1. Designing dynamic Earth sciences ontologies Hassan Babaie Georgia State University Process and Event Ontologies

2. Ontologies should not just describe the spatial things in the world Ontologies should characterize the structure of the world; i.e., the inter- relationships between the objects occupying spacetime, and the facts and constraints about them Ontologies should characterize the structure of the world; i.e., the inter- relationships between the objects occupying spacetime, and the facts and constraints about them What matters in an ontology is the way the constituent objects are put together (i.e., structure), their characteristics, and the relations between them What matters in an ontology is the way the constituent objects are put together (i.e., structure), their characteristics, and the relations between them Image from: http://www.earthscienceworld.org/images Sheep Mountain Anticline WY

3. Can we formalize this statement? “ The folding of the Late Cretaceous sedimentary units, which was the last phase of a prolonged contractional process, was followed by uplift, which translated the deformed rocks to the surface and exposed them to weathering and erosion during Eocene. This was followed by continued erosion, which partly overlapped with the deposition of Oligocene fluvial sediments, which were deposited through a sudden flood event in a channel that formed above the erosional surface.” Image from: www.grisda.org/colorado/index.htm

4. Processes shown in yellow “The folding of the Late Cretaceous sedimentary units, which was the last phase of a prolonged contractional process, was followed by uplift, which translated the deformed rocks to the surface and exposed them to weathering and erosion during Eocene. This was followed by continued erosion, which partly overlapped with the deposition of Oligocene fluvial sediments, which were deposited through a sudden flood event in a channel that formed above the erosional surface.” “The folding of the Late Cretaceous sedimentary units, which was the last phase of a prolonged contractional process, was followed by uplift, which translated the deformed rocks to the surface and exposed them to weathering and erosion during Eocene. This was followed by continued erosion, which partly overlapped with the deposition of Oligocene fluvial sediments, which were deposited through a sudden flood event in a channel that formed above the erosional surface.”

5. Temporal components “The folding of the Late Cretaceous sedimentary units, which was the last phase of a prolonged contractional process, was followed by uplift, which translated the deformed rocks to the surface and exposed them to weathering and erosion during Eocene. This was followed by continued erosion, which partly overlapped with the deposition of Oligocene fluvial sediments, which were deposited through a sudden flood event in a channel that formed above the erosional surface.” “The folding of the Late Cretaceous sedimentary units, which was the last phase of a prolonged contractional process, was followed by uplift, which translated the deformed rocks to the surface and exposed them to weathering and erosion during Eocene. This was followed by continued erosion, which partly overlapped with the deposition of Oligocene fluvial sediments, which were deposited through a sudden flood event in a channel that formed above the erosional surface.”

6. Substantial entities “The folding of the Late Cretaceous sedimentary units, which was the last phase of a prolonged contractional process, was followed by uplift, which translated the deformed rocks to the surface and exposed them to weathering and erosion during Eocene. This was followed by continued erosion, which partly overlapped with the deposition of Oligocene fluvial sediments, which were deposited through a sudden flood event in a channel that formed above the erosional surface.” “The folding of the Late Cretaceous sedimentary units, which was the last phase of a prolonged contractional process, was followed by uplift, which translated the deformed rocks to the surface and exposed them to weathering and erosion during Eocene. This was followed by continued erosion, which partly overlapped with the deposition of Oligocene fluvial sediments, which were deposited through a sudden flood event in a channel that formed above the erosional surface.”

7. All parts of the statement shown “The folding of the Late Cretaceous sedimentary units, which was the last phase of a prolonged contractional process, was followed by uplift, which translated the deformed rocks to the surface and exposed them to weathering and erosion during Eocene. This was followed by continued erosion, which partly overlapped with the deposition of Oligocene fluvial sediments, which were deposited through a sudden flood event in a channel that formed above the erosional surface.” “The folding of the Late Cretaceous sedimentary units, which was the last phase of a prolonged contractional process, was followed by uplift, which translated the deformed rocks to the surface and exposed them to weathering and erosion during Eocene. This was followed by continued erosion, which partly overlapped with the deposition of Oligocene fluvial sediments, which were deposited through a sudden flood event in a channel that formed above the erosional surface.”

