Post on 20-Dec-2015
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The Cornucopia of Formal-Ontological Relations
Barry Smith and Pierre Grenon
Institute for Formal Ontology and Medical Information Science
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Realist Perspectivalism
There is a multiplicity of ontological perspectives on reality, all equally veridical i.e. transparent to reality
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Anatomy vs. Pathology
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The Problem
The tumor developed in John’s lung over 25 years
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The Problem
____ developed in _____ over 25 years
process
state
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The Problem
The tumor developed in the lung over 25 years
substances
things
objects
continuants
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The Problem
The tumor developed in John’s lung over 25 years
PARTHOOD NOT DETERMINATE
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The Problem
The tumor developed in the lung over 25 years
substances
GLUING THESE TOGETHER YIELDS ONTOLOGICAL MONSTERS
processes
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Substances and processes exist in time in different ways
substance
t i m
e
process
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SNAP vs SPAN
Endurants vs perdurants
Continuants vs occurrents
In preparing an inventory of reality
we keep track of these two different kinds of entities in two different ways
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Need for different perspectives
Not one ontology, but a multiplicity of complementary ontologies
Cf. particle vs. wave ontologies in quantum mechanics
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Three kinds of SNAP entities
1. Substances
2. Dependents (SPQR… entities)
3. Spatial regions, contexts, niches, environments
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SPQR… entitiesStates, powers, qualities, roles …
functions, dispositions, plans, shapes, status, habitus, liabilities …
= dependent SNAP entities
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SPQR… entities:
one-place:
your temperature, color, heightmy knowledge of French
the whiteness of this cheese the warmth of this stone
the fragility of this glass
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relational SPQR… entities
John Mary
love
stand in relations of one-sided dependence to a plurality of substances simultaneously
specific dependence
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Generic dependence of relational SPQR… entities
legal systems
languages (as systems of competences)
religions (as systems of beliefs)
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Three kinds of SNAP entities
1. Substances
2. Dependents (SPQR… entities)
3. Spatial regions, contexts, niches, environments
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Three kinds of SNAP entities
1. Substances
2. Dependents (SPQR… entities)
3. Spatial regions, contexts, niches, environments
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Spatial regions, contexts, niches, environments
Organism species evolve into environments
Domesticated spatial regions: rooms, nostrils, your alimentary tract
Fiat spatial regions: JFK designated airspace
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SNAP: Entities existing in toto at a time
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Substances
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SPQR …
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Spatial regions
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The SPAN Ontology
t i m e
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here time exists as part of the domain of the ontology
The SPAN ontology
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mereology works without restriction everywhere here
t i m e
clinical trial
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Processes, too, are dependent on substances
One-place vs. relational processes
One-place processes:
your getting warmer
your getting hungrier
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Examples of relational processes
kissings, thumpings, conversations,
dancings,
join their carriers together into collectives of greater or lesser duration
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SPAN: Entities extended in time
SPANEntity extended in time
Portion of Spacetime
Fiat part of process *First phase of a clinical trial
Spacetime worm of 3 + Tdimensions
occupied by life of organism
Temporal interval *projection of organism’s life
onto temporal dimension
Aggregate of processes *Clinical trial
Process[±Relational]
Circulation of blood,secretion of hormones,course of disease, life
Processual Entity[Exists in space and time, unfolds
in time phase by phase]
Temporal boundary ofprocess *
onset of disease, death
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Two kinds of SPAN entities
1. Processes (including events: process-boundaries)
2. Spatio-temporal regions
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Processes
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Spatio-temporal regions
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4-dimensional environments
Lobsters have evolved into environments marked by cyclical patterns of temperature change
Tudor EnglandThe Afghan winterThe window of opportunity for an invasion of Iraq
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How do you know whether an entity is SNAP or SPAN?
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problem cases
forest fire
anthrax epidemic
hurricane Maria
traffic jam
ocean wave
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forest fire:
a process
a pack of monkeys jumping from tree to tree and eating up the trees as they go
the Olympic flame:
a process or a thing?
