=Paper=
{{Paper
|id=Vol-2239/article_9
|storemode=property
|title=On the Ontological Nature of REA Core Relations
|pdfUrl=https://ceur-ws.org/Vol-2239/article_9.pdf
|volume=Vol-2239
|authors= Nicola Guarino,Guizzardi Giancarlo,Tiago Prince Sales
|dblpUrl=https://dblp.org/rec/conf/vmbo/GuarinoGS18
}}
==On the Ontological Nature of REA Core Relations==
https://ceur-ws.org/Vol-2239/article_9.pdf
On the Ontological Nature of REA Core
Relations
Nicola Guarino1 , Giancarlo Guizzardi2 , and Tiago Prince Sales1,3
1
ISTC-CNR Laboratory for Applied Ontology, Trento, Italy
nicola.guarino@cnr.it
2
Free University of Bolzano-Bozen, Trento, Italy
giancarlo.guizzardi@unibz.it
3
University of Trento, Italy
tiago.princesales@unitn.it
Abstract. In this paper we review and discuss some recent attempts
at ontological re-engineering of REA in the light of the UFO ontology
and the OntoUML language, focusing in particular on different choices
concerning the UFO notion of relator. We also take this as an opportunity
to clarify and revise Guarino and Guizzardi’s general theory of reification
and truthmaking proposed in the past.
Keywords: REA accounting model, ontological analysis, relators
1 Introduction
REA (Resources, Events, Agents) is a well-known accounting model with an
established community of users. It was proposed by W. McCarthy in 1982 [15]
and evolved as an ISO standard in 2007 [16] after a re-visitation in the light
of ontological principles [4]. Since then, various scholars contributed to enhance
REA’s understandability and applicability [3,10,11,22], aiming at the same time
at considering REA (or a suitably extended and revised version of it) as a foun-
dation for business modeling and enterprise modeling in general. More recently,
two groups of authors [1,2] attempted an ontological re-engineering of REA in
the light of the UFO ontology and the OntoUML language, developed by Gian-
carlo Guizzardi and his group [7]. However, mapping the REA primitives on the
UFO primitives was not an easy task, so that different choices were made.
In particular, as shown in Table 1, rather different choices were made about
the nature of resources, events and commitments, and especially about the REA
core relations: duality, reciprocity, stockflow, and participation [16, p. 17]. The
different choices mainly concern the UFO notion of relator, which is a very
powerful notion but also one that is sometimes difficult to grasp.
The original motivation of this paper—which is still its main purpose—was
to reconcile these different views by clarifying the ontological nature of REA
core relations, and especially the duality relation, which, despite its fundamental
role, is sometimes considered as a bit mysterious. In this perspective, we decided
Table 1. REA’s core relations and related classes mapped to UFO.
Fischer &
REA Class Gailly et al.[2] This Paper
Schwaiger [1]
Economic Resource Role Kind RoleMixin
Economic Event Relator Univ. Kind Event Univ.
Commitment Relator Univ. Kind Mode Univ.
Stockflow Mediation Rel. Formal Rel. Internal Non-
Descriptive Rel.
Participation Mediation Rel. Formal Rel.
Duality Formal Rel. Material Rel. External Non-
Descriptive Rel.
Reciprocity Formal Rel. Material Rel.
to discuss the mapping choices mentioned above in the light of a recent re-
visitation of the original Guizzardi’s notion of relator, and more in general of
the foundations of relationship reification [5,6].
There is however an additional motivation that led us to write this paper.
Analyzing the subtleties of REA relations gave us the opportunity to test the
generality and the limits of our new account of relators and relationship reifica-
tion based on [6], and at the same time to acknowledge the difficulty of using
relators in concrete cases. We decided therefore to make a further clarification
effort (especially with respect to the terminology adopted), whose results are
presented here for the first time, although in a compact form. So, this paper
can be also seen as a compact presentation of our revised theory of relationship
reification, with concrete examples taken from the REA domain.
In the next section we recap the distinctions among different kinds of binary
relations discussed in the literature, focusing on how they can help us to decide
which relations can be reified, and clarifying some terminological ambiguities
concerning the original Guizzardi’s distinction between formal and material re-
lations. Then we discuss the ontological nature of the four REA core relations
(and their arguments) in detail, pointing to some misconceptions on their map-
pings to UFO categories that sometimes accumulated in the REA literature,
partially influenced by the terminological confusion mentioned above. Finally,
we conclude with the proposal of an integrated OntoUML model that links to-
gether the duality and the reciprocity relation, explicitly grounding the former
in the contractual relationship among the trading partners.