8. Static and dynamic aspects of reality It’s the facts about the things in the world, e.g., relation to processes that change them, not the things themselves that matter It’s the facts about the things in the world, e.g., relation to processes that change them, not the things themselves that matter Ontologies need to depict both static and dynamic aspects of the domain of discourse Ontologies need to depict both static and dynamic aspects of the domain of discourse

9. Two categories of entities in reality Entities that occur on the surface of Earth, below its surface, and in the atmosphere around it, can be grouped into two general, non-overlapping categories based on their mode of existence and persistence: Entities that occur on the surface of Earth, below its surface, and in the atmosphere around it, can be grouped into two general, non-overlapping categories based on their mode of existence and persistence: 1. Endurants 2. Perdurants

10. Endurants (Continuants) Include substantial entities (both material and immaterial) e.g., fault, rock, river, aquifer, pore, cave, glacier, and gas Include substantial entities (both material and immaterial) e.g., fault, rock, river, aquifer, pore, cave, glacier, and gas Occur and interact (through processes) in the lithosphere, hydrosphere, atmosphere, and cryosphere Occur and interact (through processes) in the lithosphere, hydrosphere, atmosphere, and cryosphere San Andreas Fault Photo by: Robert E. Wallace pubs.usgs.gov

11. Qualitative changes to endurants in time Connectivity (topological relations) Connectivity (topological relations) Dimension; e.g., a fault eroding into a 2D trace Dimension; e.g., a fault eroding into a 2D trace Position Position Location – defined by distance & direction Location – defined by distance & direction changes by: translation, rotation changes by: translation, rotation Orientation Orientation Size Size Shape Shape Configuration (structure) Configuration (structure)

12. Perdurants The perduring entities (perdurants) include the processes and events that involve the endurants The perduring entities (perdurants) include the processes and events that involve the endurants These include such things as eruption, displacement (process), deformation and flow (process aggregate), and the instantaneous part of the beginning phase of a landslide (event) These include such things as eruption, displacement (process), deformation and flow (process aggregate), and the instantaneous part of the beginning phase of a landslide (event) www.geo.mtu.edu/volcanoes /hazards/primer/images/ volc-images/puuoo.jpg

13. Mereology of endurants e.g., SAF An endurant is part of reality that occupies spatial regions at different or same times, and has spatial parts At each instant of time, occur in its entirety Preserves its identity through time despite continuous qualitative change

14. Wood River’s spatial parts: meanders, channel, flood plains, point bars, occupy spatial regions Spatial Region: U.S.A, Alaska; Fairbanks Latitude: 64.8 Longitude: -147.7 Alaska FairbanksAlaska Fairbanks ( www.earthscienceworld.org ), © Society for Sedimentary Geology www.earthscienceworld.orgSociety for Sedimentary Geology www.earthscienceworld.orgSociety for Sedimentary Geology

15. Mereology of Perdurants A perdurant (occurrent) entity (e.g., process, event), on the other hand, occurs in an interval of time through a succession of temporal parts (i.e., phases), that each occur in subintervals of time A perdurant (occurrent) entity (e.g., process, event), on the other hand, occurs in an interval of time through a succession of temporal parts (i.e., phases), that each occur in subintervals of time A process unfolds itself over time, and at each time slice (instant, t), it presents an incomplete part of the whole; i.e., it is mereologically incomplete at t. Need a video! A process unfolds itself over time, and at each time slice (instant, t), it presents an incomplete part of the whole; i.e., it is mereologically incomplete at t. Need a video! Slumgullion Earthflow, Hinsdale, Colorado http://landslides.usgs.go v/learningeducation/slumg ullion.php#aerial

16. Hurricane as a process Hurricane Katrina: Hurricane Katrina: Time interval: Time interval: Started: August 23, 2005 (Wikipedia.com) Started: August 23, 2005 (Wikipedia.com)August 232005August 232005 Dissipated: August 31, 2005 Dissipated: August 31, 2005August 312005August 312005 Highest winds involved in the hurricane (280 km/h) Highest winds involved in the hurricane (280 km/h)km/h The whole process unfolded over the interval The whole process unfolded over the interval Only parts of it were seen at every instant Only parts of it were seen at every instant Different snapshots of it are temporal parts (phases)! Different snapshots of it are temporal parts (phases)!

