BFO: Basic Formal Ontology 1

Abstract

Basic Formal Ontology (BFO) is a top-level ontology consisting of thirty-six classes, designed to support information integration, retrieval, and analysis across all domains of scientific investigation, presently employed in over 350 ontology projects around the world. BFO is a genuine top-level ontology, containing no terms particular to material domains, such as physics, medicine, or psychology. In this paper, we demonstrate how a series of cases illustrating common types of change may be represented by universals, defined classes, and relations employing the BFO framework. We provide discussion of these cases to provide a template for other ontologists using BFO, as well as to facilitate comparison with the strategies proposed by ontologists using different top-level ontologies.

Keywords

BFO top-level ontology ontological analysis formal ontology

1. Introduction

In this paper, we demonstrate how Basic Formal Ontology (BFO) may be used to represent six cases involving change. These cases, their goals, and their accompanying focus statements are discussed in order to provide a template for other ontologists using BFO, as well as to facilitate comparison with the strategies proposed by ontologists using different top-level ontologies. Basic Formal Ontology2

²
International Organization for Standardization. (2021). Information technology – Top-level ontologies (TLO) – Part 2: Basic Formal Ontology (BFO) (ISO Standard No. 21838-2:2020). Retrieved from https://standards.iso.org/ittf/PubliclyAvailableStandards/c074572_ISO_IEC_21838-2_2021(E).zip.

is a top-level ontology designed to support information integration, retrieval, and analysis across all domains of scientific investigation. Containing only general terms common across disciplines, BFO serves as the top-level ontology of the Open Biomedical and Bioinformatic Ontology (OBO) Foundry [Smith et al., 2007] and the Industrial Ontology Foundry (IOF) [Smith et al., 2019]. Moreover, BFO provides a starting point for over 350 known ontology extensions3

Users of BFO. Accessed December 25, 2020 at http://basic-formal-ontology.org/users.html.

covering more specific domains, such as infectious disease [Cowell & Smith, 2010], plant development [Walls et al., 2019], and processed materials [Smith et al., 2019]. BFO has been designated an ISO standard [Smith et. al., 2021] and BFO’s ISO 21838-2 specification has been axiomatized in First-Order Logic, OWL 2, and CLIF [Ruttenberg, 2020].4

⁴

To see the full axiomatization and track issues, see https://github.com/BFO-ontology/BFO-2020/tree/master/21838-2.

BFO is committed to the following principles, which distinguish it from other top-level ontologies [Masolo et al., 2004]:

Ontological Realism – The goal of an ontology is to describe reality. Scientific investigation is concerned with general features of reality and relations among them. Consequently, BFO consists fundamentally of representations of reality rather than language, concepts, or mental representations about reality [Arp, Smith, & Spear, 2015].

Fallibilism – Whereas universals themselves do not change, our understanding of them must in light of new discoveries. While present scientific theories are assumed to be our best sources of accurate statements about reality, BFO recognizes, of course, that present scientific theories may be incorrect. Consequently, BFO is committed to tracking scientific developments over time, and updating ontologies in accordance with scientific developments [Arp, Smith, & Spear, 2015].

Adequatism – Entities in a domain should not be assumed to be reducible to other kinds of entities. All scientific disciplines are worthy of representation in their own terms, and it is not necessary to paraphrase talk of these entities in terms of a privileged set of entities (e.g. those described by physics). This commitment contrasts with reductionism, which seeks to reduce entities described by some domain of science to another deemed more fundamental [Arp, Smith, & Spear, 2015].

2. Principles and structure of BFO

BFO adopts the following fundamental categories [Arp, Smith, & Spear, 2015, Smith & Ceusters, 2010, Bittner & Smith, 2001]:

universal and particular – Particulars are individual denizens of reality restricted to specific times and places, which instantiate universals, but which cannot be instantiated. Universals are repeatable across time and space and may have an indefinite number of instantiated particulars [Grenon, 2003, Arp & Smith, 2008].

continuant and occurrent – BFO is largely partitioned into disjoint universals.5

⁵
The exceptions to disjointedness are BFO’s classes fiat object part, object, and object aggregate. Some instances may belong to more than one of these classes.

The upper bifurcation is distinguished by how particulars relate to time. Continuants endure through time maintaining identity, have no temporal parts, and are fully-present at any time they exist. Examples include house cats, the color of an apple, the function of mitochondria. By contrast, occurrent entities unfold over time or have temporal parts. Examples include: the history of Japan, drinking a cup of coffee, the temporal interval on which a mitotic division occurs [Smith & Mulligan, 1982].

relations – BFO adopts three basic relation types: universal-universal, universal-particular, and particular-particular, the latter two of which may be time indexed. Universal-universal relations in BFO relate subtypes to parent types, whereas the sole universal-particular relation is the instance of relation, which holds between particulars and the universals under which they fall [Zemach, 1970].

We discuss here only those classes necessary for the comprehension of the cases.6

⁶

We leave aside discussion of fiat object part, spatial region and its subclasses, process boundary, spatiotemporal region, relational quality, history, and continuant fiat boundary and its subclasses, as these classes were not necessary to represent the cases under discussion.

In what follows, definitions are indicated with the use of “

=_{def}

”, and those entries regarding classes that lack this symbol are elucidations. First, subclasses of continuant:

a is an independent continuant $=_{def}$ a is a continuant which is such that there is no b such that a specifically depends on b and no b such that a generically depends on b.

material entity – an independent continuant that at all times at which it exists has some portion of matter as continuant part.

object – a material entity that manifests causal unity and is of a type instances of which are maximal relative to the sort of causal unity manifested.

object aggregate – a material entity consisting exactly of ( $⩾ 1$ ) object(s) as member(s).

a is an immaterial entity $=_{def}$ a is an independent continuant which is such that there is no time t when it has a material entity as continuant part.

site – a three-dimensional immaterial entity whose boundaries either (partially or wholly) coincide with the boundaries of one or more material entities or have locations determined in relation to some material entity.

An independent continuant may bear dependent continuants, including:

generically dependent continuant – an entity that exists in virtue of the fact that there is at least one of what may be multiple copies; it is the content or the pattern that the multiple copies share.

b is a specifically dependent continuant $=_{def}$ b is a continuant and there is some independent continuant c which is not a spatial region and which is such that b specifically depends on c.

realizable entity – a specifically dependent continuant that inheres in some independent continuant that is not a spatial region and is of a type some instances of which are realized in processes of a correlated type.

role – a realizable entity that exists because there is some single bearer that is in some special physical, social, or institutional set of circumstances in which this bearer does not have to be and which is not such that, if it ceases to exist, then the physical make-up of the bearer is thereby changed.

disposition – a realizable entity such that if it ceases to exist, then its bearer is physically changed, and whose realization occurs when and because its bearer is in some special physical circumstances, and this realization occurs in virtue of the bearer’s physical make-up.

function – a disposition that exists in virtue of the bearer’s physical make-up and this physical make-up is something the bearer possesses because it came into being either through evolution (in the case of natural biological entities) or through intentional design (in the case of artifacts), in order to realize processes of a certain sort.

quality – a specifically dependent continuant that, in contrast to roles and dispositions, does not require any further process in order to be realized.

