Existence Intervals

This example demonstrates various ontologies' representations of the period of time in which a thing exists. Some effort is put into describing differences in representing the existence of endurants vs. perdurants.

Take as an example a thing---and the thing might be endurant, perdurant, physical, cyber, thought, event, etc.---that exists starting at a time t0 and ceases to exist at a time t1. In the illustrations below, the start will be labeled t0, the end t1, the interval bounded by start and end i, the thing t.

The starting time of this thing is 2020-01-02T03:04:05.6789Z. The ending time of this thing is 2021-02-03T04:05:06.7890Z. Each illustration goes as far as it can with concepts in the referenced ontology to eventually tie the thing t to these timestamp-literals. Where available, reified "instant" objects will be favored over literal-valued properties.

This suggests a mapping table:

Example class or triple	Corresponding class or triple
`ex:TimeBoundedThing`	...
`ex:ExistenceInterval`	...
`ex:Instant`	...
`kb:T ex:hasExistenceInterval kb:E`	...
`kb:T ex:existsAtAndSince kb:T0`	...
`kb:T ex:existsUntil kb:T1`	...
`kb:T ex:hasCreationTimestamp "2020-..."^^xsd:dateTime`	...
`kb:T ex:hasTerminationTimestamp "2021-..."^^xsd:dateTime`	...
`kb:E ex:hasStart kb:T0`	...
`kb:E ex:hasEnd kb:T1`	...
`kb:E ex:hasBeginningTimestamp "2020-..."^^xsd:dateTime`	...
`kb:E ex:hasEndingTimestamp "2021-..."^^xsd:dateTime`	...
`kb:T0 ex:hasTimestamp "2020-..."^^xsd:dateTime`	...
`kb:T1 ex:hasTimestamp "2021-..."^^xsd:dateTime`	...

The mapping table is filled in for the various ontologies below with:

Corresponding statements (class IRIs or full triples);
"N/A", for not-available when a concept is known to not be mappable now, typically because no corresponding class or property is currently defined; and
"TBD", when a design decision can be taken, typically because of a potential class- or property-equality declaration.

Note that "N/A" does not mean that a mapping is not possible. It only means that classes and properties are not defined at the present moment.

UCO 1.3.0

UCO declares two property-pairs setting time boundaries:

core:startTime and core:endTime, used to bound core:Events and core:Relationships.
action:startTime and action:endTime, used to bound action:Actions.

The following table shows the time coverage for the three UCO classes that currently encode constraints on time properties:

UCO Class	Figure
`uco-action:Action`
`uco-core:Event`
`uco-core:Relationship`

The mapping for uco-action:Action would be as follows.

Example class or triple	Corresponding class or triple
`ex:TimeBoundedThing`	`uco-action:Action`
`ex:ExistenceInterval`	TBD
`ex:Instant`	N/A
`kb:T ex:hasExistenceInterval kb:E`	TBD
`kb:T ex:existsAtAndSince kb:T0`	N/A
`kb:T ex:existsUntil kb:T1`	N/A
`kb:T ex:hasCreationTimestamp "2020-..."^^xsd:dateTime`	`kb:T uco-action:startTime "2020-..."^^xsd:dateTime`
`kb:T ex:hasTerminationTimestamp "2021-..."^^xsd:dateTime`	`kb:T uco-action:endTime "2021-..."^^xsd:dateTime`
`kb:E ex:hasStart kb:T0`	N/A
`kb:E ex:hasEnd kb:T1`	N/A
`kb:E ex:hasBeginningTimestamp "2020-..."^^xsd:dateTime`	TBD
`kb:E ex:hasEndingTimestamp "2021-..."^^xsd:dateTime`	TBD
`kb:T0 ex:hasTimestamp "2020-..."^^xsd:dateTime`	N/A
`kb:T1 ex:hasTimestamp "2021-..."^^xsd:dateTime`	N/A

uco-core:Event and uco-core:Relationship will look similar.

The "TBD"s above pertain to a decision UCO can make on how endurants and perdurants relate to time, under discussion UCO Issue 544.

OWL-Time

OWL-Time provides the class time:TemporalEntity. Guidance offers options on how to relate time-things (time:TemporalEntity) to things that exist in time (like an activity or an object), drawn from Section 3.1.