17. Hurricane Katrina: A phase of the process in a spatio-temporal region This first image was taken at 03:24 UTC 28 August 2005 (11:24 pm EDT 27 August) just as Katrina was about to become a Category 4 hurricane in the central Gulf of Mexico. www.nasa.gov

18. Another temporal part in a different spatio- temporal region; hurricane is changed The second image was taken at the same time on 29 August 2005 and shows a 3D perspective of Katrina with a cut-away view through the eye of the storm. www.nasa.gov

19. Unfolding of phases of the Sumatra Tsunami over an interval of 3 hours on December 26, 2004 Each snapshot only shows a temporal part, but not the whole! To see the whole we need the video! Simulation: Kenji Satake, Geological Survey of Japan, AIST http://www.notur.no/notur2005/kenjisatake.htm

20. Basic Formal Ontology, BFO Basic Formal Ontology, BFO Institute for Formal Ontology and Medical Information Science, University of Leipzig Developed at a highest and most domain-neutral level of generality (Grenon, 2002, 2003) Developed at a highest and most domain-neutral level of generality (Grenon, 2002, 2003) Applies equally to Earth sciences as it does to biology Applies equally to Earth sciences as it does to biology The bi-categorical BFO ontologies include the two endurant and perdurant perspectives, which are referred to as SNAP and SPAN ontologies, respectively The bi-categorical BFO ontologies include the two endurant and perdurant perspectives, which are referred to as SNAP and SPAN ontologies, respectively BFO has similarities and differences (Grenon, 2003) with the top-level DOLCE ontology BFO has similarities and differences (Grenon, 2003) with the top-level DOLCE ontology

21. SNAP & SPAN ontologies (Grenon & Smith, 2003; Grenon, 2003c) SNAP ontologies represent snapshot perspective on reality SNAP ontologies represent snapshot perspective on reality SPAN ontologies characterize a four- dimensional view and hence a temporal aspect of existence SPAN ontologies characterize a four- dimensional view and hence a temporal aspect of existence These ontologies characterize the static and dynamic views of the world, respectively These ontologies characterize the static and dynamic views of the world, respectively

22. Measuring Change Change in a SNAP ontology may be measured by comparing the discrepancies (from snapshots) among the qualities (e.g., shape, location) of the continuants measured at different time indexes, t Change in a SNAP ontology may be measured by comparing the discrepancies (from snapshots) among the qualities (e.g., shape, location) of the continuants measured at different time indexes, t However, change and dynamic reality can better be captured through SPAN entities (e.g., processes) which unfold themselves over an interval of time (  t) However, change and dynamic reality can better be captured through SPAN entities (e.g., processes) which unfold themselves over an interval of time (  t)

23. SNAP Hierarchy Our domain entities ‘specialize’ these top-level classes through the ‘is-a’ relation

24. (1) Independent SNAP entities Substantial entities Substantial entities e.g., mineral, river e.g., mineral, river Aggregates of substances Aggregates of substances e.g., a sequence of rock layers at all scales e.g., a sequence of rock layers at all scales Boundaries Boundaries e.g., unconformities, contacts, grain boundary e.g., unconformities, contacts, grain boundary Fiat parts (vs. bona fide parts) Fiat parts (vs. bona fide parts) e.g., the equator, 30 o N latitude, U.S. Canada border e.g., the equator, 30 o N latitude, U.S. Canada border Sites, which include empty spaces Sites, which include empty spaces e.g., cavity, pore, cave, and conduit e.g., cavity, pore, cave, and conduit

