1. DEPICTION OF GEOLOGICAL PROCESSES WITH ONTOLOGY
BABAIE, Hassan
Geoscience/Computer Science Dept. Georgia State University
Atlanta, GA

2. Endurant (Continuant)
There are two types of entities:
Endurant and Perdurant
An endurant exists as a whole in time
Endurant’s spatial parts all exist at the same time
Each endurant object changes in time by acquiring different properties at different times
We use the SNAP perspective to model endurants
i.e., we take a snapshot of them at an instant of time, t
Example: all ordinary things, e.g., fault, rock
Database record of an outcrop or a mineral

3. Perdurant (Occurrent)
A perdurant occurs in spacetime
Perdurant has temporal parts that are different from the whole
A perdurant whole unfolds over a time interval by adding temporal parts
Past parts do not exist anymore!
Need the SPAN perspective to model them
i.e., we need data (e.g., a video) over an interval of time

4. Two Types of Perdurant Events Happen in an instant of time
Define the boundaries of states of entities
Start and end processes and subprocesses
e.g., the beginning/ending instants of a volcanic eruption
Process
An occurrence: may not be a whole
Complex process:
Temporal parts may not be of the same type
Is spatio-temporal:
May occur over several spatial and temporal regions
e.g. landslide, rock deformation

5. Life of an Endurant
Endurants (e.g., lava) are created (P1: eruption), transformed (P2: cooling), or destroyed (P3: erosion) by perdurants
e.g., in the case of eruption (P1), the change occurs between the instant the lava starts to erupt (event E1) and the instant it completely freezes (event E2)
Perdurants change the state of the endurants over time intervals
Endurants keep their state between events
But change their properties at different times

6. Endurant: Nankai Trough Accretionary Prism Perdurant (process): Subduction Subprocesses: see hierarchy!
Subduction
Accretion
Offscraping
Underplating
Subduction_Erosion

7. An earlier temporal part (phase, stage) of the perdurant Katrina Hurricane

8. A later temporal part (phase, stage) of the perdurant Katrina Hurricane

9. Lawful State Space
An endurant object X (e.g., fault, mineral) has a lawful state space, SL(X), which represents the collection of its possible states (e.g., sliding, stuck) over time (through its properties)
The lawful state space is a subset of a larger conceivable state space: SL(X)  S (X)
For every object, there is a series of lawful states: Si(x), Sj(X), …  SL(X)

10. State Trajectory
Every possible state of a thing is given by a point Si in the lawful state space SL(X)
The trajectory of the actual state of a thing at a given time and space, represents the actual change (due to process between events) for the individual thing
Function F (e.g., constitutive law) maps the states (Si) w.r.t. a reference frame, along the state trajectory
History is a segment of the trajectory
Transition from state s1 to s2 occurs in a possible event space, E(x), which starts a series of processes characterized by specific functions

11. Spatial and Temporal Regions
Temporal Region: interval of time in which active processes act on the interacting endurant objects that happen to be present in the spatial region where the starting/ending events occur
Spatial Region: space in which the objects of our interest occupy a specific interval of time
Sumatra Tsunami

12. Handling Spatio-temporal Knowledge
Geological processes occur in spatial and temporal regions
Sumatra tsunami in spacetime
For example, a seismic rupture initiates the propagation of a series of different types of seismic waves, which occupy different spatial regions at different time intervals

13. For spatio-temporal entities, a database or knowledge base should be able to answer questions like the following:
Where were the P- & S-wave 5 s after a rupture?
Which process followed the melting of ice on a volcano 10 minutes after the eruption of lava?
Was pyroclastic flow partially synchronous with lahar?
For this capability, we need time and process ontologies

14. Spatio-temporal Technology
OWL does not include a standard for spatial data
W3C’s OWL-Time is an ontology of temporal concepts (
XML XSD typed literals provide some support for time
GeoRSS provides support for point, line, box, and polygon ( based on the WGS84 standard
Basic Geo Vocabulary is an RDF encoding of long/lat values based on WGS84 standard (