2 Kinds of Relationships
In his early work on UFO, Guizzardi borrowed from Heller and Herre [9] a crisp
distinction between formal relations, intuitively understood as holding between
two or more entities “directly without any further intervening individual” [7,
p. 236], and material relations, which require the existence of an intervening
individual. A modeling proposal at the core of OntoUML was to systematically
introduce – for all material relations – a specific construct, called the relator,
standing for such intervening individual.
In the philosophical literature, the formal/material distinction varies signif-
icantly among different authors both in content and terminology, and overlaps
with other distinctions, most notably that between internal and external rela-
tions. The original idea behind internal relations is that they hold in virtue of
the ‘nature’ of their relata. However, different opinions exist on whether such
nature is determined by the actual intrinsic properties of relata (whether essen-
tial or not), or just by their essential properties. Accordingly, internal relations
are defined in two main ways [13], which we shall label with internal1 and
internal2 . The first definition is due to Moore [17], and it says that a relation is
internal1 iff it necessarily holds just in virtue of the mere existence of its relata,
and external1 otherwise. In other words, an internal1 relation is essential to its
relata. The second definition, due to Russell [20] and slightly refined by Lewis
[12], says that a relation is internal2 iff it is definable in terms of the intrinsic
properties of its relata, and external2 otherwise.
Let us see now how Guizzardi’s distinction among formal and material re-
lations, which is crucial for his notion of relator, is mapped to the two defini-
tions above. To avoid confusions, we shall use the terms essential/contingent
as synonyms of internal1 /external1 , using just internal/external as synonyms
of internal2 /external2 . In his book [7, p. 236], Guizzardi pointed explicitly to
Moore while talking of formal relations, but, in retrospective, what he actually
had in mind was more in line with Russel’s and Lewis’ tradition, since for him
formal relations included comparative relations like taller than, which is not
essential since it may not necessarily hold when the relata exist. However, he
defined formal relations as the complement of material relations, and his defini-
tion of the latter [7, p. 241] is stricter than that of external relations, since for
him a material relation holds in virtue of the existence of a relator composed
of particularized properties called modes that inhere in the relata and are exis-
tentially dependent on a common external entity called foundation. The typical
example he makes is that of a marriage relationship, whose relator is composed
of modes existentially dependent on a common wedding event. So, Guizzardi’s
‘material’ is narrower than ‘external’, and, since the formal/material distinction
is exhaustive, his ‘formal’ turns out to be broader than ‘internal’.
As a result, relations like being both observed by John or being both parts of the
same whole, which are external since they can’t be derived from the properties
of their relata, turn out to be formal according to [7], because there is nothing
that inheres in the relata in virtue of which the relation holds. In other words,
there is no truthmaker inhering in the relata, so there is no relator. Rather,
the truthmaker is outside the relata, since it inheres in John or in the whole
that includes the two parts. As we shall see, this is exactly what happens with
REA’s duality relation, which was intuitively classified as material by Fisher and
Schwaiger [1], but turns out to be formal according to Guizzardi’s definitions.
Let us now go back to the main reason of the formal/material distinction
in conceptual modeling, which is deciding whether or not a relationship can
be reified. In a recent paper [6], Guarino and Guizzardi showed that none of
the distinctions considered so far (essential/contingent, internal/external4 , for-
mal/material) can help in this decision. Their analysis was mainly motivated by
the confusing behavior of comparative relations.
Fig. 1. Kinds of relationships (revised from [6]).
On one hand, as observed by Simons [23], some comparative relations turn
out to be essential, but others are contingent. For instance, the mere existence of
an electron e and a proton p is enough to conclude that heavier(p, e) holds (since
both of them have that particular mass essentially), but the mere existence of
John and Mary is not enough to conclude that taller(John, M ary) holds, since
they do not have that particular height essentially. Moreover, Simons noticed
that, within the same relation, some individual relationships (like heavier(p,e))
may be essential, while others (like heavier(John,Mary)) may be just contingent.