25. (2) Dependent SNAP entities Could be monadic (e.g., mineral density) Could be monadic (e.g., mineral density) or relational, e.g., sutured or unconformable contact or relational, e.g., sutured or unconformable contact Qualities (tropes) (e.g., density, color, temp.) Qualities (tropes) (e.g., density, color, temp.) Functions (river transports sediment load) Functions (river transports sediment load) Conditions (altered/unaltered, dormant/active Conditions (altered/unaltered, dormant/active Shape (clast shape, sigmoidal megacryst) Shape (clast shape, sigmoidal megacryst) Role (role of water in hydraulic fracturing or hydrolytic weakening) Role (role of water in hydraulic fracturing or hydrolytic weakening)

26. SPAN Hierarchy Our domain processes/events ‘specialize’ these top-level classes through the ‘is-a’ relation

27. (1) SPAN Processuals entities Processes - e.g., alteration of rocks at the surface; mylonitization in a shear zone Processes - e.g., alteration of rocks at the surface; mylonitization in a shear zone Instantaneous temporal boundaries, i.e., events Instantaneous temporal boundaries, i.e., events e.g., the instant a meteorite hits the Earth e.g., the instant a meteorite hits the Earth the instant a landslide starts to move the instant a landslide starts to move Temporal aggregates, i.e., a successive series of processes that lead into one another Temporal aggregates, i.e., a successive series of processes that lead into one another e.g., the arrival of series of body and surface waves to a location at different times, and the consequent compressional or shear particle motion e.g., the arrival of series of body and surface waves to a location at different times, and the consequent compressional or shear particle motion

28. SPAN entities cont’d (2) Temporal regions which are part of time and could be scattered or connected (2) Temporal regions which are part of time and could be scattered or connected intervals and instants intervals and instants (3) Spatio-temporal regions which are part of spacetime (3) Spatio-temporal regions which are part of spacetime can also be scattered or connected can also be scattered or connected

29. Processes have patterns/structure Spacetime is punctuated by a series of events that mark the beginning and end of processes that lead to qualitative change in endurants Spacetime is punctuated by a series of events that mark the beginning and end of processes that lead to qualitative change in endurants Some of these processes coincide or overlap in time and space Some of these processes coincide or overlap in time and space Processes can occur synchronically (i.e., within same time intervals) or di-, poly-chronically, involving same or different objects, in the same or different spatial regions Processes can occur synchronically (i.e., within same time intervals) or di-, poly-chronically, involving same or different objects, in the same or different spatial regions

30. Laplace causal determinism “The idea that every event is necessitated by antecedent events and conditions together with the laws of nature” (Stanford Encyclopedia of Philosophy) “The idea that every event is necessitated by antecedent events and conditions together with the laws of nature” (Stanford Encyclopedia of Philosophy) The enduring entities provide the spatial location for the events by participating in these processes The enduring entities provide the spatial location for the events by participating in these processes However, the span of processes, which is the spatio-temporal region in which the process occurs (Simons, 1987), depends on (i.e., determined by) the spatial and temporal distribution of the qualitative features of rocks and external fields (e.g., gravity, stress/strain field) (Laplace determinism) However, the span of processes, which is the spatio-temporal region in which the process occurs (Simons, 1987), depends on (i.e., determined by) the spatial and temporal distribution of the qualitative features of rocks and external fields (e.g., gravity, stress/strain field) (Laplace determinism)

31. Examples of causal determinism Landslide: the transition from stable to unstable states in a landslide depends on the angle of slope, which relates to gravitational field, amount of clay and water along the potential plane of failure, and existence of discontinuities (e.g., fractures) Landslide: the transition from stable to unstable states in a landslide depends on the angle of slope, which relates to gravitational field, amount of clay and water along the potential plane of failure, and existence of discontinuities (e.g., fractures) Volcanic eruption, depends on such things as presence and type of magma, heat, and strength of the rocks Volcanic eruption, depends on such things as presence and type of magma, heat, and strength of the rocks Fault zone, the processes of sliding and earthquake are controlled by the far-field as well as local stresses, and the conditions along the fault, such as pore fluid pressure, and rock’s mechanical and chemical properties Fault zone, the processes of sliding and earthquake are controlled by the far-field as well as local stresses, and the conditions along the fault, such as pore fluid pressure, and rock’s mechanical and chemical properties