15. Some Code from OWL-Time (Feng Pan and Jerry R. Hobbs)
<owl:Class rdf:ID="Instant">
<rdfs:subClassOf rdf:resource="#TemporalEntity"/>
</owl:Class>
<owl:Class rdf:ID="Interval">
<owl:Class rdf:ID="TemporalEntity">
<owl:unionOf rdf:parseType="Collection">
<owl:Class rdf:about="#Instant" />
<owl:Class rdf:about="#Interval" />
</owl:unionOf>

16. Ontologies Need to Have Concepts of Temporal Relations

17. OWL-Time Defines Properties for Process http://www. w3
OWL-Time’s interval relations: intervalEquals, intervalBefore, intervalMeets, intervalOverlaps, intervalStarts, intervalDuring, intervalFinishes and their reverse interval relations: intervalAfter, intervalMetBy, intervalOverlappedBy, intervalStartedBy, intervalContains, intervalFinishedBy <owl:ObjectProperty rdf:ID="begins"> <rdf:type rdf:resource="&owl;FunctionalProperty" /> <rdfs:domain rdf:resource="#TemporalThing" /> <rdfs:range rdf:resource="#InstantThing" /> </owl:ObjectProperty>

18. Process Relations
Processes can occur synchronically (i.e., within same time intervals) or polychronically, involving same or different objects, in the same or different spatial regions
Complex processes are aggregates of one or more processes
The temporal region of an aggregate process (e.g., deformation) may be divided into several sub- intervals within which unique, but possibly (causally) related, subprocesses occurred

19. Processes and Spacetime

20. Taxonomy of Processes P P1
SPAN processes, like SNAP entities, can be organized in hierarchical structures using the ‘is-a’ and ‘part-of’ relations, reflecting specialization and part-whole relations, respectively
If a process P subsumes another process P1 (i.e., P1 is-a P), then for all x, if x is an occurrence of P1, x is also an occurrence of P
x P1(x)  P(x)
Oxidation is-a Weathering or Folding is-a Deformation, state that instances of Oxidation or Folding are also instances of the Weathering or Deformation processes, respectively P
Brittle_ Deformation
is-a P1
Cataclasis

21. Dynamic_ Recrystallization
<owl:Class rdf:ID=“Dynamic_Recrystallization">
<rdfs:subClassOf rdf:resource=“#Crystal_Plastic_Def/>
</owl:Class>
<owl:Class rdf:ID=“Boundary_Migration">
<rdfs:subClassOf rdf:resource="#Dynamic_Recrystallization/>
</owl:Class>
These assertions mean that the actual (individual) occurrences of grain-boundary migration recrystallization or subgrain rotation, that occur during an actual mylonitization in a specific shear zone, are also occurrences dynamic recrystallization which is a mechanism of crystal plasticity
These explicit assertions implicitly mean (through OWL inference rules) that the actual (individual) mylonite that participated in the two subprocesses also participated in the super-process (i.e., crystal plasticity)
Crystal_ Plastic_Def
Dynamic_ Recrystallization
Recovery
Boundary_ Migration
Subgrain_ Rotation

22. Meronomy of Processes
An individual process p1 is ‘part-of’ p if and only if an instance of p1 is also an instance-level part-of p
Rotation part-of Cataclasis
Shearing part-of Frictional_Sliding
The mereological (part-whole) structure of processes is defined by temporal parts
Flow, diffusion, or subduction may have parts (i.e, phases or stages) that occur say faster than other parts
The parts are assumed to be contiguous, and without temporal gaps (which lead to subprocess or a new process) P
Part-of P1
Rotation

23. Axioms Parthood is denoted by: Pxy or P(x, y) or part-of(x,y)
Reflexivity: Pxx, which means x is part of itself
Antisymmetry: Pxy  Pyx  x=y
two distinct things cannot be part of each other
Transitivity: Pxy  Pyz  Pxz
if x is part of y, and y is part of z, then x is part of z
part-of (Faulting, Extension)  part-of (Extension, Plate_Divergence)  part-of (Faulting, Plate_Divergence)
part-of (Fluid_Inclusion, Quartz)  part-of (Quartz, Vein)  part-of (Fluid_Inclusion, Vein)