From the occurrent portion of the hierarchy, we include the following:

p is a process $=_{def}$ p is an occurrent that has some temporal proper part and for some time has some material entity as participant.

temporal region – an occurrent over which processes can unfold.

temporal instant – a zero-dimensional temporal region that has no proper temporal part.

temporal interval – a one-dimensional temporal region that is continuous, thus without gaps or breaks.

There is often a practical need to accommodate terms in scientific discourse that do not correspond to universals. Examples of such terms include ‘medical doctor’ and disjunctions such as ‘dog or cat’. BFO uses ‘defined classes’ to accommodate such terms. The extension of a defined class is characterized by necessary and sufficient conditions whose non-logical symbols denote relations, universals, or instances of universals. Thus, ‘medical doctor’ is only a short-hand way of referring to instances of persons who bear a medical doctor role, and to be a ‘dog or cat’ is nothing over and above being an instance of dog or an instance of cat. All defined classes are characterized by necessary and sufficient conditions, but the converse is not true. The distinction between a defined class and a universal is unique to BFO.

3. Formalization of BFO in first-order logic

We describe a fragment of the BFO ISO 21838-2 First-Order Logic (FOL) axiomatization [Ruttenberg, 2020]. The domain is comprised of particulars that stand in the primitive instance of relation to universals at times. BFO’s hierarchy of universals can be represented by defining the relation:7

⁷
This relation is not included in the BFO-ISO specification, but is defined here to simplify discussion.

\begin{array}{l} \forall x, t, A, B is a (A, B) =_{def} instance of (x, A, t) \to instance of (x, B, t) \end{array}

For example, material entity is a independent continuant. Visual representation of BFO’s hierarchy can be found in Fig. 1 and Fig. 2 .

Fig. 1.

BFO continuant hierarchy.

Fig. 2.

BFO occurrent hierarchy.

By rigid universal $U_{r}$ , we mean any entity that is instantiated by $U_{r}$ , instantiates $U_{r}$ for the whole of its existence. All classes in BFO are rigid other than the three subclasses of material entity: fiat object part, object, and object aggregate. For example, an instance of object aggregate at some time may later instantiate object.

BFO’s theory of parts is modeled after Minimal Extension Mereology (MEM) [Simons, 1987]. MEM is described in terms of binary part relations, but is extended to handle the time-indexed relations. The MEM axioms state that a part relation is reflexive, antisymmetric, transitive, weakly supplemented, and exhibits the unique product property. Any time-indexed relation implies that the first two relata exist, and holds at any time the relata exist. For instance, when a time-indexed relation is reflexive we mean that the self-relationship refers to the first two relata and it must hold at any time the relata exist.

BFO has two part of relations, one for continuants, called continuant part of and one for occurrents called occurrent part of. Continuant part of is time indexed, whereas occurrent part of is not. Worth noting is the treatment of the anti-symmetry of continuant part of applied to object aggregates. If a continuant part ofb at some t and bcontinuant part ofa at the same time t, we do not conclude that $a = b$ .

Using these relations we can define irreflexive, asymmetric, transitive proper occurrent part of and proper continuant part of relations in the usual way.

Starting at the continuant side of the BFO hierarchy in Fig. 1 , an independent continuant is distinguished from other continuants in that they neither generically nor specifically depend on other entities. In contrast, a specifically dependent continuant specifically depends on an independent continuant8

⁸

In a number of relations involving independent continuants the relation is actually valid only if the entity is a spatial region. In order to keep the discussion simpler, we do not mention it in the body.

rigidly. If xspecifically depends ony, then as long as x exists, the relation holds. If y ceases to exist, then x does as well.

A specifically dependent continuant is said to inhere in – a relation defined in terms of specifically depends on – an instance of independent continuant. The inverse of inheres in is bearer of. A generically dependent continuant is concretized by a process or specifically dependent continuant. When the concretization is a specifically dependent continuant the generically dependent continuant generically depends on the specifically dependent continuant’s bearer.

All independent continuants other than spatial regions occupy a spatial region, and so are extended in space and time. Some may be located in others at some time, as the food you ingest is at some point located in the lumen of your stomach after you have eaten. Located in is transitive.

A material entity can be continuant part of another material entity at some time. Material entities can have material and immaterial parts. An object can be member part of an object aggregate. Member part of is not transitive but implies continuant part of. An object aggregate always has at least one member, and must, at some time, have more than one.

Any independent continuant, specifically dependent continuant, or generically dependent continuant can participate in a process. In the latter two cases, it is implied that their bearer also participates in the process. When a process realizes a realizable entity, the realizable entity’s bearer also participates in the process. When a generically dependent continuant participates in a process p, some concretization of the generically dependent continuant participates in p. If that concretization is a process, it is temporal part of p.

A process occupies temporal region some temporal region. Processes have at least one process boundary as part. The temporal region that a process occupies must have as part a temporal interval. A process boundary can only occupy a temporal instant.

An occurrent can be a temporal part of some other. Occurrent parts can differ from what they are part of both spatially and temporally (e.g. the process which occurs in the left half of a soccer field during the first period of a game). By contrast, temporal part of an occurrent differs in that there is no difference in the spatial extent of the part and the whole.

Temporal regions provide the indices for all the time-indexed ternary relations in BFO. A temporal region has first instant and has last instant a temporal instant marking its extrema. A first or last instant can be temporal part of the region or not. A temporal instant that precedes the last instant of a temporal interval and are preceded by the interval’s first instant are necessarily part of the interval. Using these relations, the familiar and widely used Allen’s interval algebra may be formulated [Smith, et. al., 2011].

4. Analysis and formalization in BFO: Examples

In this section, we examine several cases reflecting composition, roles, property and event change, and scientific progress. As BFO is a small top-level ontology comprised of domain-neutral terms, the examples use either terms we define in this paper, or wherever possible, existing terms from BFO-aligned ontologies within the OBO Foundry library9

⁹
https://obofoundry.org/

and The Common Core Ontologies (CCO) [Rudnicki, 2016].

