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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>How an Aggregate View of Social Roles Meets Dispositions</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Fumiaki Toyoshima</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Adrien Barton</string-name>
          <email>adrien.barton@irit.fr</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Ludger Jansen</string-name>
          <email>ludger.jansen@uni-rostock.de</email>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Jean-François Éthier</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>CNRS-IRIT</institution>
          ,
          <addr-line>118 Route de Narbonne, F-31062 Toulouse Cedex 9, Toulouse</addr-line>
          ,
          <country country="FR">France</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>GRIIS, Université de Sherbrooke, 2500 Boulevard de l'Université</institution>
          ,
          <addr-line>Sherbrooke, QC, J1K 2R1</addr-line>
          ,
          <country country="CA">Canada</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>University of Rostock, Institute of Philosophy</institution>
          ,
          <addr-line>August-Bebel-Straße 28, 18051 Rostock</addr-line>
          ,
          <country country="DE">Germany</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>Social roles remain nebulous, although they are vital for an accurate understanding of the socioeconomic world. In this paper, we sketch out a dispositional approach to social roles by leveraging F. Loebe's account of social roles that is based on his tripartite classification of roles (relational, processual, and social): that is, social roles “aggregate” various relational and processual roles. More specifically, we articulate the thesis that socially relevant processual and relational roles are intimately connected with intrinsic and extrinsic dispositions, respectively. This aggregate and dispositional view of roles will serve as an initial step towards a full-fledged analysis of social roles and their contexts (“social contexts”).</p>
      </abstract>
      <kwd-group>
        <kwd>1 social role</kwd>
        <kwd>social context</kwd>
        <kwd>processual role</kwd>
        <kwd>relational role</kwd>
        <kwd>disposition</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>The socio-economic world is replete with roles: money, students, professors, and presidents, to
borrow Masolo et al.’s [1] examples, are all based on role. Roles are thus crucial for social ontology.
For instance, in the analysis of multiagent systems, enterprise modeling, as well as in formal ontology,
it is now well-established to model organizations (whether totally or partially) in terms of interrelations
among roles (see Toyoshima’s [2] survey of related work). Closely related is the active discussion about
status or status entities in social ontology [3][4][5]. Roles nevertheless remain elusive entities and
Boella et al. [6] list several open questions about roles, including whether there can be a single
overarching definition of roles or not.</p>
      <p>Social roles are notoriously difficult to analyze in formal ontology. According to Loebe [7], the
challenge of understanding social roles is partly due to the intricacy of the so-called “social contexts”
from which they emanate. As Boella et al. [6] point out, one of the most frequently discussed examples
of (social) roles is the role of being a student. The social context for this role is often taken to be schools,
but it is not clear what it really means to say that schools can serve as a social context for student roles.
Moreover, the issue of social contexts is closely connected with the broader problem of how to
understand the complicated notion of context, as its relevance to roles in general is widely
acknowledged (see, for thoughts, Baclawski et al.’s [8] general discussion on contexts and Toyoshima’s
[2] meta-ontological (grounding-based) approach to contexts vis-à-vis roles).</p>
      <p>This paper aims to propose a promising way of considering social roles and their contexts. To
achieve this purpose, we take full advantage of Loebe’s [7] tripartite classification of roles: relational,
processual, and social roles. For one thing, he explicitly theorizes upon roles, their contexts, and their
relationship and his approach will be helpful in considering social contexts. As Loebe points out “[t]he
contexts of social roles are much harder to grasp” than relational and processual roles (ibid., p. 137),
and he concedes that social roles “appear to be the least understood role type” in his model (ibid., p.
136). At the same time, he propounds the view (which will be detailed below) that “social roles rather
aggregate various relational and processual roles” (ibid., p. 137). We call this an “aggregate view” of
social roles. This aggregate perspective will suggest one way of explicating social contexts: social
contexts can be further elucidated in terms of the contexts for relational and processual roles. We will
also utilize an ontology of dispositions [9][10] because they will be useful for scrutinizing the
relationships among these three kinds of roles. This dispositional investigation into this aggregate
account of social roles can be expected to lay the groundwork for their full-fledged ontology.</p>
      <p>The paper is organized as follows. Section 2 introduces Loebe’s [7] tripartite classification of roles:
relational, processual, and social roles. Section 3 develops a dispositional formulation of a Loebe-style
aggregate view of social roles. Section 4 is devoted to the discussion on related work. Section 5
concludes with the paper with some brief remarks on future work.</p>
    </sec>
    <sec id="sec-2">
      <title>2. F. Loebe’s Tripartite Classification of Roles</title>
      <p>Loebe [7] provides a general account of roles, including social ones. It is built in alignment with the
upper ontology General Formal Ontology (GFO) [11][12], but its general value for considering roles is
recognized, e.g., by Guarino [13]. In his basic schema, an entity (player) bears the playing relation
towards a role such that the role bears the role-of relation with a context: for example, Mary (player)
plays a role of being a student that bears the role-of relation towards the XYZ school (context) (see
Toyoshima’s [2] discussion on different interpretations of the phrases “have a role” and “play a role”).