(anthrax spores are little monkeys)
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Formal-ontological concepts
come for free
do not add anything to being
are domain-independent
are expressed linguistically by closed-class items …
HOW TO GENERATE THEM?
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The idea (first rough version)
Formal relations are those relations which are not captured by either SNAP or SPAN because they traverse the SNAP-SPAN dividethey glue SNAP and SPAN entities together
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This generates a first list of formal relations,
e.g. dependence,
but we find some of these relations also within SNAP or within SNAP
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The idea (modified version)
Formal relations are the relations that hold SNAP and SPAN entities/ontologies together
and analogous relations
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Example:Individuation, segmentation
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Substances
tokens separated by bona fide boundaries
form natural kinds, types
(universals, species + genera)
separated by bona fide boundaries
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Processes
Process tokens merge into one another
Process kinds merge into one another
… few clean joints either between tokens or between types
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boundaries are mostly fiat
t i m e
everything is flux
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SNAP entities
provide the principles of individuation/segmentation for SPAN
entities
No change without some THING or QUALITY which changes
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Example:Ontological Dependence
(SPAN, SNAP): process substance
The erosion of the rock necessitates the existence of the rock
(SNAP, SNAP): SPQR substance
The token redness of the sand necessitates the existence of the sand
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Generating a typology
Two main types of formal relations:
meta-ontological: obtain between entities of different ontologies
intra-ontological: obtain between entities of the same ontology (intra-SNAP, intra-SPAN)
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Three parameters:
- the arity of the relation
- the types of the relata, expressed as an ordered list, called the signature of the relation
- the formal nature of the relation
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Principal Signatures
In the binary case:
SNAP-SNAP - (SNAPi, SNAPi), i = i
- (SNAPi, SNAPi), i < j, i > j
SPAN-SPAN
SNAP-SPANSPAN-SNAP
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Transtemporal relations
Examples:
Genidentity
(transtemporal generalization of identity/part-whole)
Successive causality
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Genidentity
Also SPAN-SPAN? Is there a form of genidentity among processes?
The such-has-to-have-come-forth-from relation.
Signature: SNAPi-SNAPj
Cut a chunk of matter in two, the sum of the remaining pieces is genidentical to the chunk before cutting
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Successive Causality
SNAP-SPAN: Agent causationA substance produces causally a process
SPAN-SPAN: Process causationOne process causes another process
SPAN-SNAP: Causal repercussionA process results in the modification of a substance (always mediated by process causation)
SNAP-SNAP: Causal originOne substance is the causal origin of another (mediated by other types of causal relations)
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Successive Causality
SNAP-SPAN: Agent causation
SPAN-SPAN: Process causation
SPAN-SNAP: Causal repercussion
SNAP-SNAP: Causal origin
do not apply on all levels of granularity(holds of examples given below also)
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Our main target: Temporally extended relations
Simultaneous Causality Participation
(holds between a substance and a process such as an action or a life or history)
Realization(holds between SPQR… entities and their SPAN expressions)
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Simultaneous causality
SPAN-SPAN
The rise in temperature causes the (simultaneous) increase in pressure
(Boyle’s law)
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Substance Process
PARTICIPATION(a species of dependence)
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Participation (SNAP-SPAN)
A substance (SNAP) participates in a process (SPAN)
A runner participates in a race
A voter participates in an election
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Participation
x
y
substances x, y participate in process B
time
Bx
y
SNAP-ti.
time
SPAN
B
slice of x’s life
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Axes of variation
activity/passivity (agentive)
direct/mediated
benefactor/malefactor (conducive to existence) [MEDICINE]
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SNAP-SPAN
Participation
Perpetration (+agentive)
Initiation
Perpetuation
Termination
Influence
Facilitation
Hindrance
Mediation
Patiency(-agentive)
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Perpetration
A substance perpetrates an action (direct and agentive participation in a process):
The referee fires the starting-pistol
The captain gives the order
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Initiation
A substance initiates a process:
The referee starts the race
The attorney initiates the process of appeal
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Perpetuation
A substance sustains a process:
The singer sings the song
The charged filament perpetuates the emission of light
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Termination
A substance terminates a process:
The operator terminates the projection of the film
The judge terminates the imprisonment of the pardoned convict
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Influence
A substance (or its quality) has an effect on a process
The steepness of the slope affects the movement of the troopsThe politicians influence the course of the war
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Facilitation
A substance plays a secondary role in a process (for example by participating in a part or layer of the process)
The catalyst provides the chemical conditions for the reaction
The traffic-police facilitate our rapid progress to the airport
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Facilitation
is this really a binary relation?
