A Formal View on Commitment Change

The previous chapter covered a methodical approach to tackling the reconfiguration prob-

lem: when maintaining a collective intention during plan execution, it is crucial that

agents re-plan properly and efficiently according to the situation changes. The essence of the reconfiguration algorithm is the dynamics of social and collective attitudes during teamwork. In a formal specification of these notions in BDI systems, different kinds of modal logics are exploited. Dynamic, temporal and epistemic logics are extensively used to describe the single agent case. Inevitably, social and collective aspects of teamwork should be investigated and formalized, again, in a combination of different kinds of modal logics. As the static part of TeamLog, individual, social and collective attitudes have been defined in Chapters 2, 3 and 4. Now we aim to formally describe the maintenance of collective commitments during reconfiguration.

In case some action performance fails during team action, the realization of the collec- tive commitment is threatened. Thus, some effects of the previous, potentially complex and resource consuming stages of teamwork may be wasted. However, to save the situation, often a minor correction of the social plan and the corresponding collective commitment suffices. For example, it might be enough to reallocate some actions to capable team members. If this is not feasible, a new plan may be established, slightly changing the existing one, etc. In the best case, the necessary changes are insignificant, re-using most of the previously obtained results.

As we argued in Chapter 5, the reconfiguration algorithm reflects a rigorous method- ological approach to these changes, resulting in an evolution of collective commitment. In the current chapter, we characterize the properties of this process using dynamic logic.

Teamwork in Multi-Agent Systems: A Formal Approach Barbara Dunin-K ¸eplicz and Rineke Verbrugge  2010 John Wiley & Sons, Ltd

100 Teamwork in Multi-Agent Systems

This approach will allow us to precisely describe the results of complex actions and to highlight the change of motivational and informational attitudes during reconfiguration. Various aspects of evolution will be performed from a system developer’s perspective, rather than the one of an agent. Finally, the properties describing system behavior, update or revision of agents’ attitudes and properties of complex stage-related procedures provide a high-level specification of the system. This will enable a system designer to construct a correct system from the specification and to formally verify its behavior.

The reconfiguration procedure is based on the four-stage model of teamwork pre- sented in Chapter 5. Before arguing formally that particular cases of reconfiguration are treated correctly, it has to be ensured that the stages are properly specified and then con- structed. As a sort of an idealization, we introduce stage-associated procedures, viewed as complex social actions. These actions are highly context- and application-dependent. Therefore, they do not obey any generic axiomatization and a logical system characteriz- ing them cannot be provided. Instead we formulate in an extended language of dynamic logic relevant high-level properties in the form of semantic requirements. These condi- tions should be ensured by the system developer when constructing a specific system (see Section 6.4).

6.1.1 Temporal versus Dynamic Logic

The effects of agents’ individual actions and plans, as well as other changes in a system, can be modeled using variations of either dynamic logic or temporal logic. Because dynamic logic has been designed especially to represent reasoning about action and change, we decided to adopt the action-oriented dynamic logic approach here. Tempo- ral logic is well-suited to describe more general changes over time, not those related to actions solely. Usually, BDI-logics are based on a linear or branching temporal logic, sometimes with some dynamic additions (Cohen and Levesque, 1990; Rao and Georgeff, 1991; Singh, 1990; Wooldridge, 2000). In the Appendix we present the temporal approach based on computation tree logic CTL (Emerson, 1990), that can be considered as an alter- native to describe teamwork dynamics. This will give the interested reader a chance to compare the two approaches. Apparently, a full specification of the system includes com- plex temporal aspects, such as persistence of certain properties over time, usually until a given deadline. However, we will not introduce these procedural temporal elements into the logical framework. It is known that the combination of dynamic and temporal logic is extremely complex, especially in the presence of other modal operators, as is the case here (Benthem and Pacuit, 2006). Therefore, instead of making the logical system even more intractable and much harder to understand, we decided that temporal aspects should be left to the system developer to implement them in a procedural way.

This chapter is organized in the following way. In Section 6.2, the logical language and semantics are introduced. Section 6.3 is devoted to Kripke models and dynamic logic for actions and social plans. Section 6.4 gives a short overview of the four stages of teamwork. The central Section 6.5 presents in a multi-modal language how collective commitments evolve during reconfiguration. Finally, Section 6.6 focuses on discussion and options for further research.

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