Processes as Continuants

Antony GaltonSchool 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 ONEContinuants 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

• A person• An aircraft• An orchestra• A volcano• A heart

OCCURRENTS

• 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 time-independent 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 SPAN

Objects Events Processes

EXP HISTObjects Processes

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: VTok = O U P U ETyp = 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 P• walking(john) P.• Isa(walking(john),walking)• walking51 P• InstOf(walking51,walking(john))• InstOf(walking51,walking)

Event Types and Tokens

• walk E • walk(john) E • Isa(walk(john),walk)• walk85 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) [unit: distance/time]– density(f,s,t) [unit: vehicles/distance]– rate(f,s,t) [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.