32. Ontologies of events/processes require ontology of time Ontologies should include both the spatial and temporal aspects of reality Ontologies should include both the spatial and temporal aspects of reality It is only through events and processes and other perdurant entities, during which changes occur to spatial entities and regions, that time becomes meaningful It is only through events and processes and other perdurant entities, during which changes occur to spatial entities and regions, that time becomes meaningful “It is neither the point in space, nor the instant in time, at which something happens that has physical reality, but only the event itself” Albert Einstein (quoted in: Kennedy, 2003) “It is neither the point in space, nor the instant in time, at which something happens that has physical reality, but only the event itself” Albert Einstein (quoted in: Kennedy, 2003)

33. Formalization of instants of time Instants define ‘state transitions’ by events Instants define ‘state transitions’ by events Like real numbers, time is a continuum of an unbounded number of possible parts that follow each other in an ordered succession Like real numbers, time is a continuum of an unbounded number of possible parts that follow each other in an ordered succession ‘ t 1  t 2 ’ reads: ‘t 1 precedes t 2 ‘, or ‘t 1 is earlier than t 2 ‘, or ‘t 1 is before t 2 ‘ ‘ t 1  t 2 ’ reads: ‘t 1 precedes t 2 ‘, or ‘t 1 is earlier than t 2 ‘, or ‘t 1 is before t 2 ‘ Irreflexive relation: no instant precedes itself Irreflexive relation: no instant precedes itself  t  (t  t) Which says: for all t, t does not precede itself

34. Time instant is transitive For all instants t, t, t , if t precedes t and t precedes t , then t precedes t  For all instants t, t, t , if t precedes t and t precedes t , then t precedes t 

35. Unbounded time For any instant t, there is always another instant t, which precedes it For any instant t, there is always another instant t, which precedes it i.e., for all t, there exists a t where t is earlier than t

36. Subintervals Subintervals in which related processes occur: Subintervals in which related processes occur:

37. Dense time Time is also dense like real numbers, meaning that if an instant t precedes another instant t, there is another instant in between them which is later than the first and earlier than the second instant: Time is also dense like real numbers, meaning that if an instant t precedes another instant t, there is another instant in between them which is later than the first and earlier than the second instant: i.e., for all t and t, if t is earlier than t, there exists another instant t  where t precedes t , and t  precedes t

38. Time is discrete An instant t’ is called the ‘immediate successor’ of another instant t, if t precedes t’, and there is no other instant between them An instant t’ is called the ‘immediate successor’ of another instant t, if t precedes t’, and there is no other instant between them i.e., t is earlier than t and there is no instant t  between t and t

39. Intervals of time in which processes occur Thirteen exhaustive, mutually exclusive, basic relations for linear and totally ordered time are defined by Allen (1983, 1984) Thirteen exhaustive, mutually exclusive, basic relations for linear and totally ordered time are defined by Allen (1983, 1984) This is done using the ‘immediate precedence’ relation in which the end of interval ‘i’ is simultaneous with the beginning of interval ‘j’, denoted by: This is done using the ‘immediate precedence’ relation in which the end of interval ‘i’ is simultaneous with the beginning of interval ‘j’, denoted by: i  j (reads: i meets j) end(i) = beg(j)