Since the cases reflect changes over time, temporal intervals will be used throughout. We introduce some formalization here to avoid repetitions. In each case, we will use “i” to represent the interval during which the case unfolds. We will use subscripts on “i” to represent proper10

¹⁰

Any “proper” relation $R (x, y)$ used here should be understood as $R (x, y) \land x \neq y$ .

interval parts of i ordered by precedence. Formally:

instance of(i, temporal interval, i)

$⋀_{1 ⩽ k ⩽ n}$ instance of( $i_{k}$ , temporal interval, $i_{k}$ )

$⋀_{1 ⩽ k ⩽ n}$ proper temporal part( $i_{k}$ , i)

$⋀_{1 ⩽ k < n}$ precedes( $i_{k}$ , $i_{k + 1}$ )

In our examples, there are cases where we mention the possibility of enrichment using representations of information content entities. The term originates in the Information Artifact Ontology (IAO), an ontology that extends BFO. In what follows, we attempt to convey the flavor of such representations.

An information content entity (ICE) is a generically dependent continuant that is about some entity and can be concretized as, e.g., as one’s name may be concretized in the shape quality of the ink that inheres in a piece of paper. We say the ICE generically depends on one or more material entities. An information bearing entity (IBE) is a material entity designed to be a carrier of information content e.g., a piece of paper.

Fig. 3.

Relationships among information content entities and bearers.

In Fig. 3 we illustrate11

¹¹

In figures throughout, we use circular nodes to represent both universals and defined classes, and diamonds to represent particulars.

one representation involving a measurement ICE that is about a process of walking. ICEs can be concretized on multiple bearers. A novel may be concretized by patterns of ink in multiple physical books or may be concretized by the digital patterns in different network servers; when this occurs, the novel (an information content entity) then generically depends on the physical books and network servers.

In Fig. 3 , the concretization of the measurement ICE can be understood as some text (understood as a quality) written on the IBE. The relationship “has text value”, with the target being a string, should be understood as a shorthand representation of the relationship of the IBE to the concretization that is the phrase “2 miles per hour” recorded on the IBE.

4.1. Composition/constitution

CASE 1: There is a four-legged table made of wood. Sometime later, a leg of the table is replaced. Even later, the table is demolished so it ceases to exist although the wood is still there after the demolition.

GOAL: The example aims to show if and how the ontology models materials, objects, and components and the relationships among them.

FOCUS: The relationship between the wood and the table and the table’s parts over time. (Artefacts and functions are not the focus.)

Table 1
Classes used to formalize Case 1

Class Definition or elucidation

Portion of wood A material entity that was formerly part of one or more tree trunks or branches

Table function A function that inheres in a material entity with a flat surface that has realization a process during which a material entity is placed on the bearer without it falling off

Leg function A function that inheres in a stiff object and which has realization a process of support and elevation of other objects

Table destruction process A process during which a material entity bearer of a table function loses that table function

Class	Definition or elucidation
Portion of wood	A material entity that was formerly part of one or more tree trunks or branches
Table function	A function that inheres in a material entity with a flat surface that has realization a process during which a material entity is placed on the bearer without it falling off
Leg function	A function that inheres in a stiff object and which has realization a process of support and elevation of other objects
Table destruction process	A process during which a material entity bearer of a table function loses that table function

Table 2

Particulars used to formalize Case 1

Particular	Description
wood	The portion of wood that has continuant partleg 1 at i2 and leg 2 at i5
leg 1	The object that is bearer ofleg function 1. leg 1 is replaced in the example.
leg 2	The object that is bearer ofleg function 2. leg 2 replaces leg 1 in the example.
table function	The table function that inheres inwood
leg function 1	The leg function that inheres inleg 1
leg function 2	The leg function that inheres inleg 2
leg replacement process	A process during which leg 1 is replaced by leg 2
table destruction process	A process resulting in wood losing table function
i1	The temporal interval during which wood is bearer oftable function
i2	The temporal interval during which leg 1 is proper continuant part ofwood
i3	The temporal interval during which leg 1 is bearer ofleg function 1
i4	The temporal interval occupied byleg replacement process, which leg 1, leg 2, and woodparticipate in
i5	The temporal interval during which leg 2 is proper continuant part ofwood
i6	The temporal interval at which leg 2exists at
i7	The temporal interval occupied bytable destruction process in which wood loses table function

BFO does not have a constitution relation such as “made of”, typically related to an entity described as a mass noun. Instead, our example directly represents the particular portion of wood and its parts which are, when the table exists, part of the table. In Tables 1 – 3 , we describe the classes, particulars, and relations we will use in our discussion. The portion of wood exists throughout the interval but changes. At the beginning of the interval, the portion of wood bears a table function and has parts that bear leg functions. The portion of wood participates in a leg replacement process, during which one of its proper parts that bears a leg function is replaced by a material entity bearing a leg function. After the replacement, the original leg is no longer part of the portion of wood, and the replacement leg is now part of it. Afterward, the portion of wood participates in a destruction process, during which it loses its table function.

Table 3

Relations used to formalize Case 1

Relation	Usage
bearer of	Holding between a portion of wood and a function it bears. bearer of is the inverse of inheres in
exists at	Holding between an entity and a temporal interval when it exists
occupies temporal region	Holding a process and just those temporal intervals over which the process unfolds.
has participant	Holding between a process, a material entity involved in that process, and the temporal region at which the process occurs
proper continuant part of	Holding between a proper mereological part of wood and wood itself, at the temporal region during which they are parts.

wood is an instance of portion of wood throughout i1–i7 and so throughout the interval i12

¹²

See the introduction to Section 4 for formalization of the relationship between i and its sub-intervals.

which they comprise:

is a(portion of wood, material entity)

instance of(wood, portion of wood, i)

wood bears a table function and has proper continuant part several legs. We focus on leg 1. We relate respective functions and material bearers:

instance of(leg function 1, leg function, i3)

instance of(table function, table function, i1)

instance of(leg 1, object, i3)

instance of(wood, object, i2)

bearer of(wood, table function)

bearer of(leg 1, leg function 1)

proper continuant part of(leg 1, wood, i2)

wood, leg 1, and leg 2participate inleg replacement process:

instance of(leg function 2, leg function, i6)

instance of(leg 2, object, i6)

bearer of(leg 2, leg function 2)

¬continuant part of(leg 2, wood, i3)13

¹³

Strictly speaking, leg 2 is also not a continuant part ofwood at earlier times. Corresponding axioms are assumed but not displayed here.

instance of(leg replacement process, leg replacement process, i4)

occupies temporal region(leg replacement process, i4)

participates in(leg 1, leg replacement process, i4)

¬continuant part of(leg 1, wood, i5)14

¹⁴

Strictly speaking, leg 1 is also not a continuant part ofwood at later times. Corresponding axioms are assumed but not displayed here.

participates in(leg 2, leg replacement process, i4)

proper continuant part of(leg 2, wood, i5)

Afterwards, wood and its parts participate in an instance of table destruction process:

instance of(table destruction process, table destruction process, i7)

occupies temporal region(table destruction process, i7)

participates in(wood, table destruction process, i7)

$\exists t$ occurrent part of(t, i7) $\land \neg$ exists at(table function, t)

We leave open whether proper parts of wood maintain their respective functions. That is compatible with the case that most proper parts of wood parts maintain their functions but are arranged such that wood loses table function. In any event, woodexists ati7 though table function does not. Fig. 4 provide an illustration of the change described in this case.

