiential Perspective (EXP)
• EXP relates to the world as experienced,
when it is present.
• The EXP world is constantly changing – it
is a world in flux.
• Time-dependent properties belong in EXP.
• Hence both objects and processes, which
have time-dependent properties, are EXP
entities.
The Historical Perspective (HIST)
• HIST relates to the faits accomplis, the
historical record.
• It contains synoptic overviews that span a
succession of experiential ‘snapshots’.
• HIST entities are (mostly) extended in time.
• They do not themselves change, but are
static configurations of changes that have
occurred.
The passage of time: two metaphors
1. The advancing ice front: the future is a
fluid ‘sea’ of possibility, which
incrementally freezes into a fixed and
determinate past.
2. The moving spotlight: past and future are
laid out like a map, successive portions of
which are sequentially illuminated by a
moving spotlight (the ‘present’)
Do not take these metaphors too
seriously!
• They are mutually inconsistent, so they
cannot both be right.
• And probably, they are individually
incoherent, so neither of them can be right.
• But even so, they appeal to the imagination,
and can therefore be useful for illustrative
purposes.
Change
• On either metaphor, EXP is where all the
change is.
• The HIST world only changes insofar as its
relationship to the EXP world changes.
• Changes in HIST entities are purely
relational (e.g., the most recent disaster
becomes the second most recent disaster) –
this is not ‘real’ change.
EXP is a dynamic snapshot
• The EXP world contains things which can
exist at one time.
• Hence it is like a ‘snapshot’.
• But it is a dynamic snapshot: it is a world of
ongoing processes as well as objects.
• Processes, on this view, are like states of
change, which can themselves change.
The physical view
• This accords well with the view of the
world according to classical physics.
• At any time an object is in possession of
momentum and kinetic energy, quantities
which can be conserved, dissipated,
transferred, etc.
• In physics, states of motion are every bit as
real as static states such as position.
Zeno’s Arrow
• Suppose we do not admit processes in EXP.
• So the world at one time is a static
configuration of objects.
• Somehow, the events in HIST must emerge
from a sequence of static configurations.
• How can it do this? I believe that this is the
essential point of Zeno’s Arrow Paradox.
Zeno’s Arrow II
• Zeno: the motion of an arrow consists of a
sequence of states in each of which the arrow has
a single position and therefore does not move. So
motion is paradoxical!
• Why is the arrow in a different position now from
a split second ago? Because it is moving!
• But if ‘moving’ is defined as ‘being in a different
position now from immediately before’, this
explains nothing.
• The arrow’s motion must exist in its own right as
an ingredient of the world at one time: a process.
Processes in EXP
• That is why EXP must contain processes as
well as objects.
• Processes are the dynamo which drives the
advancing ice front, converting fluid
possibilities into solid actualities.
• If there were no processes in EXP then
HIST would be devoid of events!
SNAP/SPAN
Barry Smith’s
SNAP/SPAN
framework
encapsulates the
traditional view of
processes as
occurrents. My view
contrasts with this.
SNAP
Objects
EXP
Objects
Processes
SPAN
Events
Processes
HIST
Events
PART FOUR
Describing Processes
and Events
Types and Tokens
• The type/token distinction applies to both
events and processes.
• ‘A lecture’ is an event type; this lecture you
are attending is an event token.
• ‘Lecturing’ is a process type; my lecturing
right now is a process token.
• Types are abstract, tokens are concrete.
Deriving types from types
• We can often define event types in terms of
other event types or in terms of process
types.
• And we can define process types in terms of
other process types or in terms of event
types.
• We’ll look at a few ways in which these
things can be done.
Processes from Processes
• Processes may be described in terms of
more general processes by specialisation.
E.g., walking may be qualified by any of
–
–
–
–
–
agent (e.g., John walking)
manner (e.g., walking with a limp)
direction (e.g., walking north)
location (e.g., walking in the garden)
time (e.g., walking in the evening)
Events from Processes I
• Events can be derived from processes by adding a
delimiting qualification, e.g.,
–
–
–
–
–
End-points (walk from Buda to Pest)
Spatial extent (walk a mile)
Temporal extent (walk for an hour)
Configuration (walk around the house)
Boundedness (have a walk)
These are events, not processes, because they are
neither open-ended nor dissective.
Events from Processes II
• An important class of event consists of
those events which are described as the
starting or stopping of some process:
– Start to walk
– Stop walking
• These are, at most granularity levels,
instantaneous events.
Processes from Events I
• A process may be described as consisting of some
event in progress, e.g.,
– ‘I am [in the process of] walking a mile’
– ‘I am [in the process of] walking from Buda to
Pest’
– ‘I am [in the process of] walking around the
house’
• These are processes defined in terms of some
event that they do, or can, form part of.
Processes from Events II
• A process may be described as the open-ended
repetition of some event type:
– Walking in circles (repetition of walk in a
circle)
– Reading books (repetition of read a book)
– Swatting flies (repetition of swat a fly)
• The process we describe as the heartbeat is the
open-ended repetition of the event-type we
describe as a heartbeat.
PART FIVE
Formalising EXP and
HIST
Ontology
• Objects: O
• Object types: O
• Process instances:
P
• Process types: P
• Event tokens: E
• Event types: E
• Times: T
• Spatial locations: S
• Values: V
Tok = O U P U E
Typ = O U P U E
EXP and HIST
• EXP contains the
time-dependent
components of the
ontology, i.e., O
and P.
• HIST contains the
time-independent
components, i.e., E.
