# maintenance_of_social_commitments_in_multiagent_systems__d69b9ba4.pdf

Maintenance of Social Commitments in Multiagent Systems

Pankaj Telang1 Munindar P. Singh2 Neil Yorke-Smith3

1 SAS Institute, Cary, NC 27513, USA 2 North Carolina State University, Raleigh, NC 27695, USA 3 Delft University of Technology, Delft, 2600GA, The Netherlands ptelang@gmail.com, singh@ncsu.edu, n.yorke-smith@tudelft.nl

We introduce and formalize a concept of a maintenance commitment, a kind of social commitment characterized by states whose truthhood an agent commits to maintain. This concept of maintenance commitments enables us to capture a richer variety of real-world scenarios than possible using achievement commitments with a temporal condition. By developing a rule-based operational semantics, we study the relationship between agents achievement and maintenance goals, achievement commitments, and maintenance commitments. We motivate a notion of coherence which captures alignment between an agents achievement and maintenance cognitive and social constructs, and prove that, under specified conditions, the goals and commitments of both rational agents individually and of a multiagent system are coherent.

1 Introduction Social commitments enable flexible coordination between agents. Research has primarily focused on achievement commitments (Castelfranchi 1995; Singh 1991, 2012). Consider an agent, such as an aircraft operator, who wishes to maintain a condition, such as an aircraft being fit to fly. Fig. 1 shows a high-level process flow of aerospace aftermarket services (van Aart et al. 2007). Its participants are an airline operator (OPER), an aircraft engine manufacturer (MFR), and a parts manufacturer (PMFR). Such situations highlight the need for understanding maintenance. We motivate a new family of social commitments wherein a debtor agent commits to a creditor agent that if some antecedent condition holds it would maintain a consequent condition until some discharge condition holds. Maintenance here means ensuring that the condition does not become false or, if it does become false, then to re-establish its truthhood. Specifically, we address how maintenance arises in connection with goals and commitments, as needed for multiagent systems. In this manner, our work contrasts with previous work on maintenance, which emphasizes single-agent settings and primarily addresses maintenance goals. Commitments are a natural basis for modelling interaction between agents by representing the meanings of communication (Chocron and Schorlemmer 2018; Mallya and Singh 2007; Singh 2000) and for reasoning about safety and control

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Operator Engine Mfr Parts Mfr

Operate Aircraft Monitor Engine Health

Request Maintenance

Pull Aircraft Remove Engine

Supply Parts

Arrange Maintenance

Replace Refurbish

Unscheduled

Figure 1: Aerospace aftermarket (van Aart et al. 2007).

(Marengo et al. 2011). Understanding maintenance commitments opens up the realm of social interaction. For example, maintaining a green lawn or paying down a mortgage are naturally modelled as maintenance commitments. A major theme of this paper is capturing the dynamic relationships between an agent s beliefs and goals (i.e., cognitive state) and its commitments (i.e., social state). Maintenance commitments enable richer relationships than otherwise possible, thereby supporting expanded forms of collaboration. Specifically, a commitment can relate to both end and means goals. For example, (1) an end goal of paying for a house may lead you to a maintenance commitment of mortgage: paying down a loan incrementally until it s paid up. (2) The mortgage commitment may lead you to a maintenance (means) goal of making loan payments, which (3) may lead you to commit to doing a job to get paid every month. Prior research has not adequately addressed maintenance commitments, treating them instead as achievement commitments for temporal formulae of the form always in the future p (Mallya, Yolum, and Singh 2003; Chesani et al. 2013). Such a formulation cannot capture the lawn example above. In contrast, we treat maintenance commitments as a

The Thirty-Fifth AAAI Conference on Artificial Intelligence (AAAI-21)

first-class construct, accommodating both reactive and proactive interpretations, and incorporating enactments wherein the condition may be negated and resurrected. Recent research characterizes coherence between a rational agent s (achievement) commitments and its (achievement) goals (Telang, Singh, and Yorke-Smith 2019). Building on this approach, we motivate an enhanced notion of coherence and with it study the synergy between an agent s maintenance commitments and its achievement and maintenance goals. We also show how coherence applies to a multiagent system as a whole with respect to specific maintenance commitments and achievement and maintenance goals. Our formal operational semantics develops two sets of conditional rules. First, life cycle rules specify the mandatory progression of goal and commitment states as the agents update their beliefs or perform social actions on the goals and commitments. Second, practical rules represent patterns of reasoning that specify potential social actions for an agent based on its goals and commitments. This paper advances the state of the art as follows. First, we introduce a new powerful type of social commitment, along with its life cycle. Second, we specify a formal semantics of multiagent system configuration, encompassing both achievement and maintenance commitments and goals. Third, we provide a methodology and an exemplar set of practical rules. Fourth, we define coherence and prove conditions under which it is maintained in the multiagent system.