40. 1 ‘i’ meets an interval which meets j end(i) < beg (j) Interval between two seismic events. Erosion after a period of uplift 2 Primitive end(i) = beg(j) End of hydraulic fracturing immediately initiating flow of fluid in a reservoir End of crystallization out of magma immediately followed by crystal settling 3 Some final subinterval of i is an initial subinterval of j beg(i) < beg(j) < end(i) < end(j) Eruption of lava partly overlapping continued extension Interval ‘i’ ends before ‘j’:  k, l (i  k  k  l  j  l) 4 i is an initial subinterval of j beg(i) = beg(j)  end(i) < end(j) Recrystallization and shearing starting at the same time Synchronous of dialation and uplift i and j begin together:  k (k  I  k  j), k is initial subinterval of both 5 i is an internal subinterval of j beg(j) < beg(i)  end(i) < end(j) Contractional tectonics with a period of magmatic intrusion Melting period during frictional sliding 6 ‘i’ is a final subinterval of ‘j’ beg(j) < beg(i)  end(i) = end(j) End of pyroclastic ejection ending a period of volcanic eruption ‘i’ and j end together:  k (i  k  j  k) and k is subinterval of both 7 i = j beg(i)=beg(j)  end(i)= end(j) Synchronous folding and thrusting in an area Synchronous heating and melting

41. 8 j is a final subinterval of i beg(i) < beg(j)  end(i) = end(j)  Deformation and uplift ending sedimentation in a basin 9 j is an internal subinterval of i  Period of cataclastic flow during brittle deformation 10 j is an initial subinterval of i  Interval of magma rising initiating a volcanic eruption 11 Some final subinterval of j is an initial subinterval of i  Interval of veining overlapping with fracturing 12 j meets i  Flow coming to an end, initiating deposition in a delta 13 j meets an interval which meets i  Sea level rising after sea floor spreading  Subduction of oceanic lithosphere after a period of spreading

42. Perdurant ‘is-a’ and ‘part-of’ relations A process P is-a subclass of another process P 1, if for all p, if p is instance of P, then p is also an instance of P 1 A process P is-a subclass of another process P 1, if for all p, if p is instance of P, then p is also an instance of P 1 For example, in the Oxidation is-a Weathering, or Folding is- a Deformation, instances of Oxidation and Folding are also instances of Weathering and Deformation, respectively For example, in the Oxidation is-a Weathering, or Folding is- a Deformation, instances of Oxidation and Folding are also instances of Weathering and Deformation, respectively A process P is part-of P 1 if and only if an instance of P is also an instance-level part-of P 1 (Smith et al., 2005) A process P is part-of P 1 if and only if an instance of P is also an instance-level part-of P 1 (Smith et al., 2005) For example, Rotation part-of Cataclasis Shearing part-of Frictional_Sliding For example, Rotation part-of Cataclasis Shearing part-of Frictional_Sliding

44. Other perdurant relation The has-participant ternary relation relates an instance of a process p to an instance of a continuant, c at time t (p has-participant c at t). For example: The has-participant ternary relation relates an instance of a process p to an instance of a continuant, c at time t (p has-participant c at t). For example: Hydrolytic_Softening has-participant Water at t Hydrolytic_Softening has-participant Water at t Folding has-participant Dike at t Folding has-participant Dike at t The occurring-at relation relates an instance of a process, p, to time t (p occurring-at t). For example: Recrystallization occurring-at t The occurring-at relation relates an instance of a process, p, to time t (p occurring-at t). For example: Recrystallization occurring-at t

46. Other relations … An instance of a process p preceded-by an instance of another process, p 1 (i.e., p preceded-by p 1 ) if for all t and t 1, if p occurring-at t and p 1 occurring at t 1, and t 1 earlier t An instance of a process p preceded-by an instance of another process, p 1 (i.e., p preceded-by p 1 ) if for all t and t 1, if p occurring-at t and p 1 occurring at t 1, and t 1 earlier t Earthquake preceded-by Dilatation and Fracturing Earthquake preceded-by Dilatation and Fracturing The has-agent relation is a ternary relation between a process, a causally responsible continuant and time (p has-agent c at t). 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 Only continuants (not processes) can be agent Hydraulic_Fracturing has-agent Water at t (due to its pore_fluid_pressure quality) Hydraulic_Fracturing has-agent Water at t (due to its pore_fluid_pressure quality) Fracturing has-agent Stress at t Fracturing has-agent Stress at t