Process Types and Tokens
•
•
•
•
•
•
walking e P
walking(john) e P.
Isa(walking(john),walking)
walking51 e P
InstOf(walking51,walking(john))
InstOf(walking51,walking)
Event Types and Tokens
•
•
•
•
•
•
walk e E
walk(john) e E
Isa(walk(john),walk)
walk85 e E
InstOf(walk85,walk)
InstOf(walk85, walk(john))
How are Processes related to
Events?
• If walking51 exists from t1 to t2, then there
is an event of type walk, say walk85, with
the property that time(walk85)=[t1,t2].
• walk may be defined as that event-type
whose instances are delimited instantiations
of the process walking. We write this as
walk = PO(walking).
Time-independent Properties
• Time-independent properties are expressed
using functions from Tok to V.
• These apply to both EXP and HIST entities.
• Examples:
– date-of-birth(john) = 23/02/1984
– agent(walking51) = john
– time(walk85) = [t1,t2]
Time-dependent Properties
• Time-dependent properties (fluents) are
expressed using functions from (OUP) X T
to V.
• These apply only to EXP entities.
• Examples:
– height(john,t) = 1.87m
– speed(walking46,t) = 5 km/hr
PART SIX
Illustrative studies
Illustration 1: Motion of Point
Particles
• Particles o1,o2,… of type O.
• At times t1,t2,… each particle relays its
position to a central computer.
• The position of oi at tj is pos(oi,tj).
• The computer makes inferences about
motion-processes and movement-events.
Motion processes
• So long as pos(o,ti)=pos(o,ti-1), the
computer regards o as being at rest.
• As soon as it finds
pos(o,ti) =/= pos(o,ti-1) = pos(o, ti-2)
it creates a motion process m of type
moving(o).
Rate of change
• The velocity of a particle o is the rate of
change of its position pos(o,t) with t.
• This is a time-dependent attribute rate(m,t)
of the process m (of type moving(o)),
computed using
pos(o,ti)-pos(o,ti-1)
rate(m,ti) = -----------------------ti-ti-1
Second-order rates of change
• Likewise, the computer can monitor the values of
rate(m,t), and if necessary create a second-order
process
changing(rate(m,t))
whose rate corresponds to the acceleration of the
particle o in the usual way.
• The point here is that the standard mathematical
treatment of motion and acceleration fits into the
view of processes proposed here.
Illustration 2: Monitoring process
profiles
• Raw data, delivered by sensors, take the
form of quantitative fluents.
(Examples: wind speed and direction, wave
height, air temperature, …)
• Ongoing change in a fluent constitutes a
process.
• Salient demarcated episodes in the
evolution of a process are events.
An ‘Increasing’ Process
• Given fluent f, a process of type
increasing(f) exists at time ti if f(ti)>f(ti-1).
• We create a process p of this type when we
detect that f(ti)>f(ti-1)<f(ti-2).
• We destroy p when we detect that
f(tk+1)<f(tk)>f(tk-1).
Properties of the process p
• rate(p,ti) = [f(ti)-f(ti-1)]/(ti-ti-1)
• age(p,ti) =
if p exists at ti-1, age(p,ti-1)+ti-ti-1
otherwise ti-ti-1.
An ‘Increase’ Event
• If process p of type increasing(f) is destroyed at
tk, then we can record an event e of type
increase(f)=PO(increasing(f)), with properties
–
–
–
–
end(e) = tk
duration(e) = age(p,tk)
beginning(e)= end(e)-duration(e)
totalIncrease(e,f) = f(end(e)) - f(beginning(e))
• ‘Decrease’ events are handled similarly.
Peaks and Troughs
• peak(f) is an event type which occurs when f
reaches a transitory local maximum, i.e. at ti such
that an increasing(f) process p exists at ti and a
decreasing(f) process q at ti+1.
• Event e of type peak(f) has attributes
–
–
–
–
time(e) = ti
processBefore(e) = p
processAfter(e) =q
height(e) = f(ti) – f(ti – age(p,ti))
• trough(f) is defined similarly.
Illustration 3: Traffic Flow in a Road
Network
• We can regard traffic flow as a process f
which exists at all points on the network at
every time.
• Its attributes include
– speed(f,s,t)
– density(f,s,t)
– rate(f,s,t)
[unit: distance/time]
[unit: vehicles/distance]
[unit: vehicles/time]
• rate(f,s,t) = speed(f,s,t).density(f,s,t)
Two views of the flow
• Flow past a point (flow(s)):
– speed(flow(s),t) = speed(f,s,t)
– density(flow(s),t) = density(f,s,t)
– rate(flow(s),t) = rate(f,s,t)
• Flow experienced by a vehicle (flow(v)):
– speed(flow(v),t) = speed(f,pos(v,t),t)
– density(flow(v),t) = density(f,pos(v,t),t)
– rate(flow(v),t) = rate(f,pos(v,t),t)
Traffic Events
• The pattern of evolution of the traffic flow process
gives rise to traffic events such as traffic jams.
• Conversely, events such as accidents will affect
the traffic flow.
• The details require quantitative analysis, but to
translate them into a qualitative understanding
requires an appropriate representational ontology.
PART SEVEN
Conclusions
Processes as continuants
• Processes are like objects, and unlike
events, in possessing time-dependent
properties.
• Therefore, they should be considered to be
continuants rather than occurrents.
• Or at least, to partake of some of the
properties of continuants.
• This has implications for how we represent
processes formally.
• And in particular it requires us to keep
processes separate from events.
• Even though processes and events are
intimately related.