According to Loebe’s classification, roles fall into social roles and abstract roles, the latter being in turn
classified into relational roles and processual roles. These three different kinds of roles are individuated
according to the different kinds of player categories, playing relations, “role-of” relations, and context
categories (see Table 1). Relational, processual, and social roles are briefly explained as follows:
• A relational role corresponds to the way in which an entity participates in some relation. As
Toyoshima [2] says, the notion of relational role can be understood in connection with a
“positionalist” account of relations: roughly, relations have “positions” or “places” or “roles” for the
relata. For instance, Abelard’s loving relation towards Heloise can be said to have as part (albeit in
a broad sense of the term) the “lover role” occupied by Abelard and the “lovee role” occupied by
Heloise.2 A relational role is part (in this broad sense) of some relational property and it is a kind of
property (refer to Loebe [14] for more thoughts on relations and relational roles). It also depends
existentially on the player (the “non-migration principle” about relational roles). Example: When
the number 2 plays a relational role of being a factor of the number 4, the number 2 bears that
property of “being a factor” that is part of the “being a factor of” relation between the number 2 and
the number 4. The role is here identified with the property of “being a factor”; playing this role is
identified with bearing that property; the context is identified with the relation “being a factor of”;
and the relation between this role and this context is a relation of parthood (in a general sense of the
term).
• A processual role corresponds to the way a single participant behaves in some process. (The
term “process” is used in the GFO sense, but it can admit of an intuitive reading.) Example: When
John plays a processual role of moving his pen, he participates in that “pen-moving process” that is
part of the process of John moving his pen. Loebe [7] explains: “When John moves his pen, he and
the pen form participants of that process, and the processual role which John plays captures what
John does in that participation. Thinking of a mime who moves an imaginary pen should be a good
illustration of the notion of a processual role” (ibid., p. 135). The role is here identified with John’s
pen-moving process (the “miming-like process” mentioned by Loebe, which does not have the pen
as a participant); playing this role amounts to participating to this process; the context is identified
2 “The view of role-of as subsumed by a general notion of part-of may appear debatable in particular for relational roles and relators, due to
the question of what a part of a relator should be. We consider relational roles as homogeneous, “indivisible” entities which form “atomic”
parts of relators. Moreover, we conjecture that relators are mereologically extensional with respect to their roles. (…) In spite of this possibly
uncommon view, relational roles have definitely found their place in modeling and representation, and there they exhibit the character of parts
with relations as their wholes” ([7], pp. 134-135). Note that our discussion below will not hinge much on this potentially contentious view of
relational roles as parts of relations.</p>
      <p>with the larger process of John moving his pen (which has not only John, but also the pen as a
participant); and the relation between the role and the context is a relation of process-parthood.
• A social role corresponds to the involvement of a material object within some society. Loebe
builds his conception of social roles upon Searle’s [3][4] analysis of social objects to elucidate the
playing and role-of relations concerning social roles. (We will henceforth treat the terms “social
role” and “social object” synonymously.) For Searle, material objects offer a foundation for social
objects and a social object emerges when a new “status-function” is imposed on the material object.
He creates a general formula of this “constitutive rule” for social objects: “X counts as Y (in
context C)” where X is a material object and Y is a social one. A material entity playing a social role
that bears the role-of relation (as Loebe calls it) towards a context would correspond to the material
entity “counting as” the social role “in” the context. A social role is, very roughly, a kind of object
that has all properties of the player, but that also has some additional properties which the player
does not. As said, a context for a social role is difficult to analyze and Loebe categorizes loosely as
a “social individual”, as illustrated by the XYZ school. For example, when Mary plays the social
role of being a student of the XYZ school, she “counts as” that student “in” the XYZ school. Here,
the role is the object that has the same properties (e.g., shape) as Mary does but that has additional
properties (which would be grouped under the name of “student-ness”) which Mary does not have;
the relation of Mary playing this role is identified with the relation of Mary “counting as” this object;
the context is the XYZ school; and the “in” relation between the role and the context is still unclear
because so are social roles and their contexts, as Loebe says: “Currently, we stick to the phrase
‘belonging to a (social) context’ for role-of in the social case” ([7], p. 136).</p>
      <p>As for social roles, Loebe [7] discusses an intimate connection between social roles and abstract
roles, while surmising that a meticulous analysis of social roles will require a full-fledged theory of
social ontology (see Section 3.4 for preliminary thoughts). Social roles are often defined with their own
properties, relations and processes in which they (may) participate. For example, Mary’s social role of
being a student of the XYZ school would pertain to Mary’s inherent properties (e.g., her abilities), her
“student-teacher relation” towards schoolteachers, and processes of her taking classes at school. In other
words, Mary’s playing this role of being a student is underpinned by her playing relational roles whose
contexts are student-teacher relations and processual roles whose contexts are class-taking processes.