24. Formal, Perdurant Relations
Querying knowledge bases that use the two diverse SNAP and SPAN perspectives requires trans-ontloogical relations that relate endurants to the processes/events
The formal relations should traverse across the:
(1) border between the two perspectives, connecting the endurants and processes together:
<SNAP, SPAN>, <SPAN, SNAP>
<SNAPi, SNAPj> of distinct time indices i and j
<SPAN, SPAN>
(2) granularity boundaries (microscopic-lithospheric)
(3) temporal divide, e.g., between now and later times

25. Special Spatio-temporal Relations
The ternary has-participant relation relates an instance of a process p to an instance of a continuant c at time t, i.e., p has-participant c at t
Hydrolytic_Softening has-participant Water at t
Cataclasis has-participant Rock at t
The occurring-at relation relates an instance of a process p, to time t (p occurring-at t)
Recrystallization occurring-at t
Frictional_Sliding occurring-at t
The ‘terminate’ relation holds where a SNAP entity terminates a process
Free surface terminates fracture propagation

26. Special Relations, cont’d
The ‘facilitate’ relation holds where a SNAP entity facilitates a process
Rain or clay facilitate landslide
hydroxyl ions (OH-) facilitate deformation of silicates (by substituting for O)
The ‘hinders’ or ‘prevents’ relation holds when a SNAP entity has a negative effect on a process
Point defect hinders dislocation glide
The ‘mediates’ relation obtains when a SNAP entity indirectly brings participants of a process together
Water or heat mediates alteration of rock (by bringing ions in contact with mineral constituents)

27. The ‘realize’, and its subtypes: ‘initiate, ‘persist’, and ‘terminate’, are types of relation that hold between a SNAP dependent (i.e., qualities, roles, functions) and a process
Water realizes hydrolytic_Weakening of rock (at high T)
Pore pressure realizes hydraulic_Fracturing of rock
Volume increase realizes dilation of rock
Growth of high-density minerals realize metamorphism (at high pressure)
The ternary realizes relation holds between a SNAP (mineral), a SNAP dependent entity (increase in volume), and a process (dilation)
(e.g., Mineral volume_increase realizes Rock_Dilation)

28. Mylonitization involves Rock
Relations between SPAN processes and SNAP entities include the ‘involves’ relation, which is the converse of the ‘participates’ relation that obtains between a SNAP and SPAN entities
Mylonitization involves Rock
A process can also ‘destroy’ a SNAP entity
Mylonitization destroys original rock texture

29. Temporal Relations
The ‘preceded-by’ relation gives the relative timing of two processes along ordered, linear, continuous time
The statement: p2 preceded-by p1 means: an instance of a process p2 is preceded by an instance of an earlier process p1, if for all t2 and t1, p2 occurring-at t2 and p1 occurring-at t1, and t1 earlier than t2
Earthquake preceded-by Dilatation
Offscraping preceded-by Subduction_Erosion
The ‘has-agent’ relation is a ternary relation between a process, a causally responsible continuant, and time: p has-agent c at t
Only continuants (not processes) can be agent:
Hydraulic_Fracturing has-agent Water at t Fracturing has-agent Stress at t

30. Conclusions: 1) Processes are first class entities with a full set of ontological relations, taxonomy, and meronomy 2) Process ontology requires time ontology 3) W3C provides some technology for building geoprocess ontologies

31. Spatial Region
The space in which the objects of our interest occupy at a specific interval of time
Depending on granularity of our study, it can be represented as:
a point, with long/lat or KML point
a polygon on a GIS layer
an address (e.g., Portland Convention Center)

32. Temporal Region
This is the interval of time in which active processes act on the interacting endurant objects that happen to be present in the spatial region where the starting/ending events occur
Temporal data can refer to:
instants (e.g., October 18, 2009 at 10:00 AM)
Discrete interval of time (Thanksgiving)
Continuous period of time (Century)