2 Preliminaries and Necessary Background We suppose a finite set of agents, x1, x2, . . . A , and a finite set of propositional atoms, a1, a2, . . . Ω. We write Ψ for the set of all propositional formulae over Ω. The symbol abbreviates a a for any atom a, and the symbol abbreviates . We assume classical propositional logic. Specifically, given a set of propositions Φ Ψ and a proposition ψ Ψ, Φ |= ψ denotes that Φ entails ψ. We say that a set of propositions Φ is consistent iff Φ |= .

2.1 Beliefs Definition 1. A belief state function B : A Ψ { , } applies to agent-atom pairs and returns exactly if the agent believes the atom. We lift B to all propositions and close it under entailment: if B(x, p) and p |= q then B(x, q). An agent s beliefs are consistent: B(x, ). We write Bx = {p Ψ : B(x, p)} for the set of all current beliefs of x.

An agent x may have no belief about p or p, meaning that B(x, p) = and B(x, p) = can coexist.

Definition 2. The belief addition function + : B Ψ B adds a belief to the belief set.

E.g., B = +(B, p) means p is added to B; hence B (x, p) = .

2.2 Achievement Commitments and Goals We adopt achievement commitment and achievement goal as defined by Telang, Singh, and Yorke-Smith (2019), hereinafter TSY, denoting achievement commitments by C and achievement goals by G. We adopt and enhance TSY s definitions of state functions, maximal sets, and consistency.

2.3 Maintenance Goals

We define a maintenance goal and its life cycle based on Duff, Thangarajah, and Harland (2014). Let M = M(x, m, s, f) be agent x s maintenance goal for condition m. M s success condition is s and its failure condition f. Bx |= m means that x believes that m is false: thus, x adopts a recovery achievement goal. Let πx capture x s lookahead mechanism (provided by the agent designer), independent of M (Duff, Harland, and Thangarajah 2006). Then, Bx |= m πx( m) means that x believes that m will become false unless it acts appropriately: thus, x adopts a preventive achievement goal. Figure 2 depicts a state-based life cycle for a maintenance goal. We do not include the state Suspended from Duff et al., for reasons explained in the next section. Note the labels denote events (e:fail, e:succeed) and actions (all others). The actions are performed by the agent whereas the events are observed in the environment.

Definition 3. A maintenance goal is a tuple x, m, s, f , where x A is an agent, and m, s, f Ψ are the goal s maintenance, success, and failure conditions, respectively, where s f |= and m f |= .

We write a maintenance goal as M = M(x, m, s, f).

3 Maintenance Commitments

Informally, in a maintenance commitment, debtor x commits to creditor y that if the antecedent holds true, then until the discharge condition d becomes true, agent x will sustain the maintenance condition m. The symbol S stands for sustains.

Definition 4. A maintenance commitment is a tuple x, y, l, m, d , where x, y A are agents, x = y, and l, m, d Ψ are formulas. We call x and y debtor and creditor of this commitment and call l, m, and d its antecedent, maintenance condition, and discharge condition, respectively. We write a maintenance commitment as S = S(x, y, l, m, d). We write Sx for the set of all non-Null maintenance commitments in which agent x is either debtor or creditor.

Figure 3 shows the life cycle of a maintenance commitment. Both debtor x and creditor y represent the changing states of a commitment according to this life cycle. We elide the concerns of communication and alignment for simplicity. We define commitment strength, enhancing prior definitions (Singh 2008; Chopra and Singh 2009), to enable defining the important commitment closure properties below.

Inactive (I) Monitoring (M) Active (A)

Terminated (T) Failed (F) Satisfied (S)

reactivate m

terminate e:fail f e:succeed s

Figure 2: Life cycle of a maintenance goal.

Expired (E) Null (N)

Conditional (C) Detached (D) Sustain (B)

Terminated (T) Satisfied (S) Violated (V)

antecedent failure l Bx |= πx(l)

consequent failure m Bx |= πx(m) discharge d release

respond l m

sustained m

Figure 3: Life cycle of a maintenance commitment.

