BABAIE, HassanGeoscience/Computer Science Dept.

Georgia State UniversityAtlanta, GA

www.gsu.edu/~geohab

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

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

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

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

Subduction

Accretion

Subduction_Erosion

UnderplatingOffscraping

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)

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

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

Geological processes occur in spatial and temporal regions

◦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

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

OWL does not include a standard for spatial data

W3C’s OWL-Time is an ontology of temporal concepts (www.w3.org/TR/owl-time/)

XML XSD typed literals provide some support for time

GeoRSS provides support for point, line, box, and polygon (www.georss.org) based on the WGS84 standard

Basic Geo Vocabulary is an RDF encoding of long/lat values based on WGS84 standard (www.w3.org/2003/01/geo)

<owl:Class rdf:ID="Instant"> <rdfs:subClassOf rdf:resource="#TemporalEntity"/>

</owl:Class> <owl:Class rdf:ID="Interval">

<rdfs:subClassOf rdf:resource="#TemporalEntity"/></owl:Class> <owl:Class rdf:ID="TemporalEntity">

<owl:unionOf rdf:parseType="Collection"> <owl:Class rdf:about="#Instant" /> <owl:Class rdf:about="#Interval" />

</owl:unionOf> </owl:Class>

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>

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

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

PBrittle_

Deformation

P1

Cataclasis

is-a

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

Subgrain_Rotation

Boundary_Migration

Recovery

<owl:Class rdf:ID=“Boundary_Migration"> <rdfs:subClassOf rdf:resource="#Dynamic_Recrystallization/>

</owl:Class>

<owl:Class rdf:ID=“Dynamic_Recrystallization"> <rdfs:subClassOf rdf:resource=“#Crystal_Plastic_Def/>

</owl:Class>

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

P1

Rotation

Part-of

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)

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

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

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)

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)

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

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)

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)