Fig. 4.

Wood undergoing change in Case 1.

4.2. Roles

CASE 2: Mr. Potter is the teacher of class 2C at Shapism School and resigns at the beginning of the spring break. After the spring break, Mrs. Bumblebee replaces Mr. Potter as the teacher of 2C. Also, student Mary left the class at the beginning of the break and a new student, John, joins in when the break ends.

GOAL: The example aims to show if and how the ontology models the relationships between roles, players and organizations.

FOCUS: The change of roles/players; the vacancy of the teaching position; persistence of the class while students come and go.

Mr. Potter is – we assume – the only teacher of class 2C prior to Spring Break and participates in an act of resignation prior to this break. Classes at Shapism School are not in session during the break, but during this time Mrs. Bumblebee and Shapism School agree that Mrs. Bumblebee will bear a 2C teacher role at the end of Spring Break. We focus on only Mr. Potter and Mrs. Bumblebee in our formalization, as the loss of student Mary and gain of student John during this interval does not differ greatly from the loss of teacher Mr. Potter and gain of teacher Mrs. Bumblebee. We use the following assignment in our formalization (Tables 4–6).

Table 4
Classes used to formalize Case 2

Class Definition or elucidation

Person An object belonging to the species Homo sapiens and distinguished by a high level of intelligence.

Organization An independent continuant that can bear roles, has members, and has a set of organization rules.

Class	Definition or elucidation
Person	An object belonging to the species Homo sapiens and distinguished by a high level of intelligence.
Organization	An independent continuant that can bear roles, has members, and has a set of organization rules.

Table 5

Particulars used to formalize Case 2

Particulars	Descriptions
Mr. Potter	An instance of person
Mrs. Bumblebee	An instance of person
Shapism School	An instance of organization, the academic employer of Mr. Potter and Mrs. Bumblebee
2C	A member part ofShapism School, including the teachers and the students they teach
2C teacher role 1	The role borne by Mr. Potter as the teacher of class 2C
2C teacher role 2	The role borne by Mrs. Bumblebee as the teacher of class 2C
act of resignation	The process during which Mr. Potter resigns from his role as teacher of class 2C
act of teaching assignment	The process during which Shapism School and Mrs. Bumblebee coordinate resulting in Mrs. Bumblebee becoming teacher of 2C
spring break	A process during which Spring Break occurs
i1	The interval during which Mr. Potter is a member part of2C
i2	The interval during which 2C is a member part ofShapism School
i3	The interval during which Mr. Potterparticipates inact of resignation
i4	The interval during which Mrs. Bumblebeeparticipates in an act of teaching assignment
i5	The interval occupied by the act of teaching assignment in which Mrs. Bumblebee and Shapism Schoolparticipate
i6	The interval during which Shapism Schoolparticipates in an act of teaching assignment
i7	The interval during which Mrs. Bumblebee is a member part of2C

Table 6

Relations used to formalize Case 2

Relations	Descriptions
bearer of	Holds between instances of person and the teacher roles which inhere in that person
proper temporal part of	Holds between temporal intervals and the larger interval of which they are occurent part
occupies temporal region	Holds between processes and just those temporal intervals over which they unfold
participates in	Holds between material entities and the processes in which they are involved
member part of	Holds between object aggregates and their members
has specified output	Holds between act of teaching assignment and Mrs. Bumblebee’s 2C teacher role

Mr. Potter and Mrs. Bumblebee are instances of person [Rudnicki, 2016]. Shapism School is an instance of organization [Bandrowski, 2016, Smith, et. al., 2019]. Organizations may have other organizations as member parts, allowing for class 2C to be member part ofShapism School:

is a(person, object)

is a(organization, object aggregate)

instance of(Mr. Potter, person, i)

instance of(Mrs. Bumblebee, person, i)

instance of(Shapism School, organization, i)

member part of(2C, Shapism School, i)

Mr. Potter was a member part of2C prior to the start of spring break. Mrs. Bumblebee was not a member of2C during this time. Before spring break begins, Mr. Potterparticipates in an act of resignation so that during and after spring break Mr. Potter is no longer a member part of2C. We leave open whether Mr. Potter remains a member ofShapism School during and after spring break:

member part of(Mr. Potter, 2C, i1)

¬member part of(Mrs. Bumblebee, 2C, i1)

instance of(spring break, process, i)

instance of(act of resignation, process, i3)

participates in(Mr. Potter, act of resignation, i3)

¬member part of(Mr. Potter, 2C, i4)15

¹⁵

Mr. Potter is, additionally, not a member part of2C during subsequent intervals.

Shapism School and Mrs. Bumblebeeparticipate inact of teaching assignment resulting in Mrs. Bumblebee being a member part of2C after spring break.

occupies temporal region(act of teaching assignment, i5)

proper temporal part of(i4, i5)

proper temporal part of(i6, i5)

participates in(Shapism School, act of teaching assignment, i6)

participates in(Mrs. Bumblebee, act of teaching assignment, i4)

Fig. 5.

Resignation and assignment of 2C teacher roles in Case 2.

member part of(Mrs. Bumblebee, 2C, i7)

With respect to relevant roles, Mr. Potter bears 2C teacher role 1 – a role borne by a unique person who is a member part of2C at a given time. Following the act of teaching assignment in which Shapism School and Mrs. Bumblebee participate, Mrs. Bumblebee is the unique bearer of 2C teacher role 2. There is, to date, no well developed treatment of titles, organizational positions, and offices as such, where these are understood to be independent of the particular role that persons bear when holding such offices. This may arise in cases, for instance, where one wishes to refer to advertise an open teaching position at the school. A plausible representation might be as generically dependent continuants.

bearer of(Mr. Potter, 2C teacher role 1)

¬exists at(2C teacher role 1, i4)16

¹⁶

2C teacher role does not exist during subsequent intervals.

has specified output(act of teaching assignment, 2C teacher role 2)17

¹⁷

2C teacher role does not exist before interval i5.

bearer of(Mr. Bumblebee, 2C teacher role 2)

4.3. Property change

CASE 3: A flower is red in the summer. As time passes, the color changes. In autumn the flower is brown.

GOAL: The example aims to show if and how the ontology models change in qualities/properties.

FOCUS: The change of the color of a flower.