Definition 5. A maintenance commitment S1 = S(x, y, l1, m1, d1) is stronger than S2 = S(x, y, l2, m2, d2), written S1 S2 or S2 S1, iff l2 |= l1, l2 m1 |= l2 m2, and l2 d1 |= l2 d2. For example, let S1 = S(x, y, pay, green lawn bug free lawn, year end), meaning that x commits to maintaining the yard green. Let S2 = S(x, y, pay provide fertilizer, green lawn, year end). Then S1 is stronger than S2. Note commitment strength is a partial order. Definition 6. Let χS = {N, C, E, D, B, T, V, S} be the set of states in Figure 3. The maintenance commitment state function S maps each maintenance commitment to a state in χS. For simplicity, we write S(S(x, y, l, m, d)) as S(x, y, l, m, d). This function satisfies the following closure properties: If S(S1) {C, S, E}, S1 S2, then S(S2) = S(S1). If S(S1) {D, B, V, T}, S2 S1, then S(S2) = S(S1). The closure properties ensure that an agent configuration is semantically viable. The states assigned to maintenance commitments in any configuration respect the following property: if a commitment is in one of the states Conditional, Satisfied, and Expired, then so is any weaker commitment; whereas if a commitment is in one of the states Detached, Sustained, Violated, Terminated, then so is any stronger commitment. The properties are valuable for states that are not based on the content of a commitment. For example, when a commitment S is cancelled, all stronger commitments must be cancelled, else the S would be immediately resurrected from a stronger commitment. Using S1 and S2 as above, we see that if S2 is in Detached, then so must S1 be. Intuitively, a maximal maintenance commitment w.r.t. a state σ is a commitment in state σ such that no strictly stronger maintenance commitment is in the same state σ. We express practical rules over such commitments. Below, we identify sets of maximal commitments w.r.t. sets of states.

Update state per life cycle

Choose at most one enabled practical rule for each C and each G

Perceive GOALS

Apply chosen practical rules

COMMITMENTS

Update state per life cycle

Environment

receive messages

send messages

Figure 4: Simple agent architecture and operations.

Definition 7 (Maximal m-commitment set, maxc( )). Let Σ χS be a set of maintenance commitment states. maxc(Σ) = {S1 Σ | ( S2 Σ: S2 S1 S2 = S1)}.

Some of our theorems require an agent s configuration to have consistent maintenance commitments. Informally, an agent will not try to maintain a condition and its complement.

4 Configurations and Life Cycle Rules

Figure 4, adapted from TSY, describes how an agent operates with respect to its beliefs, goals, and commitments. The simple agent architecture provides an illustrative context for our semantics; it is not intended to be an alternative to the fully-fledged architectures in the literature. Although the agent may consider multiple actions, in each deliberation cycle the agent can choose at most one action (based on an enabled practical rule) for each commitment and goal. Suspension and reactivation of goals and commitments occurs through the operational model of Figure 4. A goal or commitment is deemed suspended if no practical rule pertaining to it is chosen. When the agent subsequently chooses a practical rule pertaining to that goal or commitment, that means it is reactivated. We treat the agent s operations on its cognitive and social state through our practical rules. We do not treat the agent s plans or domain actions (box Act ). Since we do not model an agent s domain actions, we do not reason about the agent s success or failure with its goals and commitments, just about the coherence of the goals and commitments of a single agent or of a multiagent system. We now define the configuration of a multiagent system and begin to study its consistency according to the life cycle rules of commitments and goals.

4.1 Agent Configuration

An agent s configuration comprises elements both of its cognitive state (i.e., beliefs and goals) and its social state (i.e., commitments of which the agent is creditor or debtor).

Definition 8. The configuration of an agent x is the tuple S(x) = Bx, Gx, Mx, Cx, Sx where Bx is state function for x s beliefs, Gx and Mx are state functions of achievement and maintenance goals respectively, and Cx and Sx are state functions for achievement and maintenance commitments respectively, in which agent x is either debtor or creditor.

To reduce clutter, we write the configuration of agent x as B, G, M, C, S x instead of Bx, Gx, Mx, Cx, Sx . An agent s goals and commitments must be consistent with its beliefs. For example, if agent x believes in the success condition of a goal, then the goal s state must be Null (i.e., whereupon it is not in Gx) or Satisfied. We also assume the goals are mutually consistent (Winikoff et al. 2002). How goals and commitments cohere, within and across agents, is a main theme of this paper see Section 5.

4.2 System Configuration and Traces

In our model, computation in a multiagent system is realized entirely in its member agents. A goal is private to an agent. Each commitment is represented by both its creditor and its debtor. For simplicity, we assume for each commitment that its creditor and debtor agree on its state.

Definition 9. The system configuration of a multiagent system of agents A = x1, . . . , xn is given by n-tuple S(1), . . . , S(n) , where S(i) is the configuration of xi.

