On the Ontological Nature of REA Core Relations

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 di erent 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 rei cation and truthmaking proposed in the past.

Keywords

• REA accounting model
• ontological analysis
• relators

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 foundation 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 Giancarlo Guizzardi and his group [ 7 ]. However, mapping the REA primitives on the UFO primitives was not an easy task, so that di erent choices were made.

In particular, as shown in Table 1, rather di erent choices were made about the nature of resources, events and commitments, and especially about the REA core relations: duality, reciprocity, stock ow, and participation [16, p. 17]. The di erent choices mainly concern the UFO notion of relator, which is a very powerful notion but also one that is sometimes di cult to grasp.

The original motivation of this paper|which is still its main purpose|was to reconcile these di erent 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 to discuss the mapping choices mentioned above in the light of a recent revisitation of the original Guizzardi's notion of relator, and more in general of the foundations of relationship rei cation [ 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 rei cation based on [ 6 ], and at the same time to acknowledge the di culty of using relators in concrete cases. We decided therefore to make a further clari cation e ort (especially with respect to the terminology adopted), whose results are presented here for the rst time, although in a compact form. So, this paper can be also seen as a compact presentation of our revised theory of relationship rei cation, with concrete examples taken from the REA domain.

In the next section we recap the distinctions among di erent kinds of binary relations discussed in the literature, focusing on how they can help us to decide which relations can be rei ed, and clarifying some terminological ambiguities concerning the original Guizzardi's distinction between formal and material relations. Then we discuss the ontological nature of the four REA core relations (and their arguments) in detail, pointing to some misconceptions on their mappings to UFO categories that sometimes accumulated in the REA literature, partially in uenced by the terminological confusion mentioned above. Finally, we conclude with the proposal of an integrated OntoUML model that links together 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 speci c construct, called the relator, standing for such intervening individual.

In the philosophical literature, the formal/material distinction varies significantly among di erent authors both in content and terminology, and overlaps with other distinctions, most notably that between internal and external relations. The original idea behind internal relations is that they hold in virtue of the `nature' of their relata. However, di erent opinions exist on whether such nature is determined by the actual intrinsic properties of relata (whether essential or not), or just by their essential properties. Accordingly, internal relations are de ned in two main ways [ 13 ], which we shall label with internal1 and internal2. The rst de nition is due to Moore [ 17 ], and it says that a relation is internal1 i 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 de nition, due to Russell [ 20 ] and slightly re ned by Lewis [ 12 ], says that a relation is internal2 i it is de nable in terms of the intrinsic properties of its relata, and external2 otherwise.

Let us see now how Guizzardi's distinction among formal and material relations, which is crucial for his notion of relator, is mapped to the two de nitions 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 de ned formal relations as the complement of material relations, and his de nition 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 existentially 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 classi ed as material by Fisher and Schwaiger [ 1 ], but turns out to be formal according to Guizzardi's de nitions.

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 rei ed. In a recent paper [ 6 ], Guarino and Guizzardi showed that none of the distinctions considered so far (essential/contingent, internal/external4, formal/material) can help in this decision. Their analysis was mainly motivated by the confusing behavior of comparative relations.

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(J ohn; 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 rei cation, there may be good reasons to talk of them [ 5 ], and therefore reify them: for instance, one may want to keep track of the di erence in height between a mother and her son, or of the temperature di erence between two bodies. So, comparative relations seem to share something in common with the other relations that deserve to be rei ed. 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 different behavior of individual relationships belonging to the same comparative relation, strictly speaking the picture describes kinds of relationships. Relationships are classi ed along two main orthogonal distinctions: internal/external and descriptive/non-descriptive. Descriptive relationships are those deserving rei cation, 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 rei cation choice.

Let us now brie y 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 quadrant 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, holding 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 a ect 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 rst clarify the nature of its arguments, which are economic events. REA de nes them as \occurrences in time wherein ownership 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 ] classi ed 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 rst 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 de ned [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 ]).

Let us now discuss whether duality can be rei ed 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 speci c 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 ful llment 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 ful ll.

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 former 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 simpli ed OntoUML model showing this account of duality and its link with reciprocity (to be discussed below) appears in Fig. 2. 4

The Reciprocity, Participation and Stock ow Relations

In the REA documentation [ 16 ], reciprocity is de ned 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 rst 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 de nitely 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 relationship is a descriptive external relationship between two agents, rei ed 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 relation between the two commitments is of mutual existential dependence, which is an external non-descriptive relation, and therefore is not rei ed. The two mutual commitments, together, form the truthmaker of the contractual relationship.

Concerning the participation and stock ow relations, let us rst 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 di erent roles).

Participation is an essential relation, which holds just in virtue of the existence 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 antipatterns [ 21 ] which will be hopefully automatically checked by the OntoUML environment [ 18 ] in the future. 7 We are assuming a simpli ed picture. See [ 14 ] for an in-depth ontological analysis.

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