In this chapter we investigate how organizations can be represented as graphs endowed with formal semantics. We distinguish different dimensions of organizations. Each of these dimensions leads to a different structure in the organizational graph. By giving the graphs a formal semantics in Description Logic we show that it is possible to formalize the effect of the organization on the activities of the agents playing the roles of the organization. Such perspective, which combines quantitative (graph-theory) and qualitative (logic) methods is shown to provide a formal ground for the study and analysis of properties of organizations which are commonly addressed only informally.
“Als je voor elke positie de beste speler kiest, heb je nog geen sterk elftal maar een team dat als los zand uiteen valt.''
“If you choose the best player for each position, you still don't get a strong team but a group which falls apart as loose sand.''
J. Cruijff, Dutch football folkloreTop
In Multi-agent Systems (MAS) software agents enjoy some degree of autonomy (Wooldridge & Jennings, 1995), exactly like human agents in human societies. As a consequence, in MAS the same problem arises of guaranteeing the designed system to exhibit some desired global properties without hampering the agents' autonomy. The opportunity of a `technology transfer' from the field of organizational and social theory to distributed Artificial Intelligence first (Fox, 1988), and then to MAS (V. Dignum 2003; Vázquez-Salceda, 2004) has often been advocated. In recent years, some research in MAS is even aiming at the explicit incorporation of entities such as organizations and institutions (normative systems) in computer systems, as testified by several contributions in the AAMAS conference series (Gini et al., 2002; Rosenschein et al., 2003; Jennings et al. 2004; F. Dignum et al., 2005; Weiss & Stone, 2006), the ALFEBIITE project (Pitt, 1999) and the COIN workshop series (Boissier et al., 2006; V. Dignum et al., 2007). Furthermore, several methodologies for MAS are based on organizational structures as their cornerstones such as, for instance, OperA (V. Dignum, 2003) and TROPOS (Bresciani et al., 2004), and GAIA (Zambonelli et al., 2003).
Notwithstanding this interest for organizations in MAS, little has been done to answer the key question “ What is an organization?'' or, less ambitiously, “ How can an organization be formally represented?''.
As a matter of fact, formal tools for the rigorous representation of organizational structure in MAS are not yet available and the study of organizational structure is still mainly informal. The literature on MAS ---with very few exceptions such as in particular Hannoun et al. (2002) and Hübner et al. (2002)--- addresses this type of structures only in an informal way by means of diagrams and charts like in Decker & Lesser (1995). In such informal studies, many issues remain hidden in the figures. We believe that, in order to successfully import the notion of organization for the design of MAS, “the space of organizational options must be mapped, and their relative benefits and costs understood'' (Horling & Lesser, 2004), and to provide such a “map'' a rigorous analysis of organizational structure plays a crucial role. If we want the notion of structure to be of any practical use for MAS, figures are plainly not enough, since they fail to address two fundamental aspects of organizational structures: 1) The formal (graph-theoretical) properties of the links between the roles in the structure; 2) The `meaning' of those links, that is to say, the effects they have on the activities of the agents populating the organization. These considerations lead us to the research question of the present chapter: “How can we formally represent organizational structures and their effect on the activities of the agents?”. More specifically, we will be addressing the following two issues:
What are the graph-theoretical properties of the links connecting the roles in the structure?
What is the `meaning' of those links, that is to say, the effects they have on the activities of the agents operating the organization?