Accordingly: “social roles rather aggregate various relational and processual roles” (ibid., p. 137; and
see also Boella et al.’s [6] statement that relational roles can be “intermingled with” social ones).</p>
      <p>To explore this aggregate view of social roles, we will assume that social roles are characterized by
a selected group of relational and processual roles that have social import, as exemplified by
studentteacher relational roles and class-taking processual roles. Being inspired by Loebe, we say that social
roles aggregate “socially relevant relational roles” and “socially relevant processual roles”.
Furthermore, we will aim for a minimal characterization of social roles from the viewpoint of an
ontology of roles, while leaving serious engagement with their social dimension for future work (see
Section 3.4 for a brief discussion).</p>
      <p>We will also presuppose that socially relevant processual roles are prior to socially relevant
relational roles in the sense that the latter can be elucidated (or may be sometimes defined) in terms of
the former, but not vice versa. Loebe [7] puts forward the idea that “one route to a stronger theory of
contexts could be to reduce certain types of roles to others” and “[r]elations and relational roles may
appear suitable in this respect” (ibid., p. 144) because relations can be further analyzed by dint of their
“constituents”, namely their relata (unless one advocates the very specific idea of “relations without
relata”, which is off the table in this paper). Certainly, not all relational roles could be connected with
processual roles: for instance, a relational role of being a factor of some number would have nothing
essential to do with any processual roles. Nonetheless, it would be reasonable to link some relational
roles with processual ones, insofar as they figure prominently in the social world because socially
relevant relational roles typically involve corresponding processual ones. For example, Mary’s
relational role of being a student at school could not exist unless she can play a processual role of taking
classes at school. In this direction of inquiry, we will consider socially relevant processual roles (Section
3.2), socially relevant relational roles (Section 3.3), and social roles (Section 3.4) in order. Through this
exploration, it is expected that contexts for social roles will be elucidated by contexts (which are relation
instances) for socially relevant relational roles and these contexts will be in turn further elucidated by
contexts (which are processes) for socially relevant processual roles.</p>
    </sec>
    <sec id="sec-3">
      <title>3. A Dispositional Approach for an Aggregate View of Social Roles</title>
    </sec>
    <sec id="sec-4">
      <title>3.1. Preliminaries</title>
      <p>In the text, we will write terms for type-level entities (universals, classes) in italics and terms for
token-level entities (particulars, instances) in bold for expository purposes. In first-order formalization,
variables stand only for tokens and free variables are universally quantified. Predicates stand for types
(unary predicates) and relations. Figure 1 provides an is-a hierarchy of ontological categories with their
corresponding unary predicates, where a type A being a subtype of a type B (which is expressed by the
indentation) amounts to the thesis that all instances of A are instances of B, and is represented by an
indentation (for example, the class Material object is a subtype of the class Material entity).</p>
      <sec id="sec-4-1">
        <title>Property</title>
      </sec>
      <sec id="sec-4-2">
        <title>Material entity</title>
      </sec>
      <sec id="sec-4-3">
        <title>Material object</title>
        <sec id="sec-4-3-1">
          <title>System (SYS)</title>
        </sec>
        <sec id="sec-4-3-2">
          <title>Social role (SR)</title>
        </sec>
      </sec>
      <sec id="sec-4-4">
        <title>Process</title>
      </sec>
      <sec id="sec-4-5">
        <title>Relational role</title>
        <sec id="sec-4-5-1">
          <title>Socially relevant relational role (SRRR)</title>
        </sec>
      </sec>
      <sec id="sec-4-6">
        <title>Disposition</title>
        <sec id="sec-4-6-1">
          <title>Intrinsic disposition (INTD)</title>
        </sec>
        <sec id="sec-4-6-2">
          <title>Joint disposition (JD)</title>
        </sec>
        <sec id="sec-4-6-3">
          <title>Extrinsic disposition (EXTD)</title>
        </sec>
      </sec>
      <sec id="sec-4-7">
        <title>Processual role</title>
        <sec id="sec-4-7-1">
          <title>Socially relevant processual role (SRPS)</title>
          <p>x (material entity instance) is a bearer of y (property instance)</p>
          <p>x (disposition instance) fully grounds y (disposition instance)
x (material entity instance) is part (proper or not) of y (material entity instance)</p>
          <p>x (object instance) plays y (role instance)
x (disposition instance) is realized in y (process instance)
x (extrinsic disposition) relies existentially on y (intrinsic disposition)</p>
          <p>To examine Loebe’s aggregate account of social roles, we will deploy an ontology of dispositions
which is theoretically underpinned by McKitrick’s [15] pragmatically motivated and causal approach
to dispositions (which she calls “disposition pluralism”). As a matter of fact, this approach is useful for
representing multifarious entities dispositionally (see Toyoshima et al.’s [16] detailed examination of
her theory). In particular, we will avail of the following characterization of dispositions [9][10]. A
disposition is a causal property that is connected with a realization, namely a specific possible behavior
of the bearer (paradigmatically a material object) of the disposition. To be realized in a process, a
disposition typically needs to be triggered by some other process (trigger). Classical examples include