Color is a messy phenomenon. Color ascriptions can be described at different levels of granularity, for example, the whole flower, flower petals, or proper surface parts of petals. Distributions of colors at one level of granularity often determine color at higher levels of granularity. For example, classification of a petal as “red” depends on the distribution of red on proper parts of the petal’s surface. Additionally, color may be understood as qualities, or dispositions to cause color experiences, or the color experiences themselves. We will thus need to simplify our formalization. We focus on a specific petal of the flower for simplicity, noting our formalization can be applied to lower or higher levels of granularity. Moreover, we focus on colors as qualities of entities, rather than dispositions to cause experiences or as experiences. Broadly speaking then, the petal bears a red color quality during summer, the type of which changes to brown during fall. During this time, the flower participates in an act of withering. We use the following assignments in our formalization (Tables 7–9).

Table 7
Classes used to formalize Case 3

Class Definition or elucidation

Petal A material entity that often surrounds reproductive parts of some flower

Flower A material entity that generates seeds during a reproductive cycle

Color A quality borne by a material entity that underwrites the reflection of light

Red A color with wavelength between 625 and 740 nanometers

Brown A color with wavelength of approximately 600 nanometers, with low saturation and luminance

Class	Definition or elucidation
Petal	A material entity that often surrounds reproductive parts of some flower
Flower	A material entity that generates seeds during a reproductive cycle
Color	A quality borne by a material entity that underwrites the reflection of light
Red	A color with wavelength between 625 and 740 nanometers
Brown	A color with wavelength of approximately 600 nanometers, with low saturation and luminance

Table 8

Particulars used to formalize Case 3

Particular	Description
petal	The petal that bears a color quality that changes from red to brown
flower	The flower whose petalcontinuant part changes color through the season change
color	The color borne by the petal that changes from red to brown
summer	The process during which the petal begins as red and gradually becomes closer in color to brown
fall	The process during which the petal begins as reddish brown, but gradually becomes brown
process of withering	The process during which the flower loses elasticity and vibrancy
i1	The interval occupied by summer
i2	The interval occupied by fall
i3	The interval during which color is an instance of red, which is an occurrent part of both i1 and i6
i4	The interval occupied by process of withering, which is an occurrent part of i2
i5	The interval during which color is an instance of brown, which is an occurrent part of both i4 and i6
i6	The interval during which color is an instance of color

Table 9

Relations used to formalize Case 3

Relation	Usage
participates in	Holds between flower and process of withering
occupies temporal region	Holds between summer, fall, process of withering, and the respective temporal regions they each occupy
occurrent part of	Holds between temporal intervals and larger intervals of which they are parts
proper continuant part of	Holds between petal and the flower of which it is a part
bearer of	Holds between petal and the color that it bears

We use the classes flower and petal [Walls et al., 2019, Jaiswal et al., 2005] and assert the instance flower of the former has continuant partpetal, which is an instance of the latter:

instance of(flower, flower, i)

instance of(petal, petal, i)

proper continuant part of(petal, flower, i)

Color is a specifically dependent continuant in BFO [Smith, 2012]. We assert two subclasses of color: red and brown, and we furthermore assert that petal bears an instance of color:

is a(color, quality)

is a(red, color)

is a(brown, color)

instance of(color, color, i6)

bearer of(petal, color)

The color borne by petal is an instance of red during summer, and an instance of brown during fall:

instance of(summer, process, i1)

Fig. 6.

Petal changing color in Case 3.

instance of(fall, process, i2)

occupies temporal region(summer, i1)

occupies temporal region(fall, i2)

instance of(color, red, i3)

instance of(color, brown, i5)

occurrent part of(i3, i1)

occurrent part of(i3, i6)

occurrent part of(i5, i4)

occurrent part of(i5, i6)

The flowerparticipates in a process of withering that occurs during fall:

instance of(process of withering, process, i4)

occupies temporal region(process of withering, i4)

occurrent part of(i4, i2)

CASE 4: A man is walking when suddenly he starts walking faster and then breaks into a run.

GOAL: The example aims to show if and how the ontology models change during an event.

FOCUS: The change in the speed and mode of locomotion.

Processes do not change; they are changes. Participating in an act of locomotion, however, may have proper process walking, accelerating, and running parts. Intuitively, walking and running consist of sequences involving an agent who makes patterned contact with the ground using their feet, over some duration. For a given agent and given duration, walking is distinguished from running based on the number of moments of contact between the agent’s feet and the ground. If this number is above some threshold, which may vary given the agent’s size and shape, then it will count as running. An individual is accelerating when there is a patterned decrease in the duration between contacts with the ground and an increase in the spatial distance traversed by the agent.

In this case, a man is participating in an act of locomotion having proper process parts an act of walking, act of running, and act of accelerating. Our formalization uses the following assignments (Tables 10 and 11).

Table 10

Particulars used to formalize Case 4

Particulars	Descriptions
man	An instance ofperson who bears some male gender
act of locomotion	An instance of process in which the man changes spatial position
act of walking	An instance of process in which the man changes spatial position exerting little effort, at a low speed
act of accelerating	An instance of process in which the man increases speed at which he changes spatial position
act of running	An instance of process in which the man changes spatial position, while exerting significant effort, at a high speed
i1	The interval during which the manparticipates in an act of walking
i2	The interval during which the manparticipates in an act of accelerating
i3	The interval during which the manparticipates in an act of running

Table 11

Relations used to formalize Case 4

Relations	Usage
proper occurrent part of	Holds between acts of accelerating, walking, and the larger act of locomotion of which they are parts
participates in	Holds between the man and processes in which he participates

The man participates in an act of locomotion.

instance of(man, person, i)

instance of(act of locomotion, process, i)

participates in(man, act of locomotion, i)

This process is comprised of proper occurrent parts [Smith, 2012] – an act of walking, act of accelerating, and act of running. The man participates in each. Fig. 7 illustrates our formalization of the case.

proper occurrent part of(act of walking, act of locomotion)

proper occurrent part of(act of accelerating, act of locomotion)

proper occurrent part of(act of running, act of locomotion)

proper occurrent part of(act of accelerating, act of walking)

proper occurrent part of(act of accelerating, act of running)

participates in(man, act of walking, i1)

participates in(man, act of accelerating, i2)

participates in(man, act of running, i3)

While our characterization of this case is general, complementary refinements could be added. For example, the man’s changing speed at times during this case might be represented as measurements taken at temporal parts of the interval. Fig. 3 provides a recipe for characterizing measurements using instances of generically dependent continuant, as evidenced in the next case. Moreover, our analysis of the next case illustrates a further complementary characterization of changing motion.

Fig. 7.

Man moving with increasing speed in Case 4.

4.4. Event change

CASE 5: A man is walking to the station, but before he gets there, he turns around and goes home.

GOAL: The example aims to show if and how the ontology models change in goal-directed activities.