When required, we write the multiagent system configuration with each agent s configuration expanded to its beliefs, goals, and commitments: B, G, M, C, S 1, B, G, M, C, S 2, . . . B, G, M, C, S n . A trace is a (possibly infinite) sequence of system configurations. The rules we introduce in the coming sections apply to each agent s internal representation separately. These rules constitute a labelled transition system, with the actions being the labels and the multiagent system configuration being the state, i.e., S α S where α is an action on a cognitive or social construct. As explained above, we do not model an agent s domain actions or plans. Thus, a single transition could potentially correspond to zero or more domain actions.

4.3 Life Cycle Rules

We now define formally the life cycle of goals and commitments. For this, we need action sets for beliefs and achievement and maintenance goals and commitments For all agents combined, we define B, G, M, C, and S as the sets of beliefs, achievement goals, maintenance goals, achievement commitments, and maintenance commitments. Each agent can act on its own elements of the system configuration. The belief actions set is BACTS = {+}. The achievement goal actions set is GACTS = {consider-G, activate-G, terminate-G}. The maintenance goal actions set is MACTS = {consider-M, activate-M, terminate-M}. The achievement commitment actions set is CACTS = {create-C,

TO FROM a-goal m-goal a-comm m-comm

a-goal TSY N/A TSY practical m-goal practical closure N/A N/A a-comm TSY N/A TSY N/A m-comm practical practical N/A closure

Table 1: Possible interactions between components. TSY = achievement-only case: not the topic of this paper. Closure = follows from closure properties such as Def. 7. Practical = treated in this paper in Sect. 5.2. N/A = not applicable.

cancel-C, release-C}. The maintenance commitment actions set is SACTS = {create-S, cancel-S, release-S}. An action instance pairs an action and a corresponding belief, goal, or commitment. For example, the action instance activate, G1 corresponds to the action of activating goal G1. Valid action instances are consistent across the components. Where an action concerns a goal or commitment condition such as a consequent, it must be consistent with changes to the agent s beliefs, and actions corresponding to that belief change must occur on all goals and commitments. When a goal or commitment is affected, so are weaker or stronger goals and commitments to preserve consistency and closure properties, e.g., as in Definition 6. An action set is a set of concurrent action instances of the same agent. We define a life cycle rule as a mapping from a system configuration and an action set into a resulting system configuration. We adopt TSY s life cycle for achievement goals and commitments, with Pending and Suspended removed, respectively. The life cycles of maintenance goals and commitments capture Figures 2 and 3 in logical terms. An illustrative life cycle rules concerns agent x s maintenance goals and the belief action +, b A, b = B(x, p) corresponding to x believing p. Then: if M(x, m, s, f) {I, A, M}, p |= s, then M (x, m, s, f) = S. The intuition is that if p |= s, each maintenance goal M(x, m, s, f) that is Inactive, Active, Monitoring succeeds.

5 Relating Commitments and Goals An agent s practical rules reflect its decision-making. To organize the practical rules, we note that beliefs do not directly give rise to actions. Therefore, we consider direct interactions between achievement and maintenance goals and commitments, giving rise to the 42 = 16 possibilities in Table 1. Practical rules capture an agent s rational behaviour, for example: an agent would adopt commitments to help achieve or maintain its end goals and given its commitments, would create means goals to satisfy or sustain them. Figure 5 captures the relationships of a maintenance commitment or goal as pairs of functions. Let S, G, M respectively be a maintenance commitment, achievement goal, and maintenance goal. Then, for instance, GAS(S) identifies achievement goals such that S s antecedent models the success condition of the goals. The goals created by the creditor to detach S are in GAS(S). For each of these functions, we define an inverse as a function in the reverse direction.

M-Comms S(y, x, k, n, e)

A-Goals G(x, s, f)

A-Goals G(x, s, f)

M-Comms S(x, y, k, n, e)

M-Goals M(x, m, t, g)

M-Comms S(x, y, k, n, e)

M-Comms S(x, y, k, n, e)

M-Goals M(x, m, t, g)

M-Goals M(x, m, t, g)

A-Goals G(x, s, f)

GAS (k |= s) 1 *

SAG (s |= k) 1 *

SSM (m |= n) 1 *

MSS (n |= m) 1 *

GMM (m |= s) 1 *

Figure 5: Functions relating (s-)comms and (m-)goals.