fragility (the disposition to break when pressed with a force) and solubility (the disposition to dissolve
when put in a solvent). Dispositions may exist even if they are not realized or even triggered: for
example, a glass is fragile even if it never breaks or even if it never undergoes any shocks.</p>
          <p>Additionally, we will employ the distinction between intrinsic and extrinsic dispositions, as it is
acknowledged by McKitrick’s dispositional pluralism. Roughly speaking, a property (instance) is
intrinsic if it inheres in its bearer purely in virtue of the way the bearer is and it is extrinsic otherwise,
scilicet if it inheres in its bearer (at least partly) in virtue of the way the world that is external to the
bearer is. For instance, the fragility of this glass is intrinsic because the glass is fragile under any external
circumstances (even when packed in a bubble wrap). While dispositions are traditionally taken to be
intrinsic, extrinsic dispositions are highly useful for characterizing a wide range of entities. Canonical
examples include the disposition of this key to open this particular lock because this disposition is borne
in virtue of the existence of the lock (which is external to the disposition bearer, namely the key).</p>
          <p>Toyoshima et al. [16] propose two ways of characterizing extrinsic dispositions. First, following
Williams [17], we can hold that every realization of an extrinsic disposition is a realization of some
intrinsic disposition (“intrinsic dependee”) on which the extrinsic disposition relies (existentially). For
instance, the extrinsic disposition of this key to open this particular lock relies on the intrinsic
disposition of the key to open any instance (including this lock) of a certain lock type. Second, following
Vetter [18], we can provide a “systemic account” of extrinsic dispositions. Its cardinal tenet is that the
possession of an extrinsic disposition (“extrinsic potentiality” in her terms) by an object is both
necessary and sufficient for the possession of a joint disposition (“joint potentiality” in her terms) by a
system composed of this object and others. (More details will be given in Section 3.3.) To illustrate this
systemic theory, the extrinsic disposition of this key to open this particular lock exists in virtue of a
joint disposition to be realized in an unlocking process that is borne by the “key &amp; lock system”
composed of the key and the lock.
3.2.</p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>Socially Relevant Processual Role</title>
      <p>Taking a cue from Loebe [7], we will take a driving example of Alice playing the social role (say
srA) of being a doctor with the simplifying assumption that treating a person is a minimal element of
being a doctor. To make it simpler, we will also consider that Alice has (and will have) only one patient
in her career, named Bob. Since we are primarily concerned with first steps towards clarification of the
notion of social context, we will strive for a minimal characterization of a context (which is a social
individual in Loebe’s terms) in which Alice counts as an object such that, unlike Alice, this object has
some “doctorness-related properties”. The aggregate view of social roles consists in considering that
srA aggregates some socially relevant relational roles and socially relevant processual roles of Alice.
We will focus on the latter in this section and on the former in Section 3.3, based on the priority of
processual roles over relational roles in the social world (see Section 2). More specifically, we will
clarify the connection between socially relevant relational and processual roles using dispositions,
which will provide a solid foundation for an analysis of social roles.</p>
      <p>During her career, Alice will treat Bob several times. Accordingly, she plays each time a processual
role; when Alice plays one of those processual roles, she participates in it (but Bob does not, cf. the
remark above on the “miming-like” nature of processual roles), and this processual role is part of a full
process of Alice treating Bob (which has not only Alice, but also Bob as a participant). We will name
PRA the class of such processual roles played by Alice.</p>
      <p>Let us now consider why Alice can participate in a process of treating Bob at all. One plausible
hypothesis is that Alice has various intrinsic properties (such as her ability to observe people or her
medical abilities) that would (collectively) enable her to treat a person. From an ontological point of
view, we can think of Alice’s intrinsic disposition (say dA) to treat a person. We can then find the
following linkage between PRA and dA: any instance of PRA is part of a realization of dA.</p>
      <p>More generally, every socially relevant processual role is part of a realization of an intrinsic
disposition of the player. For one thing, it will help to analyze some paradigmatic examples of
processual roles. Consider a processual role of being a breather, taken from Loebe [7]: it can be
plausibly taken as a part of a realization of an intrinsic disposition to breathe. (Other similar examples
include eaters and walkers.) At the same time, one may wonder whether some examples of socially
relevant processual roles can be understood in this dispositional manner. Consider this piece of paper
(say p1) playing a social role of being money and suppose for the sake of argument that an associated
socially relevant processual role (say prp1) is part of a process of exchange between Mary and John
(that is, prp1 is the process of p1 being given by Mary to John in exchange of some goods, that has as
participant p1, but neither Mary nor John, since it is a “miming-like” processual role). One could wonder
whether there is any intrinsic disposition of p1 to be realized in a process having prp1 as part.</p>
      <p>There are at least two ways to handle this concern. First, Loebe’s [7] conception of social roles is
based on Searle’s [3][4] view that social objects are made (in some sense) out of material objects.
