Prototipo inicial, Williams Pond, Wellfleet, Cape Cod, Massachusetts, 1945 En 1946 la revista neoyorkina Interiors publicaba el emplazamiento de un conjunto de cinco

What is the minimal set of ingredients that are essential for building a viable notion of group commitment? In our investigation, we have isolated and separately characterized three important ingredients of group commitments. In addition, a group may stay aware of these aspects in different ways:

1. A group – usually, a strictly cooperative team has to be formed. In TeamLog, a team is established on the basis of a collective intention.

2. A plan – a social plan that details how to realize the group’s goal needs to be created. 3. A distribution of responsibilities – a set of pairwise social commitments towards the

actions from the social plan reflects the agents’ responsibilities during team action.

As collective intentions have been extensively treated in the previous chapter, we will focus on the remaining ingredients, starting from social plans.

4.3.1 Social Plans

Collective commitments are plan-based: they are defined with respect to a given social

plan. Individual actions (fromAc, see Section 4.2) may be combined into group actions by social plan expressions, as in Definition 4.4 of Section 4.2. The social plan should be effec-

tive, as reflected in the predicate constitute(ϕ, P ), to be explained in Section 6.4.1. This

predicate states that successful realization of the planP leads to the achievement of goal ϕ.

Let us give a simple example of a social plan, based on the first example in Section 4.1. Consider a team consisting of three agentst (the theorem prover), l (the lemma prover)

and c (the proof checker) who have a collective intention to prove a new mathematical

theorem. In joint deliberation, they have divided their roles according to their abilities and preferences. Suppose during planning they formulate two lemmas, which still need to be proved, and the following complex individual actions: provelemma1 , provelemma2 (to prove lemma 1, respectively 2), checklemma1 , checklemma2 (to check a proof of

Tuning Machine for Collective Commitments 61

lemma 1, respectively 2), provetheorem (prove the theorem from the conjunction of lem- mas 1 and 2) and checktheorem (to check the proof of the theorem from the lemmas). One possible social plan they can come up with is the following. First, the lemma prover, who proves lemmas 1 and 2 in succession, and the theorem prover, who proves the theorem from the two lemmas, work in parallel, and subsequently the proof checker checks their proofs in a fixed order, formally:

P =



provelemma1, l;
provelemma2, l 
provetheorem, t;

checklemma1, c;
checklemma2, c;
checktheorem, c

Consider again this group of agents with the same collective intention to prove a new mathematical theorem. In the course of planning they formulate two lemmas, but this time either one of the lemmas suffices to prove the theorem as follows:

P =




provelemma1, l;
checklemma1, c ∪

provelemma2, l ;

checklemma2, c;
provetheorem, t;
checktheorem, c We will use this context as a running example in Section 6.5.

4.3.2 Social Commitments

In our model of teamwork, pairwise or social commitments are first-class citizens. Most of the time, cooperation between two agents involves a certain asymmetric role division: the first agent (calledj ) wants some state of affairs to be achieved (an action to be performed)

while a second agent (called i) decides that it can perform the action needed. When j is

willing to havei as a helper and to oversee the achievement of the goal (the performance

of the action), they recognize their potential for cooperation. This recognition is reflected in a promise fromi to j . A social commitment is the bilateral motivational attitude that

corresponds to such a promise.

Thus, a social commitment understood this way is stronger than an individual inten- tion. If i commits to j to do something, then in the first place i has the intention to

do that. Moreover, j should be interested in i fulfilling its intention. These two condi-

tions (inspired by Castelfranchi, 1995), need to be enhanced by the condition expressing the agents’ awareness about the situation, that is about their individual attitudes.1 _Such

awareness is generally achieved by communication. In our earlier papers, awareness was expressed in terms of common belief (Dunin-K ¸eplicz and Verbrugge, 2004). In the sequel, social commitments are characterized using an awarenessG-dial. Two characterizations are given, with respect to actionsα and propositions ϕ, respectively:

COMM(i, j, α)↔ INT(i, α) ∧ GOAL(j, done(i, α)) ∧ awareness_{i,j}(INT(i, α)∧ GOAL(j, done(i, α)))

COMM(i, j, ϕ)↔ INT(i, ϕ) ∧ GOAL(j, done(i,stit(ϕ))∧

awareness_{i,j}(INT(i, ϕ)∧ GOAL(j, done(i,stit(ϕ)))

62 Teamwork in Multi-Agent Systems

Here,done(i,stit(ϕ)) stands for “agent i has seen to it that ϕ”. Indeed,stitcan be seen as a shortcut, turning the achievement of a state of the world reflected by proposition

ϕ, into a possibly complex action. To formalize it, one can move to a second-order

language to quantify over scenarios. Alternatively, Horty and Belnap (1995) propose a branching time framework. More recently, quantification over possible strategies has found a natural expression in Alternating Time Temporal Logic (ATL), which can be embedded in a logic for strategic stit (Broersen et al., 2006). We do not want to tie ourselves to a specific choice of formalization and do not analyzestitany further.