FOCUS: An activity/event is not completed and another activity/event is completed instead.

The man commits himself to a plan to walk to the station, which is specified in terms of actions he might take and the objective he seeks. Prior to arriving at the station, the man abandons his initial plan, and forms another, this time to turn around and walk home. As before, the man’s plan to walk home is specified in terms of actions he might take and the objective he seeks. In this case, the man achieves his objective.

Table 12
Classes used to formalize Case 5

Class Definition or elucidation

Plan A realizable entity that inheres in a bearer who is committed to realizing it as a planned process

Plan specification An information entity with action specifications and objective specifications as continuant parts that, when concretized, is realized in a process in that the bearer tries to achieve the objectives by taking the actions specified

Information content entity A generically dependent entity that depends on some artifact and stands in a relation of aboutness to some entity

Action specification An information entity that describes an action the bearer of the information entity will take

Objective specification An information entity that describes an intended process endpoint. When continuant part of a plan specification the concretization is realized in a planned process in which the bearer tries to effect the world so that the process endpoint is achieved

Facility A material entity that is designed as a building or campus dedicated to some specific purpose

Planned process A process that realizes a plan that is the concretization of a plan specification

Class	Definition or elucidation
Plan	A realizable entity that inheres in a bearer who is committed to realizing it as a planned process
Plan specification	An information entity with action specifications and objective specifications as continuant parts that, when concretized, is realized in a process in that the bearer tries to achieve the objectives by taking the actions specified
Information content entity	A generically dependent entity that depends on some artifact and stands in a relation of aboutness to some entity
Action specification	An information entity that describes an action the bearer of the information entity will take
Objective specification	An information entity that describes an intended process endpoint. When continuant part of a plan specification the concretization is realized in a planned process in which the bearer tries to effect the world so that the process endpoint is achieved
Facility	A material entity that is designed as a building or campus dedicated to some specific purpose
Planned process	A process that realizes a plan that is the concretization of a plan specification

Table 13

Particulars used to formalize Case 5

Particulars	Descriptions
man	The person who bears some male gender in the scenario
plan 1	The plan that the man forms to walk to the station
plan 2	The plan that the man forms to turn around and walk home
station plan specification	The plan specification having continuant partstation action specification and station objective specification
station action specification	An action specification describing the steps the man intends to take to walk to the station
station objective specification	The objective specification describing reaching the station as the objective of the station plan specification
home plan specification	The plan specification having parts home action specification and home objective specification
home action specification	The action specification describing the steps the man intends to take to turn around and walk home
home objective specification	The objective specification describing reaching home as the objective of the home objective plan
station	The facility to which the man initially intends to walk
home	The facility to which the man later walks
station description	The information content entity describing the station, that is continuant part of the station objective specification
home description	The information content entity describing the home, that is continuant part of the home objective specification
4mph walk	The process during which the man walks at an approximate velocity of 4 mph
3mph walk	The process during which the man walks at an approximate velocity of 3 mph
180 turn	The process during which the man turns 180 degrees
i1	Interval during which the station plan specification exists, and during which the station action specification and objective specification are proper continuant parts of the station plan specification
i2	Interval during which is station plan specificationconcretized byplan 1
i3	Interval during which the manparticipates in the 4mph walk process
i4	Interval during which the manparticipates in the 180 turn process
i5	Interval during which the manparticipates in the 3mph walk process
i6	Interval during which home plan specification is concretized byplan 2
i7	Interval during which the home plan specification exists, and during which the home action specification and objective specification are proper continuant parts of the home plan specification

Table 14

Relations used to formalize Case 5

Relations	Descriptions
concretized by	Holds between station plan specification, home plan specification, and plan 1 and plan 2, respectively
proper continuant part of	Holds between the action and objective specifications and the respective plan specifications, as well as between the descriptions and objective specifications
exists at	Holds between the plan specifications and the temporal intervals at which they exist
is about	Holds between descriptions and the entities they describe
bearer of	Holds between the man and plan 1 and plan 2
prescribes	Holds between an action specification and the processes that the specification prescribes
achieves planned objective	Holds between a planned process and objective specification when the criteria specified in the objective specification are met at the end of the planned process
participates in	Holds between man and the processes in which he participates

The man bears plan 1 [Smith & Ceusters, 2015, Ruttenberg et al., 2017], which is a concretization of station plan specification. Station plan specification has continuant part both the station action specification that prescribes the steps the man might take to walk to the station and the station objective specification that describes the goal of plan 1:

is a(plan, realizable entity)

is a(plan specification, information content entity)

instance of(plan 1, plan, i)

instance of(station plan specification, plan specification, i2)

instance of(station action specification, action specification, i2)

instance of(station objective specification, objective specification, i2)

inheres in(plan 1, man)

concretized by(station plan specification, plan 1, i3)

continuant part of(station action specification, station plan specification, i2)

continuant part of(station objective specification, station plan specification, i2)

Station is an instance of facility [Rudnicki, 2016]. Because plan 1 is an instance of realizable entity, it is not strictly speaking about anything, as only information content entities may be about some entity. Nevertheless, there is an instance of information content entity that is part of the station objective specification and concretized byplan 1, which includes the station in its description. We can thus say man’s plan 1 (derivatively) is about the station. Moreover, the station action specification includes the walking plan he intends to take in pursuit of that objective. Additionally, the manparticipates in a 4mph walk:

instance of(station, facility, i)

instance of(station description, information content entity, i)

continuant part of(station description, station objective specification, i2)

described by(station, station description)

participates in(man, 4mph walk, i4)

At some time, the man forms plan 2 to walk back home, then participates in an instance of180 turn, then participates in a 3mph walk until he arrives home.

instance of(plan 2, plan, i)

instance of(home plan specification, plan specification, i)

instance of(home action specification, action specification, i6)

instance of(home objective specification, objective specification, i6)

continuant part of(home action specification, home plan specification, i6)

continuant part of(home objective specification, home plan specification, i6)

inheres in(plan 2, man)

concretized by(home plan specification, plan 2, i6)

prescribes(home plan specification, 180 turn)

prescribes(home plan specification, 3mph walk)

participates in(man, 180 turn, i4)

Fig. 8.