However, Smith [19] counters that there are social objects (which he calls “free-standing Y terms”)
which do not coincide ontologically with physical reality. He provides the illustrative example of money
recorded in the bank’s computers. In this respect, the difficulty of a dispositional approach to socially
relevant processual roles may be due to the limitation of Searle’s framework for social ontology. A
discussion of this question lies outside the purview of our current investigation.</p>
      <p>Second, such apparently problematic cases as money might be possibly accommodated. A process
of exchange (having prp1 as part) in which p1 participates amounts to a process of p1 being used as a
medium of exchange by some particular person (say Pat). Now, we can think of a disposition of p1 to
be realized in a process of p1 being used as a medium of exchange by Pat. This disposition would be
extrinsic because it exists in virtue of Pat’s existence, which is external from p1. Therefore, prp1 is part
of a realization of this extrinsic disposition of p1. From the existence of intrinsic dependees of extrinsic
dispositions (see Section 3.1), we can deduce that prp1 is also part of the realization of some intrinsic
disposition of p1.</p>
      <p>There are some worries as to this tentative proposal. For instance, it can be extremely difficult to
identify explicitly what is the intrinsic disposition on which this extrinsic disposition of p1 depends.
However, we could think that these issues can arise for some kinds of social roles (e.g., money), but not
for other kinds of social roles, especially agentive ones such as students and presidents. We thus propose
the following axiom as a substantive thesis about socially relevant processual roles:
a1</p>
      <p>SRPS(x) ∧ PLAY(y,x) → ∃z,w (INTD(z) ∧ BEA(y,z) ∧ REL(z,w) ∧ P(x,w))
A socially relevant processual role is part of a realization of an intrinsic disposition of its player.
(If x is a socially relevant processual role and y plays x, then there is an intrinsic disposition z
borne by y and realized by a process w such that w has x as part.)</p>
    </sec>
    <sec id="sec-6">
      <title>Socially Relevant Relational Role</title>
      <p>We move onto Alice’s socially relevant relational role. Let us consider as before the simple case
where Alice will only have one patient during her career, named Bob. We name rrA Alice’s relational
role of being Bob’s treater (where the meaning of the term “treater” will be discussed below). As Loebe
[7] says, one distinguishing characteristic of relational roles is that they depend (existentially) on
“complementary” relational roles. In the present example, rrA depends on Bob’s relational role (say
rrB) of being Alice’s “treatee”. Note that rrA and rrB depend also on their respective players, namely
Alice and Bob.</p>
      <p>There are several ways of characterizing rrA from the viewpoint of processual roles, depending on
the understanding of the term “treater” (and also “treatee”). One idea is to construe a treater as a person
who is actually treating somebody else. However, we can also think of a treater more broadly as a
person who can treat somebody else (where the term “can” means circumstantial, but not normative,
possibility). In this view, Alice may be Bob’s treater even before she actually began to treat him, or
even when she never treated him for some reason. We will adopt this second interpretation of relational
role terms because it will be more useful for analyzing social roles that are often described with the
term “status” (see Section 1).</p>
      <p>To clarify the relationship between the relational role particular rrA and the processual role class
PRA, we will appeal to an ontology of dispositions, especially of extrinsic dispositions. We said in
Section 3.2 that Alice’s class of processual roles PRA is closely related to her intrinsic disposition dA to
treat a person in the sense that every instance of PRA is part of a realization of dA. In a parallel way, we
can think that Alice’s relational role rrA of being Bob’s treater is intimately connected with her
disposition (say dAB) to treat Bob; and note that dAB is an extrinsic disposition because Alice bears dAB
in virtue of Bob’s existence. Moreover, dAB relies on dA: for example, if dAB is realized in a process of
Alice’s treating Bob, then dA is also realized in this process [16].</p>
      <p>It will be helpful here to refer to the systemic account of extrinsic dispositions (introduced in
Section 3.1). In more details, whenever an object bears an extrinsic disposition, this disposition is “fully
grounded” (in her terms) in a joint disposition which is borne by a system composed of this object and
others; and whenever a system composed of a number of objects bears a joint disposition, each of the
objects thereby bear an extrinsic disposition which is fully grounded in that joint disposition. Close
scrutiny of the full grounding relation between a joint disposition and an extrinsic disposition is set
aside for future work, but we can at least say that one disposition fully grounds another disposition only
if the latter depends on the former (see Toyoshima et al.’s [16] work for further thoughts). As for
systems and joint dispositions, it will suffice to assume that being an aggregate of objects is a necessary
condition for being a system and being an intrinsic disposition of a system is a necessary condition for
being a joint disposition.3 For instance, Alice bears dAB and Bob also has an extrinsic disposition (say
dBA) to be treated by Alice in virtue of the fact that there is a joint disposition (say djointAB) of the “Alice
&amp; Bob system” (say systemAB) composed of Alice and Bob such that djointAB fully grounds dAB and dBA.