On the other hand, despite comparative relations were considered as formal
in Guizzardi’s sense, and therefore not deserving reification, there may be good
reasons to talk of them [5], and therefore reify them: for instance, one may want
to keep track of the difference in height between a mother and her son, or of the
temperature difference between two bodies. So, comparative relations seem to
share something in common with the other relations that deserve to be reified.
According to Guarino and Guizzardi, this commonality lies in the fact that they
are both descriptive relations, which hold in virtue of some particular aspects
inhering in the relata5 . So, their new proposal (with respect to the original
Guizzardi’s work) is that it is the mereological sum of these aspects that acts as
4
intrinsic/extrinsic in the original paper.
5
In Guizzardi’s work, such aspects have been called moments, and include individual
qualities and modes.
relator, accounting both for the fact that the relation holds and for the way the
relata are linked together, which may vary in time. Under this view, the relator
of a taller than relationship is the sum of the heights (individual qualities) of the
two relata, while for a marriage relationship the relator is a sum of externally
dependent modes, corresponding to the mutual commitments and obligations
inhering in the two partners.
Summing up, a complete picture of the various distinctions discussed so far
is shown in Fig. 1, which revises a similar picture published before [6, p. 241].
Note that, to account for the problem mentioned above concerning the dif-
ferent behavior of individual relationships belonging to the same comparative
relation, strictly speaking the picture describes kinds of relationships. Relation-
ships are classified along two main orthogonal distinctions: internal/external and
descriptive/non-descriptive. Descriptive relationships are those deserving reifica-
tion, which now include all comparative relationships among objects and events.
The ellipse shows how essential relationships are positioned orthogonally with
respect to the two main dimensions, so that just distinguishing them does not
help in the reification choice.
Let us now briefly discuss the four quadrants shown in Fig. 1. The upper
left quadrant includes all comparative relationships holding among objects and
events (some of which are essential, as we have seen). The upper right quad-
rant includes comparative relationships (such as resemblance) holding among
qualities, as well as essential relationships like essential parthood or biological
fatherhood. The bottom left quadrant includes relations such as married to, hold-
ing in virtue of actual modes of their relata, but also historical relations such
as author of, which holds in virtue of some past mode (of the author). Other
interesting examples of relations belonging to this quadrant are those holding in
virtue of an emergent aspect that inheres in the sum of relata, and not in any of
the relata themselves. Being two meters away is an example of such emergent
(or systemic) relation, whose truthmaker is a distance quality that inheres in the
sum of two bodies. Gravitational attraction is an example of a similar relation
which is also essential. Since the truthmakers of these last two relations are not
relators in the original sense, Guizzardi’s material relations are therefore just a
subset of those belonging to this quadrant. Finally, the bottom right quadrant
includes merely historical relations such as born in, that holds in virtue of an
event occurred in the past, and the so-called Cambridge relations such as being
parts of the same whole, which hold in virtue of something external that doesn’t
affect the relata. As we shall see, this is the case of the duality relation.
3 The Duality Relation
This relationship is at the core of the REA ontology, so its correct ontological
analysis is clearly crucial. Let us first clarify the nature of its arguments, which
are economic events. REA defines them as “occurrences in time wherein owner-
ship of an economic resource is transferred from one person to another person”
[16]. Strangely enough, as we see from Table 1, Gailly and colleagues [3] classified
them as relators, seeing them as “mediating entities for the relation between an
economic resource and two economic agents”. Maybe the reason of this choice
was that the first version of UFO did not elaborate on the notion of events (a.k.a.
perdurants), which were later covered, for example, in UFO-S [19]. In any case,
events cannot be relators.
To see this, consider the way relators are defined [7, p. 240]: a relator is a
mereological aggregation of ‘modes’ that inhere in the relata and are existentially
dependent on a common external entity. In the case of a marriage, such modes
include for example the commitments and claims John has towards Mary, which
inhere in him and depend on Mary, as well as the corresponding modes inhering
in Mary and depending on John. Now, there is no part of an economic event that
inheres in an economic resource or an economic agent. So, economic events do not
mediate resources and agents. In addition, it is important to note that, in UFO,
relators are assumed as continuants in time (endurants) and not occurrences in
time (perdurants), and this fact is indeed crucial to model their genuine change in
time [5]. So, no event can be a relator (despite the fact that there is an intimate
connection between events and relators as discussed in depth in [6,8]).
Fig. 2. OntoUML fragment showing the link between duality and reciprocity.