If the awarenessG-dial is placed at C-BELG for G= {i, j}, then social commitment obeys positive introspection, namely:

COMM(i, j, ϕ)→ C-BELG(COMM(i, j, ϕ))

This follows from the awareness condition included in the definition. Note that it is not possible to derive negative introspection, because agents are in general not aware of the absence of common beliefs (that is¬C-BELG(ϕ)→ BEL(i, ¬C-BELG(ϕ)) is not provable fori∈ G).

The above definitions present the bare ingredients of social commitments and not the process leading to their establishment. It may happen that the language of informational and motivational attitudes is not sufficiently fine-grained to express various subtle aspects involved. In fact, both causality and obligation come to the fore when creating social commitments. Usually agenti takes on a social commitment COMM(i, j, α) because the

other agent is interested in it, even though such causality is not explicitly reflected in the definition (see Castelfranchi, 1999 for a recent discussion of causality and commitment). Then after adoption, social commitments lead to an obligation for agent i to fulfill its

promise of performing the action or achieving the goal. In the definition, only the final formal outcome is shown, as befits the static part of our theory of teamwork. The more dynamic, process-oriented part TeamLogdynof the story will be told in Chapters 5 and 6.

4.3.3 Deontic Aspects of Social Commitments

Castelfranchi (1995) states that ‘if I commit to you to do something, then I ought to do it’. Additionally, we find that the strength of the obligation depends on the situa- tion and the agents, for example, are the agents involved responsible ones? Below we give an axiom that characterizes responsible agents by relating social commitments and obligations. It reflects our view that the obligation is related to the current state of the agent’s commitment: only as long as an agent’s commitment is still valid, it ought to fulfill it. Formally:

COMM(i, j, ϕ)→ A (OUGHT(i, ϕ) U ¬COMM(i, j, ϕ))

Here, OUGHT(a, ϕ) is a modal operator with intended reading ‘i is obliged to achieve ϕ’.

The axiom is formulated in the temporal language and means informally: ‘Ifi commits to j to achieve ϕ, then i is obliged to achieve ϕ until its social commitment has been dropped

appropriately’. The axiom above is meant only as a possible extension of TeamLog. There are many axiom systems and corresponding semantics in the literature on deontic logic (cf. Aaqvist, 1984). There are also systems in which agents have obligations not merely towards propositions, but also with respect to actions (cf. d’Altan et al., 1993).

Tuning Machine for Collective Commitments 63

It is sufficient, though, to assume a standard propositional KD-type modal logic for the obligations of each agent. In the corresponding Kripke semantics, there are the usual accessibility relationsRathat lead from worldsw to worlds that are ‘optimal’ for agent a in w. These accessibility relations are serial, corresponding to the consistency of obligations.

4.3.4 Commitment Strategies

Let us peak into agents’ differing propensities to maintain or drop their social commit- ments. The key point is whether and in which circumstances an agent is allowed to drop a social commitment. If such a situation arises, the next question is how to deal with it responsibly. The definitions are inspired by those of Rao and Georgeff (1991) for inten- tion strategies. The need for agents’ responsible behavior led us to include additionally the social aspects of communication and coordination. We assume that the commitment strategies are an immanent property of the individual agent and that they do not depend on the goal to which the agent is committed, nor on the other agent to whom it is committed. We also assume that each agent knows which commitment strategies are adopted by all agents in the group. This ‘meta-knowledge’ ensures proper replanning and coordination (Dunin-K ¸eplicz and Verbrugge, 1996). See the Appendix for the formal definitions and Dunin-K ¸eplicz and Verbrugge (1999) and Rao and Georgeff (1991) for more discussion. The strongest commitment strategy is followed by the blindly committed agent, who maintains its commitments until it actually believes that they have been achieved.

Single-minded agents may drop a social commitment when they do not believe anymore that it is realizable. However, as soon as the agent abandons a commitment, it needs to communicate and coordinate with the agent to whom it is committed.

For open-minded agents, the situation is similar as for single-minded ones, except that they can also drop social commitments if they do not aim for the respective goal anymore. As in the case of single-minded agents, communication and coordination should be involved.

There still remains the important problem of the consequences of an open-minded agent dropping a social commitment. We assume here that it is allowed to do this after communicating and coordinating with its partner. This solution, however, is not always subtle enough. We agree with Castelfranchi (1995) and Tuomela (1995) that in some cases dropping a social commitment should be more difficult and should cause real consequences for an agent, potentially expressed in extra axioms.

When analyzing the possibilities of cooperation, it turns out that blindly-committed agents, who seem most trustworthy at first sight are hard to cooperate with when replan- ning is needed (Dunin-K ¸eplicz and Verbrugge, 1996). Thus, the distribution of commit- ment strategies in a team appears to be important.

Of course it is possible to classify agents along different lines: for example one may characterize them according to eagerness to adopt new social commitments (see Cavedon

et al., 1997) etc.