djointAB would be realized in a process of Alice treating Bob, namely in an instance of PRA.</p>
      <p>Now we formulate a hypothesis about the connection among rrA and PRA or more generally between
relational roles and processual roles in the social world. The basic idea is that playing a socially relevant
relational role is a sufficient condition for the player bearing an extrinsic disposition that whose
realizations have as part a socially relevant processual role. Moreover, this extrinsic disposition is fully
grounded in a joint disposition of a system that has the player. This line of thoughts leads to the
following axiom:
3 One potentially interesting idea is that a system may be defined as an aggregate of objects that has a joint disposition. A system is typically
conceived as an aggregate of objects which “work together”, or in more detail, which displays a specific behavior in virtue of behaviors of its
components. This simple conception of systems seems to mesh well with the view that a specific behavior of a system is the realization of a
joint disposition or even is identical with its joint disposition, the latter construal implying a one-to-one correspondence between a system and
a joint disposition. We mention this as a possible dispositional inquiry into the notion of system.</p>
      <p>a2 SRRR(x) ∧ PLAY(y,x) → ∃z,s,t,u EXTD(z) ∧ BEA(y,z) ∧ SYS(s) ∧ P(y,s) ∧ JD(t) ∧ BEA(s,t) ∧
GRD(t,z) ∧ INTD(u) ∧ BEA(y,u) ∧ REON(z,u) ∧
∀v [REL(u,v) → ∃w SRPR(w) ∧ PLAY(y,w) ∧ P(w,v)]
For any socially relevant relational role and its player, the player has an extrinsic disposition
which is fully grounded by a joint disposition of a system having as part the player and which
relies on an intrinsic disposition of the player whose realizations have as part a socially relevant
processual role played by the player of the socially relevant relational role.4
(If x is a socially relevant relational role played by y, then there is some z, s, t and u, such that
z is an extrinsic disposition borne by y, s is a system that has y as part, t is a joint disposition
borne by s, t fully grounds z, u is an intrinsic disposition borne by y on which z relies, and every
realization v of u has as part a socially relevant processual role w played by y.)</p>
      <p>To exemplify (a2) with our driving example, SRRR(rrA) and PLAY(Alice, rrA) hold: informally,
rrA is a socially relevant relational role and Alice plays rrA. (a2) enables the derivation of the existence
of dAB, systemAB, djointAB, and dA. Note first that EXTD(dAB) and BEA(Alice, dAB) hold: dAB is an
extrinsic disposition and Alice bears dAB. All the following facts are also true: SYS(systemAB), P(Alice,
systemAB), JD(djointAB), BEA(systemAB, djointAB), and GRD(dAB, dAB). That is: systemAB is a system,
Alice is part of systemAB, djointAB is a joint disposition, systemAB bears djointAB, and djointAB fully grounds
dAB. We also have: INTD(dA), BEA(Alice, dA), and REON(dAB, dA). That is to say, dA is an intrinsic
disposition, Alice bears dA, and dAB relies on dA. Finally, if REL(dA, p) (that is, dA is realized in some
p), then there exists some pr such that SRPR(pr), PLAY(Alice, pr), and P(pr, p) (pr is a socially
relevant processual role played by Alice that is a part of p).