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Hindrance, prevention, inhibition
A substance has a negative effect on the unfolding of a process (by participating in other processes)
The drug hinders the progression of the disease
The strikers prevent the airplane from departing
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Hindrance, prevention, inhibition
Is this really a binary relation ? (What is the second term?)
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Mediation
A substance plays an indirect role in the unfolding of a process relating other participants:
The Norwegians mediate the discussions between the warring parties
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Patiency
Dual of agentive participation
John kisses [Mary] (John agent)
Mary is kissed [by John] (Mary patient)
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Signatures of meta-relations
SNAP Component SPAN Component
Substances
SPQR…
Space Regions
Processuals
Processes
Events
Space-Time Regions
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Signatures of meta-relations
SNAP Component SPAN Component
Substances
SPQR…
Space Regions
Processuals
Processes
Events
Space-Time Regions
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Signatures of meta-relations
SNAP Component SPAN Component
Substances
SPQR…
Space Regions
Processuals
Processes
Events
Space-Time Regions
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Signatures of meta-relations
SNAP Component SPAN Component
Substances
SPQR…
Space Regions
Processuals
Processes
Events
Space-Time Regions
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REALIZATION
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Signatures of meta-relations
SNAP Component SPAN Component
Substances
SPQR…
Spatial Regions
Processuals
Processes
Events
Space-Time Regions
participation
realization
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Realization (SPQR process)
The most general relation between a dependent (SPQR…) entity and a process
The power to legislate is realized through the passing of a law
The role of antibiotics in treating infections is via the killing of bacteria
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Realization (SNAP-SPAN)
the execution of a plan, algorithm
the expression of a function
the exercise of a role
the realization of a disposition
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SPQR… entities and their SPAN realizations
plan
function
role
disposition
algorithm
SNAP
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SPQR… entities and their SPAN realizations
execution
expression
exercise
realization
application
course
SPAN
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Material examples:
performance of a symphonyprojection of a filmexpression of an emotionutterance of a sentenceapplication of a therapycourse of a diseaseincrease of temperature
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SNAP SPAN
Participation
Substance Process
Realization
SPQR Process
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SPAN SNAP
Involvement
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SPAN SNAP
Involvement
Creation
Sustaining in being
Destruction
DemarcationBlurring
Degradation
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Involvement
process substance(sometimes the converse of participation):
Races involve racers
(but not always):
Wars involve civilians
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Creation
A process brings into being a substance:
The declaration of independence creates the new state
The work of the potter creates the vase
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Sustaining in being
A process sustains in being a substance:
The circulation of the blood sustains the body
Levying taxes sustains the army
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Degradation
A process has negative effects upon a substance
Eating sugar contributes to the deterioration of your teeth.
The flow of water erodes the rock
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Destruction
A process puts a substance out of existence
The explosion destroys the car
The falling of the vase on the floor breaks it
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Demarcation
A process creates (fiat or bona fide) boundaries of substances.
The signing of the treaty establishes fixed borders between the two nations
The tracing of the area of operation by the surgeon defines a boundary, the incision performed by the surgeon yet another one
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Blurring
A process destroys boundaries of substances:
The military stand-off creates the no man's land
The successful transplant obliterates the boundary between original and grafted tissue
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Process SPQR
Continuation
DegradationDestruction
Creation
Qualitative projection
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Qualitative Projection
A warming process yields a rise in temperature
The tenure process yields a rise in John’s status
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Creation
A process brings into being a dependent entity
The accident reshapes the car.
The baking of the clay gives the vase its rigidity and color.