The properties :hasTemporalDuration, :hasBeginning and :hasEnd, together with a fourth generic property :hasTime, support the association of temporal information with any temporal entity, such as an activity or event, or other entity. These provide a standard way to attach time information to things, which may be used directly in applications if suitable, or specialized if needed.

The following figure shows the time coverage for the general usage of time:TemporalEntity:

The mapping for time:TemporalEntity would be as follows.

Example class or triple	Corresponding class or triple
`ex:TimeBoundedThing`	`owl:Thing`
`ex:ExistenceInterval`	`time:TemporalEntity`
`ex:Instant`	`time:Instant`
`kb:T ex:hasExistenceInterval kb:E`	`kb:T time:hasTime kb:E`
`kb:T ex:existsAtAndSince kb:T0`	N/A
`kb:T ex:existsUntil kb:T1`	N/A
`kb:T ex:hasCreationTimestamp "2020-..."^^xsd:dateTime`	N/A
`kb:T ex:hasTerminationTimestamp "2021-..."^^xsd:dateTime`	N/A
`kb:E ex:hasStart kb:T0`	`kb:E time:hasBeginning kb:T0`
`kb:E ex:hasEnd kb:T1`	`kb:E time:hasEnd kb:T1`
`kb:E ex:hasBeginningTimestamp "2020-..."^^xsd:dateTime`	N/A
`kb:E ex:hasEndingTimestamp "2021-..."^^xsd:dateTime`	N/A
`kb:T0 ex:hasTimestamp "2020-..."^^xsd:dateTime`	`kb:T0 time:inXSDDateTime "2020-..."^^xsd:dateTime`
`kb:T1 ex:hasTimestamp "2021-..."^^xsd:dateTime`	`kb:T1 time:inXSDDateTime "2021-..."^^xsd:dateTime`

Some of the examples in the OWL-TIME specification include demonstrations of time:TemporalEntity that allow for endurants and perdurants as direct subclasses. Note that the examples section is non-normative.

5.4, "iCalendar" instantiates the endurant "Abraham Lincoln" (node _:TE-2).
5.6, "A Use Case for Scheduling" instantiates perdurants some teleconference and some meeting (nodes ex:telecon and ex:meeting, respectively).
5.7, "Alignment of PROV-O with OWL-Time" states that prov:Activity and prov:InstantaneousEvent can be subclasses of time:TemporalEntity and time:Instant, respectively.

gUFO

(gUFO version: 1.0.0.)

gUFO's topmost class that describes an object that exists in a period of time is "Concrete Individual" (gufo:ConcreteIndividual), defined as the disjoint union of "Endurants," "Events," and "Situations."

gufo:Endurant corresponds with UCO Issue 535's "Endurant".
gufo:Event corresponds with UCO Issue 535's "Perdurant".
gufo:Situation is mostly out of scope of this discussion, though the interested can review a footnote about temporary @type applicability¹.

Concrete individuals have first and last instants in which they exist. These instants are represented as time:Instant objects or as datatype literals (typed xsd:date or xsd:dateTimeStamp---and, pertinent to UCO, not xsd:dateTime). Two properties, "has begin point" and "has end point," assign the first and last instants that any concrete individual exists as objects. The properties have range time:Instant, inheriting the vocabulary and entailing the structures of OWL-Time as described above. None of the three subclasses of gufo:ConcreteIndividual specialize restrictions on those existence-bounding properties. Hence, without loss of generality, we can review a gufo:Endurant and see the same time-related applicability for gufo:Event.

This is an endurant (more specifically, a gufo:Object) with literal-valued instants describing the creation and termination timestamps TS0 and TS1:

[
    {
        "@id": "kb:Object-bee97e78-8e5e-4ffe-9c2b-28e960f84bbc",
        "@type": "gufo:Object",
        "rdfs:label": "T",
        "rdfs:comment": "A thing with a time-bounded existence.",
        "gufo:hasBeginPointInXSDDateTimeStamp": {
            "@type": "xsd:dateTimeStamp",
            "@value": "2020-01-02T03:04:05.6789Z"
        },
        "gufo:hasEndPointInXSDDateTimeStamp": {
            "@type": "xsd:dateTimeStamp",
            "@value": "2021-02-03T04:05:06.7890Z"
        }
    }
]

The literal-valued timestamps can also use gufo:hasBeginPointInXSDDate when only xsd:date is to be used.