Man walking to station, then home in Case 5.

participates in(man, 3mph walk, i5)

realized in(plan 2, 180 turn)

realized in(plan 2, 3mph walk)

The man’s home is a facility. There is an instance of information content entity that is part of the home objective specification and concretized byplan 2, where plan 2 includes home in its description. We can thus say the man’s plan 2is (derivatively) about the home. As before, the home action specification includes the walking plan the man intends to take. In this case, the man does achieve his planned objective, which we can represent by the man’sparticipating in an instance ofplanned process and bearing an achieves objective relation to the home objective specification, which we import from [Bandrowski, 2016].18

¹⁸

http://purl.obolibrary.org/obo/obi

is a(planned process, process)

instance of(planned process, planned process, i)

instance of(home, facility, i)

instance of(home description, information content entity, i7)

continuant part of(home description, home objective specification, i7)

described by(home, home description)

participates in(man, planned process, i6)

achieves planned objective(planned process, home objective specification)

Fig. 8 illustrates our description of the case. For further specification of the man’s walk, formalizations of distance measurement using BFO and its extensions illustrated in Fig. 3 can be leveraged to describe how far the man traveled in his initial trip before turning back.

4.5. Concept evolution

CASE 6: A marriage is a contract that is regulated by civil and social constraints. These constraints can change but the meaning of marriage continues over time.

GOAL: The example aims to show if and how the ontology models the evolution of the meaning of a term.

FOCUS: The continuity/discontinuity of the meaning of marriage in the presence of changing qualifications.

Speaking of ‘the meaning’ of marriage is spurious. Like most words, ‘marriage’ is polysemous. It can refer to a process in which spouses participate; it can refer to information content entities (i.e. the idea of marriage in the minds of particular people, or as represented in legal documents); and it can refer to a pair of mutually dependent spousal roles and their associated powers and privileges. Some uses of ‘marriage’ pull together all three meanings, as when we speak of the institution of marriage and denote a set of practices (processes) realizing marital powers (roles) that are prescribed by social or religious doctrine and law (information content entities). In representing marriage, we should take care not to conflate these different notions. As Groucho Marx once quipped: “Marriage is a wonderful institution, but who wants to live in an institution?”

Marriage license regulations vary by geographical region, population, and organizational affiliation. In the U.S., for example, marriage requirements, laws, and associated rights are established by states. All states impose eligibility requirements on individuals. For example, individuals entering marriage must have the capacity to consent to the arrangement and must be above a certain age. States also impose eligibility requirements on the couple. For example, at least one member of the union must be a U.S. citizen, before 1967 several states prohibited interracial marriage, and until 2015 several prohibited same-sex marriage [Smith, 2014]. Governments also grant obligations to spouses – married partners bear financial responsibilities to one another – and privileges – married partners are not required to testify against one another in court. Obligations and privileges can, like eligibility requirements, be changed by governing agencies.

We focus on the present status of a marriage contract issued in the U.S. between 1967 and 2015, and subsequent legal changes after 2015.

Table 15
Classes used to formalize Case 6

Class Definition or elucidation

Document A collection of information content entities intended to be understood together as a whole

Government An organization that exercises executive, legislative, or judicial authority over a region

Marriage license A document issued by a government, which legally binds agents as spouses, and invests them with associated instances of deontic role

Deontic declaration A social act that creates or revokes a deontic role

Social act A planned process that is carried out by a person or an organization, and is self-generated, directed towards another person or an aggregate of persons, an organization or an aggregate of organizations, and that needs to be perceived

Deontic role A role that inheres in a person and that is externally grounded in the normative expectations that other persons within a social context have concerning how that person should behave

Action regulation An information content entity that prescribes an act as required, prohibited, or permitted, and is the output of an act that realizes some authority role

Authority role A role that is realized by actions that create, modify, transfer, or eliminate action regulations or other authority roles, and inheres in an agent in virtue of collective acceptance of that agent’s ability to issue binding directives

Class	Definition or elucidation
Document	A collection of information content entities intended to be understood together as a whole
Government	An organization that exercises executive, legislative, or judicial authority over a region
Marriage license	A document issued by a government, which legally binds agents as spouses, and invests them with associated instances of deontic role
Deontic declaration	A social act that creates or revokes a deontic role
Social act	A planned process that is carried out by a person or an organization, and is self-generated, directed towards another person or an aggregate of persons, an organization or an aggregate of organizations, and that needs to be perceived
Deontic role	A role that inheres in a person and that is externally grounded in the normative expectations that other persons within a social context have concerning how that person should behave
Action regulation	An information content entity that prescribes an act as required, prohibited, or permitted, and is the output of an act that realizes some authority role
Authority role	A role that is realized by actions that create, modify, transfer, or eliminate action regulations or other authority roles, and inheres in an agent in virtue of collective acceptance of that agent’s ability to issue binding directives

Table 16

Particulars used to formalize Case 6

Particulars	Descriptions
U.S. Supreme Court	The branch of government able to legally create or revoke deontic powers of state government
deontic declaration 1	The deontic declaration that has specified outputmarriage license
deontic declaration 2	The deontic declaration that has specified outputaction regulation 1
deontic declaration 3	The deontic declaration that legally revokesdeontic role 1 and deontic role 3
deontic role 1	The deontic role inhering inAlexrealized inAlex legally refraining from testifying against Bailey in court
deontic role 2	The deontic role inhering inAlexrealized inAlex’s legal permission to file income taxes jointly with Bailey
deontic role 3	The deontic role inhering inBaileyrealized inBailey legally refraining from testifying against Alex in court
deontic role 4	The deontic role inhering inBaileyrealized inBailey’s legal permission to file income taxes jointly with Alex
marriage license	The marriage license issued by state government, which legally binds Alex and Bailey together as spouses, and invests them with associated instances of deontic role
state government	The government participating in the marriage of Alex and Bailey
Alex	The person acquiring a marriage license with Bailey
Bailey	The person acquiring a marriage license with Alex
marriage licensure document	A document describing the objective of issuing, and steps that must be taken to issue marriage license
action regulation 1	An action regulation requiring state government to issue instances of marriage license for consenting same-sex couples
authority role 1	An authority role borne by state government, prescribed byaction regulation 1
i1	The interval during which state government, Alex, and Baileyparticipate indeontic declaration 1 resulting in the creation of marriage contract
i2	The interval during which U.S. Supreme Courtparticipates indeontic declaration 2 requiring state government to recognize same-sex marriage
i3	The interval during which state governmentlegally revokesdeontic role 1 and deontic role 3

Table 17

Relations used to formalize Case 6

Relations	Descriptions
participates in	Holds between agents and instances of deontic declaration
has specified input	Holds between deontic declaration 1 and marriage licensure document
has specified output	Holds between instances of deontic declaration and document, and action regulation 1
inheres in	Holds between instances of deontic role and Alex and Bailey, respectively
prescribes	Holds between action regulation 1 and authority role 1
legally revokes	Holds between deontic declaration 3 and deontic role 1 and deontic role 3

The marriage license is an instance of the class marriage license, which is a subclass of document [Almeida, Slaughter, & Brochhausen, 2012, Almeida et al., 2017]. State government, which issues the marriage license, is an instance of government, which is a type of organization able to exercise judicial, legislative, or executive authority over a site.