3.4.</p>
    </sec>
    <sec id="sec-7">
      <title>Social Role</title>
      <p>We finally consider Alice’s social role srA of being a doctor so as to provide a minimal restriction
on its context (social individual). In Section 3.3, we articulated the relationship between the socially
relevant relational role rrA and the class of socially relevant processual roles PRA by way of an extrinsic
disposition whose realizations have as part instances of PRA. Before turning to srA, we remark that one
can find a broad spectrum of social roles in the relevant literature. For example, Masolo et al. [1] and
Guizzardi et al. [20] cite, as examples of social roles, catalysts (substances that make chemical reactions
happen faster without being changed themselves) and pedestrians (people walking in the street and not
travelling in a vehicle), respectively. Presumably, the sociality of such social roles is so weak that they
may be mostly explicated in terms of socially relevant processual and relational roles, as is illustrated
by Toyoshima et al.’s [16] dispositional analysis of catalyst roles.</p>
      <p>As Loebe [7] says, however, a meticulous analysis of paradigmatic social roles (e.g., students)
demands a full-fledged social ontology. This is because social roles are objects with some additional
social elements (which will be explained in more detail below) to the properties of the players, and
socially relevant relational and processual roles alone would be typically insufficient to account for
such social elements. In effect, srA would remain underspecified unless we take into account the fact
that Mary has a duty to treat Bob. Thus, srA can be at best only partially characterized with Alice’s
relational role rrA of being Bob’s treater. At the same time, our dispositional formulation of an
aggregate view of social roles will be helpful in providing a solid basis for social roles and their contexts.
For instance, we can hypothesize that the context for srA has as part systemAB because, given our
aggregate approach and (a2), contexts for social roles should involve at least systems that are essential
to extrinsic dispositions that are intimately connected with socially relevant relational roles.</p>
      <p>Nevertheless, a deeper inquiry into social roles and their contexts warrants investigation into social
elements that are necessary for a more substantive conception of social roles. We offer a few pointers
as to this by borrowing insights from the relevant literature:
4 Here we utilize Röhl &amp; Jansen’s [9] account of the identity of dispositions, for its representation can be based on the simple usage of the
universal restriction (“only”) on classes in the Web Ontology Language (OWL) and it therefore helps to give a simple first-order logical
treatment of dispositions. See, however, Barton et al.’s [10] criticism that this “ONLY theory” of dispositions would encounter the theoretical
problem of “disposition multiplicativism” (by which they mean the arbitrary proliferation of dispositions) and their alternative “PARTHOOD
framework” for dispositions, which can avoid disposition multiplicativism.</p>
      <p>(1) Human intentionality. Human intentionality is a defining characteristic of social roles. For
instance, in developing a constructivist (observation-based) approach to objects in general, Bottazzi et
al. [21] discuss a way of distinguishing social objects from non-social ones and highlight the
humanintentional dimension of social objects. Our driving example of Alice’s social role of being a doctor
concerns a person Alice (as well as her patients, including Bob), but we did not examine Alice’s
intention closely. This task will require careful consideration of intentions [22] and intentionality
(aboutness) [23].</p>
      <p>(2) Conventionality. Masolo et al. [1] distinguish two senses (weak and strong) of sociality and
explore social roles based on its weak sense. That is to say, an entity is social “if it depends on agents
who, by means of some sort of convention, constitute, make use of, communicate about and accept it”
(ibid., p. 267) and “social” in this sense is roughly synonymous with “conventional”. They argue that
social roles are (social) concepts which are defined by descriptions: roughly, a social role classifies
objects (in a time-relative way) when they fit descriptions that associated with the role. For example,
Alice plays a social role of being a doctor at a hospital because the description of what it is to be a
doctor at this hospital applies to her. Descriptions could be seen as a kind of informational entities [24]
that emerge from intentional agents’ acts.5 This would imply that analysis of the conventionality of
social roles will need theorizing upon the interaction between informational entities and intention(ality).</p>
      <p>(3) Social and deontic normativity. In Masolo et al.’s [1] strong sense of sociality, an entity (e.g.,
money) is social “if, in addition to having a conventional nature, its very conventional constitution
involves a network of relations among social agents” such that this network possesses “(collective)
intentionality, actions and deontic constraints” (ibid., p. 267). They say that many examples of social
roles (e.g., money) are social in this sense. Donohue [25] develops a framework for social and deontic
normativity that would be concordant with Searle’s [3][4] social ontology. His central thesis is that
socio-deontic phenomena (e.g., obligations and permissions) can be accounted for in terms of a
prescriptive representation content that is backed by collectively held dispositions (which we may call
“normativity-conferring dispositions”) to monitor for compliance and to sanction in case of
noncompliance. A prescriptive representation content is the kind of informational entity that prescribes