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Continuation
A process sustains the existence of an SPQR entity
The firing of the fireworks maintains the coloration of the sky
The intake of alcohol sustains the rosiness of his cheeks
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Degradation
A process affects a substance's quality or status by lowering its degree
The opening of the window diminishes the temperature in the room
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Destruction
A process destroys/changes an SPQR… entity
The accident destroys the car's shape
The burning of the vase destroys its color
The demotion relieved him of his rank as an officer
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Varieties of projection
Warming process series of temperature qualities
= qualitative projection
Process temporal interval
= temporal projection
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Spatial Projection
A process occurs in a given place or area:
The Revolution took place in Paris
The wind blows beyond the 24th parallel
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Starts in / ends at (spatial projection of process
boundaries)
A process begins/ends at a location
The race started in Paris
The race ended in Roubaix
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SNAP-SPAN
Participation
Perpetration (+agentive)
Initiation
Perpetuation
Termination
Influence
Facilitation
Hindrance
Mediation
Patiency(-agentive)
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SPAN-SNAP
Involvement
Creation
Sustenance
Destruction
Continuation
DegradationDestruction
Creation
DemarcationBlurring
Qualitative projection
Degradation
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Varieties of Projection
A process projects onto its temporal duration, onto the spatio-temporal region it occupiesonto the spatial region it occupies at a given time onto the sum of its participants at a time onto the sum of the SPQR… entities realized through it at a time
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Temporal Projection
of SPAN entities onto temporal intervals
of SNAP entities onto temporal intervals via their lives
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Formal relations not dealt with so far:
part-whole
instantiation
reference, intentionality
truthmaking
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Part-Whole
Basic relation exclusively intra-ontological: either SNAP-SNAP or SPAN-SPAN.
SNAP-SNAP: only if SNAPis have the same temporal index
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Relations crossing the SNAP/SPAN border are never part-relations
John’s lifesubstance John
physiological processes
sustaining in existence
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Granularity
spatial region substance
parts of substances are always substances
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Granularity
spatial region substance
parts of spatial regions are always spatial regions
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Granularity
process
parts of processes are always processes
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Intra-granular and cross-granular parthood
across SNAPs:Kevin’s arm is part of KevinKevin’s molecule is part of Kevin
across SPANs:Kevin’s leg-movement is part of Kevin’s runningKevin’s cytometabolism is part of Kevin’s running
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The idea (a further modification)
Formal relations are those relations which are not captured by either the SNAP or the SPAN ontologyeither because they can traverse the SNAP-SPAN divideor because they can traverse the granular divide
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Is this Kantianism?
does every ontology/perspective generate new formal-ontological relations?
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Realist Perspectivalism
There is a multiplicity of ontological perspectives on reality, all equally veridical i.e. transparent to reality
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SNAP
universals and particulars
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What about
reference, intentionality,
truthmaking ?
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SNAPEnduring Entity
[Exists in space and time,
has no temporal parts]
Spatial Entity
Tunnel
Alimentary Canal
Independent Entity
Cavity
Interior of Lung
Hollow
Nostril
State
Being pregnant, being thirsty
Dependent Entity
[±Relational]
Role, Function, Power, Disposition
[Have realizations, called processes]
To circulate blood, to secrete hormones
Quality
[Sometimes form quality-
regions or scales]
Requisite
[Have determinable/
determinate structure]
Temperature. height
Optional
Diabetes
Fiat part of substance *
Extremity, upper body
Substance
Organism, organ
Unoccupied
Occupied
Spatial region of 3
dimensions
occupied by organism
Spatial region of 2
dimensions *
occupied by burn, bruise
Boundary of substance *
Surface of skin or hide
MedO Draft 0.0004
Aggregate of substances *
Family, mother and fetus
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Are there any cases of ontological dependence involving an increase in being,
analogous to the increase in being between the thought and the thinker, the charge and the conductor, the swim and the swimmer
between SPAN and SPAN entities?
(Hypothesis: all qualities of processes are essential)
Puzzle
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Co-temporality
is a requisite for most SNAP-SPAN relations (participation, realization, etc.)
Exception: the memory of a process state of memory: SNAP(vs. episodic remembering: SPAN)