Let us now discuss whether duality can be reified as a relator: Gailly and
colleagues say no, seeing duality as a formal relation, while Fisher and Schwaiger
say yes (Table 1). Since it can’t be derived from intrinsic properties of the two
events, duality is not an internal relation. Neither is it a descriptive relation, since
it does not hold in virtue of specific aspects inherent in the relata. Therefore, it
belongs to the bottom-right quadrant of Fig. 1, that of non-descriptive external
relations. Moreover, this is not an essential relation, because the simple existence
of an increment event and a decrement event involving resources of the same
value is not enough to conclude that a duality relationship holds between the
two, since the two events may not be related. However, there is a link between
the two events, which consists in the fact that one is the fulfillment of a debt
commitment which in turn depends on a credit commitment. So, Fisher and
Schwaiger are right in observing that such link “comes from the contracting
that underlies each business transaction” [1], and that “this contracting mediates
between the economic agents in an economic event”, but this is not enough to
reify the relation, since, being it non-descriptive, its truthmaker is external to
the relata. We conclude that duality is a derived relation, which can be inferred
on the basis of the reciprocity relation, once we know what commitments the
single events fulfill.
Besides the duality relation, a further ontological constraint that links an
increment event and its dual decrement is the fact that they are both part of
the same economic exchange event. This was indeed the choice made in a for-
mer paper by Schwaiger [22], which was unfortunately changed in the OntoREA
version. We believe that putting explicitly this mereological constraint in the
model is important to avoid undesired interpretations (note that in the original
REA model no constraints are put on the duality relation). A simplified On-
toUML model showing this account of duality and its link with reciprocity (to
be discussed below) appears in Fig. 2.
4 The Reciprocity, Participation and Stockflow Relations
In the REA documentation [16], reciprocity is defined as an “association between
economic commitments where the promise by one partner to execute an economic
resource transfer in the future is reciprocated by the other partner promising
a requited transfer in the opposite direction”. Gailly and colleagues consider
it as formal relation, while Fischer and Schwaiger make the opposite choice.
Concerning the relation’s arguments, commitments are considered as relators by
the former authors and as instances of a kind by the latter. The first choice is
not argued very much by the authors, and is possibly a misunderstanding due
to the fact that they cite an early version of [4]. In any case, it is not absurd
to consider a single commitment as a relator, reifying a one-sided commitment
relationship, but what counts in our case is the bilateral contractual relationship
resulting from reciprocal commitments, so it seems definitely more appropriate
to consider single commitments just as modes (of a certain kind) being part of
a contractual relationship (Fig. 1).
Going back to reciprocity, this is modeled as a material relation in OntoREA c
[1]. They say that “this relationship acts as truthmaker for the relation6 between
6
Relationship in the original text.
economic commitments”, but they also note although the authors note that such
relationship has a double nature, due to the truthmaker role played ultimately
by the contract among the two involved agents. Fig. 1 shows how this apparent
redundancy (or ambiguity) can be eliminated: a (bilateral) contractual relation-
ship is a descriptive external relationship between two agents, reified by a relator
that has two mutually existentially dependent conditional commitments [14] as
parts: a commitment to transfer a good if the buyer commits to pay, and the
reciprocal commitment to pay if the seller commits to transfer the good7 . The re-
lation between the two commitments is of mutual existential dependence, which is
an external non-descriptive relation, and therefore is not reified. The two mutual
commitments, together, form the truthmaker of the contractual relationship.
Concerning the participation and stockflow relations, let us first observe that
they are both specializations of a more general notion of participation, used in
UFO and several other ontologies to model the relation between objects and
events. So, both agents and resources participate in economic events (of course
with different roles).
Participation is an essential relation, which holds just in virtue of the exis-
tence of its relata: if an economic event exists, its very existence implies that
it has some participants. The two papers mentioned in Table 1 agree in this
respect, but Gailly and colleagues made a stronger choice that has no grounds
in UFO, assuming that participation is a mediation relation. This is due to their
choice of considering events as relators mediating between agents and resources,
whose problems have been discussed in Section 3.
5 Conclusions
Space doesn’t allow for much further discussion. We are happy that OntoUML is
being used more and more for REA-based ontologies, and business ontologies in
general. Analyzing the literature helped us to isolate some subtle OntoUML anti-
patterns [21] which will be hopefully automatically checked by the OntoUML
environment [18] in the future.
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