what something should be done, such as a recipe for cooking (refer to Ethier et al. [26] for some thoughts
on prescriptive information entities). In playing a social role of being a doctor at hospital, for instance,
Alice should follow a designated guideline for treatment and she would be otherwise sanctioned by the
authoritative hospital committee. Therefore, a comprehensive study of social roles will call for a
welldeveloped account of the triad of intention(ality), informational entities (especially prescriptive ones),
and normativity-conferring dispositions.</p>
    </sec>
    <sec id="sec-8">
      <title>4. Related Work</title>
      <p>Social roles have long attracted attention in social sciences, but they tend to be considered with a
central focus on their social components (e.g., social norms) in these domains [27][28] and their
ontological aspects are still largely unexplored. Examples of such aspects include their relationships
with other non-social kinds of roles, although we endeavored to address this issue through a
Loebeinspired aggregate view of social roles. More generally, it remains challenging to have a clear overview
of various accounts of roles in formal ontology, in spite of Toyoshima’s [16] recent examination of
theories of roles that are developed in compliance with some prominent upper ontologies, such as GFO
(mentioned in Section 2), Basic Formal Ontology (BFO) [29] and the Unified Foundational Ontology
(UFO) [30].</p>
      <p>It may be interesting to compare our dispositional approach to roles with the UFO relational account
of roles that is based on “qua individuals” and “relators” [31]. A qua individual is an individual (e.g.,
Mary-qua-student) that bears all externally dependent moments (where “moment” would be
5 Masolo et al. ([1], p. 271) list basic features of descriptions: “Descriptions are created by (communities of) intentional agents at the time of
their first encoding in an expression of a ‘public’ (formal or informal) language.” “Different expressions (possibly in different languages) can
be associated to the same description, provided they have the same semantic content. I.e., descriptions have a unique semantic content.”
“Descriptions must be encoded on (possibly multiple) physical supports. [Footnote: Printed or recorded texts obviously count as physical
support, but memory or other cognitive processes should probably be considered as well (think of orally transmitted tales, rules and contracts.)]”
“Descriptions are usually accepted (adopted) by (communities of) intentional agents, but a description can exist even if no one accepts it, as
long as it remains encoded; acceptation can change in time.” “Descriptions cease to exist when their last physical support ceases to exist.”
synonymous with “property”) of an individual (e.g., Mary) such that those moments share the same
external dependencies (e.g., on the XYZ college) and the same “foundation” (e.g., Mary’s enrollment
in the XYZ college) which is a process (“event” in UFO’s terms). Roughly, it is an aggregate of
externally dependent properties. A relator is then an aggregate of qua individuals that share the same
foundation. Assuming that Mary and John enrolled at the XYZ college at the same time, for instance,
there is an “enrollment relator” that is composed of Mary-qua-student and John-qua-student which are
founded upon the same process of the enrollment in the XYZ college. A role is a type-level entity (e.g.,
Student) that applies contingently to an individual (e.g., Mary) that bears one or more qua individuals
(e.g., Mary-qua-student) of a certain type. It will be worthwhile to examine the possibility that some
externally dependent moments that constitute qua-individuals and relators that constitute these
quaindividuals would correspond to extrinsic dispositions and joint dispositions that are linked by (a2) with
socially relevant relational roles.</p>
    </sec>
    <sec id="sec-9">
      <title>5. Conclusion</title>
      <p>To elucidate social roles and social contexts, we focused on Loebe’s [7] “aggregate view” of social
roles based on his tripartition of roles (relational, processual, and social) and investigated dispositionally
the connections between socially relevant relational roles and processual roles, which provide a
foundation for an analysis of social roles. A key finding is that socially relevant processual and
relational roles are closely linked with intrinsic and extrinsic dispositions, respectively, and systems
that are connected (via such extrinsic dispositions) with the socially relevant relational roles would
serve as a minimal element of contexts for social roles.</p>
      <p>In the future we will continue to pursue this aggregate view of social roles. This work will necessitate
further development of a formal ontology of extrinsic dispositions [16], especially of their systemic
aspects [18]. It will be also interesting to tailor our theory for a specific ontological background. For
instance, it is conjectured that extrinsic dispositions would fall outside the category of disposition in
BFO and at least some roles in BFO may be extrinsic dispositions [16]. Our proposal may bring about
the hypothesis that some roles in BFO (especially the ones with social import) are extrinsic dispositions
that are closely related with socially relevant relational roles in the way that is specified by (a2). This
direction of research may be also theoretically deepened with recourse to the recent proposal [32][33]
that relationships are truthmakers for relations, where relationships can be seen roughly as an aggregate
of property particulars (including presumably extrinsic dispositions).</p>
    </sec>
    <sec id="sec-10">
      <title>6. Acknowledgements</title>
      <p>FT acknowledges financial support by the SPOR Canadian Data Platform (CIHR).</p>
    </sec>
    <sec id="sec-11">
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