This is the same endurant with reified instants housing the beginning and end:

[
    {
        "@id": "kb:Object-bee97e78-8e5e-4ffe-9c2b-28e960f84bbc",
        "@type": "gufo:Object",
        "rdfs:label": "T",
        "gufo:hasBeginPoint": {
            "@id": "kb:Instant-1a250c7b-19c5-4ec4-bed2-d05c9d438e9d",
            "@type": "time:Instant",
            "rdfs:label": "T0",
            "time:inXSDDateTimeStamp": {
                "@type": "xsd:dateTimeStamp",
                "@value": "2020-01-02T03:04:05.6789Z"
            }
        },
        "gufo:hasEndPoint": {
            "@id": "kb:Instant-bbd8741a-4af8-4358-802b-a6fb8a4cf7dc",
            "@type": "time:Instant",
            "rdfs:label": "T1",
            "time:inXSDDateTimeStamp": {
                "@type": "xsd:dateTimeStamp",
                "@value": "2021-02-03T04:05:06.7890Z"
            }
        }
    }
]

Intervals of existence do not appear to be defined directly in gUFO. Also, since only the first and last instant of a concrete individual are specified, it is also not explicit in gUFO whether an individual's interval of existence needs to be continuous. For instance, a gufo:Situation may be seen to hold for a period of time, such as a person temporarily being a student in a gufo:TemporaryInstantiationSituation¹, then not hold (e.g., when the person graduates from a school), then hold again (e.g., when the person later enrolls in another school).

Timestamps are constrained to xsd:dateTimeStamp, not xsd:dateTime, which is consistent with OWL-Time's deprecation of time:inXSDDateTime. For UCO, this would necessitate transcoding xsd:dateTime timestamps with a non-OWL, and likely non-SPARQL, mechanism.

The following figure shows the time coverage for gufo:ConcreteIndividual, re-using covering vocabulary from OWL-Time above:

The mapping for gufo:ConcreteIndividual would be as follows:

Example class or triple	Corresponding class or triple
`ex:TimeBoundedThing`	`gufo:ConcreteIndividual`
`ex:ExistenceInterval`	N/A
`ex:Instant`	`time:Instant`
`kb:T ex:hasExistenceInterval kb:E`	N/A
`kb:T ex:existsAtAndSince kb:T0`	`gufo:hasBeginPoint`
`kb:T ex:existsUntil kb:T1`	`gufo:hasEndPoint`
`kb:T ex:hasCreationTimestamp "2020-..."^^xsd:dateTime`	`kb:t gufo:hasBeginPointInXSDDateTimeStamp "2020-..."^^xsd:dateTimeStamp`
`kb:T ex:hasTerminationTimestamp "2021-..."^^xsd:dateTime`	`kb:t gufo:hasEndPointInXSDDateTimeStamp "2021-..."^^xsd:dateTimeStamp`
`kb:E ex:hasStart kb:T0`	N/A
`kb:E ex:hasEnd kb:T1`	N/A
`kb:E ex:hasBeginningTimestamp "2020-..."^^xsd:dateTime`	N/A
`kb:E ex:hasEndingTimestamp "2021-..."^^xsd:dateTime`	N/A
`kb:T0 ex:hasTimestamp "2020-..."^^xsd:dateTime`	`kb:T0 time:inXSDDateTimeStamp "2020-..."^^xsd:dateTimeStamp`
`kb:T1 ex:hasTimestamp "2021-..."^^xsd:dateTime`	`kb:T1 time:inXSDDateTimeStamp "2021-..."^^xsd:dateTimeStamp`

Aside: A side-by-side view of the gUFO and OWL-Time coverage show that an ontology importing gUFO and OWL-Time has complete coverage of the existence-intervals concepts suggested on this page.

OWL-Time	gUFO

BFO

(BFO version: 2020.)

BFO's topmost class that describes an object that exists in a period of time is "Entity" (obo:BFO_0000001). The direct subclasses "Continuant" and "Occurrent", which correspond with "Endurant" and "Perdurant" respectively, do not specialize the restrictions on the existence property "exists at".