is a(document, information content entity)

is a(marriage license, document)

is a(government, organization)

instance of(marriage license, marriage license, i)

instance of(state government, government, i)

State governmentparticipates indeontic declaration 1, a type of social act [Almeida, Slaughter, & Brochhausen, 2012, Almeida et al., 2017] which has specified input a marriage licensure document that has, as part, a plan specification. This plan specification describes the intended legal entities created according to the objective specification, as well as the manner in which the deontic declaration should be performed to achieve that objective – as described by the action specification. For simplicity, we do not include these continuant parts of marriage licensure document. The deontic declaration 1, moreover, has specified output the marriage license:

is a(deontic declaration, social act)

instance of(deontic declaration 1, deontic declaration, i1)

participates in(state government, deontic declaration 1, i1)

has specified input(deontic declaration 1, marriage licensure document)

has specified output(deontic declaration 1, marriage license)

Alex and Bailey each participates indeontic declaration 1 as well. Instances of deontic declaration involve the creation or revoking of deontic roles. Instances of deontic role inhere in persons or organizations, but are externally grounded in the normative expectations others have concerning how bearers should behave. In this case, instances of deontic role inhere inAlex and Bailey, respectively. These respective roles are realized in processes typically associated with marriage, such as filing taxes jointly and making medical decisions on behalf of the spouse. For simplicity, we focus on only two such deontic roles each for Alex and Bailey.

instance of(Alex, person, i)

instance of(Bailey, person, i)

participates in(Alex, deontic declaration 1, i1)

participates in(Bailey, deontic declaration 1, i1)

is a(deontic role, role)

instance of(deontic role 1, deontic role, i1)

instance of(deontic role 2, deontic role, i1)

instance of(deontic role 3, deontic role, i1)

instance of(deontic role 4, deontic role, i1)

inheres in(deontic role 1, Alex)

inheres in(deontic role 2, Alex)

inheres in(deontic role 3, Bailey)

inheres in(deontic role 4, Bailey)

At some point, following deontic declaration 1 that results in the state government issuing marriage license for Alex and Bailey, the U.S. Supreme Courtparticipates indeontic declaration 2 resulting in all state prohibitions on same-sex marriage being deemed unconstitutional. Deontic declaration 2has specified outputaction regulation 1 permitting the authorization of same-sex marriage. This prescription sanctions new realizations of state and local agent instances of authority role relevant to marriage contracts, by broadening the class of those eligible to participate in an act of marrying.

instance of(U.S. Supreme Court, organization, i)

instance of(deontic declaration 2, deontic declaration, i2)

participates in(U.S. Supreme Court, deontic declaration 2, i2)

is a(action regulation, information content entity)

instance of(action regulation, action regulation, i2)

has specified output(deontic declaration 2, action regulation 1)

is a(authority role, role)

instance of(authority role 1, authority role, i2)

prescribes(action regulation, authority role 1)

inheres in(authority role 1, state government 1)

The expansion of sanctioned realizations of instances of authority role by state government does not undermine that Alex and Bailey have a marriage license. This is because instances of deontic role borne by Alex and Bailey are not altered by action regulation 1, since action regulation 1 targets eligibility constraints on marriage.

Fig. 9.

Changing deontic roles in Case 6.

As discussed, governments may alter marriage contracts in another way, by changing spousal obligations and powers. To illustrate, suppose state governmentparticipates indeontic declaration 3 which legally revokes the deontic role 1 that inheres inAlex and deontic role 2 that inheres inBailey, which we assume correspond to privileges bearers have to refrain from testifying against their spouse. This results in Alex and Bailey losing these respective roles, though they maintain deontic role 2 and deontic role 4.

participates in(state government, deontic declaration 3, i3)

legally revokes(deontic declaration 3, deontic role 1, i3)

legally revokes(deontic declaration 3, deontic role 3, i3)

$\exists t$ occurrent part of(t, i3) $\land \neg$ exists at(deontic role 1, t) $\land \neg$ exists at(deontic role 3, t)

At least two types of change to marriage licenses can be represented with BFO, reflecting changes to eligibility requirements – which either narrow or extend participants – or changes to associated roles – which either narrow or extend spousal rights and obligations. In each case, the meaning of marriage, in some sense, remains the same.

Table 18

Relations used in cases from other BFO-conformant ontologies

Relation name and source *	Definition or elucidation
is about(IAO)	A primitive relation that relates an information artifact to an entity.
describes(CCO)	x describes y iff x is an instance of information content entity, and y is an instance of entity, such that x is about the characteristics by which y can be recognized or visualized.
achieves planned objective(OBI)	This relation obtains between a planned process and a objective specification when the criteria specified in the objective specification are met at the end of the planned process.
prescribes(CCO)	x prescribes y iff x is an instance of information content entity and y is an instance of entity, such that x serves as a rule or guide for y if y an occurrent, or x serves as a model for y if y is a continuant.
has specified output(OBI)	A relation between a planned process and a continuant which participates in that process. The presence of the continuant at the end of the process is explicitly specified in the objective specification which the process realizes the concretization of.
legally revokes(D-Acts)	d socio-legally revokes s if sparticipates in d and at the end of d s no longer exists. s going out of existence is complete and unlike the going out of existence for material entities which are always transformed into something else. After the declaration nothing is left of the socio-legal generically dependent continuant in question.

These relations come from ontologies using Basic Formal Ontology (BFO), including: The Common Core Ontologies (CCO), The Ontology for Biomedical Investigations (OBI), The Information Artifact Ontology (IAO), and The Ontology of Document Acts (D-Acts).

5. Ontology usage and community impact

BFO is committed to there being a single reality, with scientific investigation often resulting in clarifications of our picture of this reality. As science updates, ontology should follow. Other conceptions, past or present, of the way the world is, or might be, are merely informational entities and impose no further ontological commitments.

As the core architecture of The Open Biological and Biomedical Ontology (OBO) Foundry and The Industrial Ontology Foundry (IOF) [Smith et al., 2005, Smith et al., 2007, Smith et al., 2019], BFO is widely used across a range of scientific disciplines. BFO is used extensively in the biomedical domain [Bandrowski, 2016], providing domain specialists foundational support when modeling phenotypes [Buttigieg, et. al., 2013], disease [Grenon, Smith, & Goldberg, 2004, Köhler et al., 2013, Scheuermann, Ceusters, & Smith, 2009, Beverley, Babcock, Cowell, & Smith 2020], diagnosis [He et al., 2020, Babcock, Beverley, Cowell, & Smith, 2021], and resistance [Goldfain, Smith, & Cowell, 2011]. BFO is presently used in over 350 ontology products, and with its recent standardization, this number will no doubt increase in the coming years.

Footnotes

Acknowledgements

Thanks to Barry Smith for his comments on an early draft of this manuscript.

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