For reference, these are the class and property labels used in the illustration:

Structural type	IRI	Label	Notes
`owl:Class`	`obo:BFO_0000001`	(BFO 1) entity
`owl:Class`	`obo:BFO_0000002`	(BFO 2) continuant
`owl:Class`	`obo:BFO_0000003`	(BFO 3) occurrent
`owl:Class`	`obo:BFO_0000008`	(BFO 8) temporal region
`owl:Class`	`obo:BFO_0000038`	(BFO 38) one-dimensional temporal region	Not necessarily continuous (can have gaps).
`owl:Class`	`obo:BFO_0000148`	(BFO 148) zero-dimensional temporal region	"...a temporal region that is a whole consisting of one or more separated temporal instants as parts."
`owl:Class`	`obo:BFO_0000202`	(BFO 202) temporal interval	Subclass of BFO 38; continous (no gaps or breaks).
`owl:Class`	`obo:BFO_0000203`	(BFO 203) temporal instant	Subclass of BFO 148; has no proper temporal parts.
`owl:ObjectProperty`	`obo:BFO_0000108`	exists at	Range is BFO 8.
`owl:ObjectProperty`	`obo:BFO_0000222`	has first instant	Range is constrained to BFO 203, not 148 (instant, not 0-d region).
`owl:ObjectProperty`	`obo:BFO_0000224`	has last instant	(As with BFO 222.)

Restrictions:

Usage of the BFO properties 222 and 224 (first and last instant) restrict the alignment of ex:Instant to obo:BFO_0000203 (temporal instant), which is more restrictive than obo:BFO_0000148 (zero-dimensional temporal region).
If existence intervals are required by a BFO-adopting ontology ontology to be continuous, the adopting ontology must use obo:BFO_0000202 (temporal interval) rather than obo:BFO_0000038 (one-dimensional temporal region).

The referenced version of BFO does not define any owl:DatatypePropertys.

The mapping for BFO's entity (BFO-1) would be as follows:

Example class or triple	Corresponding class or triple
`ex:TimeBoundedThing`	`obo:BFO_0000001`
`ex:ExistenceInterval`	`obo:BFO_0000038`
`ex:Instant`	`obo:BFO_0000203`
`kb:T ex:hasExistenceInterval kb:E`	`kb:T obo:BFO_0000108 kb:E`
`kb:T ex:existsAtAndSince kb:T0`	N/A
`kb:T ex:existsUntil kb:T1`	N/A
`kb:T ex:hasCreationTimestamp "2020-..."^^xsd:dateTime`	N/A
`kb:T ex:hasTerminationTimestamp "2021-..."^^xsd:dateTime`	N/A
`kb:E ex:hasStart kb:T0`	`kb:E obo:BFO_0000222 kb:T0`
`kb:E ex:hasEnd kb:T1`	`kb:E obo:BFO_0000224 kb:T1`
`kb:E ex:hasBeginningTimestamp "2020-..."^^xsd:dateTime`	N/A
`kb:E ex:hasEndingTimestamp "2021-..."^^xsd:dateTime`	N/A
`kb:T0 ex:hasTimestamp "2020-..."^^xsd:dateTime`	N/A
`kb:T1 ex:hasTimestamp "2021-..."^^xsd:dateTime`	N/A

Footnotes

gUFO represents instantations that are not always true with gufo:TemporaryInstantiationSituation. In the case where a person is temporarily a student, "student" is taken to be some subclass of "person" - e.g., ex:Student rdfs:subClassOf ex:Person. For some time, it holds that kb:person-3393... a ex:Student, but this is not always true. To hold this situationally-true statement in a knowledge graph, a gufo:TemporaryInstantiationSituation is included to note the conditions when kb:person-3393... is a ex:Student, instead of encoding the unqualified triple kb:person-3393... a ex:Student. See kb:TemporaryInstantiationSituation-da1aa582-1358-49bb-b058-4c33990fb9e8 in existence_intervals.json for a demonstration of this representation. ↩ ↩²

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Existence Intervals

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BFO

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Existence Intervals

UCO 1.3.0

OWL-Time

gUFO

BFO

Footnotes