5.1 Coherence and Convergence

Goals and commitments, respectively, reflect the cognitive and social states of agents. How well these constructs cohere indicates how well a multiagent system is being enacted. Ideally, an agent should enter into commitments in accordance with its goals and take on goals that would lead to its commitments being satisfied or sustained. But an agent being autonomous may drop its goals and commitments arbitrarily. We say an agent configuration is coherent if it satisfies the stated coherence properties over beliefs, goals, and commitments of an agent. Informally, the goals and commitments in a coherent configuration reflect the agent s rationality in that their existence may be justified based on another element. For example, when an end goal is satisfied, an agent may drop its corresponding commitment and if a means goal fails, it may adopt another goal or decide to give up on the commitment. If a trace S1, S2, . . . converges infinitely often to a configuration Sk, and Sk is coherent, then the trace sustains a coherent configuration. Note that this repeated converge contrasts with the one time convergence that is adequate for achievement commitments in TSY. A judicious set of practical rules would ensure that goals and commitments in a multiagent system remain coherent even though the agents act autonomously. We demonstrate such a set below. As discussed at the end of the paper, our methodology is generic in that the same approach can be used for alternative sets of practical rules.

5.2 Practical Rules

We use TSY s syntax of a practical rule template of the form E RULENAME α. The expression E is a conjunction of the form of: this goal is (or is not) in some state and that commitment is (or is not) in some state, and about commitment and goal sets computed by the functions of Fig 5 and their states. The expression α is a commitment (or goal) action to be performed on one or more commitments (or goals). We write ant( ) for the antecedent of a (m-) commitment, maint( ) for the maintenance condition of m-comm or m-goal, and succ( ) for the success condition of a (m-) goal.

A-goal to m-comm We first describe the rules in which one or more m-commitments support an a-goal.

S-CREATE: Suppose agent x has an active achievement goal G = G(x, ., .). Then create one or more maintenance commitments that can satisfy the goal G. Let ω = V i ant(Si), where Si = S(x, y, ., ., .) and Si SAG(G), and Φ be a set of commitments such that V j ant(Sj) ω |= succ(G) and Sj Φ.

G(G) = A ω |= succ(G) S-CREATE create(Φ)

S-TERMINATE: Suppose a goal G = G(x, ., .) fails or is terminated. Then cancel each maintenance commitment supporting the goal that is not supporting some other goal.

G(G) {F, T} S SAG(G) SAG 1(S) \ G =

S-TERMINATE terminate(S)

M-goal to a-goal We describe the rules in which one or more achievement goals support a maintenance goal.

A-CONSIDER: Suppose a m-goal M is in the active state, that is maint(M) is false. Then consider one or more agoals to restore maint(M) to true. Let ω = V i succ(Gi), where Gi GMM(M), and Φ = {Gj} is a set of new goals such that V j succ(Gj) ω |= maint(M).

M(M) = A ω |= maint(M) A-CONSIDER consider(Φ)

A-TERMINATE: Suppose a goal m-goal M fails or is terminated. Then terminate each achievement goal G supporting M that is not supporting some other m-goal.

M(M) {F, T} G GMM(M)

GMM 1(G) \ M = A-TERMINATE terminate(G)

M-comm to m-goal We describe the rules in which one or more maintenance goals support a maintenance commitment.

M-CONSIDER: Suppose a m-comm S is in the detached state. Then consider one or more m-goals to maintain the condition maint(S). Let ω = V i maint(Mi), where Mi MSS(S), and Φ = {Mj} is a set of new goals such that V j maint(Mj) ω |= maint(S).

S(S) = D ω |= maint(S) M-CONSIDER consider(Φ)

M-TERMINATE: Suppose a m-comm S is expired or terminated. Then terminate each m-goal supporting S that is not supporting some other m-comm S .

S(S) {E, T} M MSS(S) MSS 1(M) \ G =

M-TERMINATE terminate(M)

M-goal to M-comm We describe the rules in which one or more maintenance commitments support a maintenance goal.

C-CREATE: Suppose a m-goal M = M(x, m, ., .) is in the monitoring state. Then create one or more commitments Cj = C(x, yj, S(yj, x, , mj, dj) = D, qj) to persuade agent yj to maintain the condition mj. Note that the antecedent of Cj is a condition that the m-comm S(yj, x, , mj, dj) is detached. Thus this enhancement conforms to the structure of an a-comm (TSY) . Let ω = V i maint(Si), where Si SSM(M), and Φ = {Cj} is a set of new commitments such that V j mj ω |= m.

M(M) = M ω |= maint(M) C-CREATE create(Φ)

MS-TERMINATE: Suppose a m-goal M fails or is terminated. Then cancel each m-comm supporting the goal M that is not supporting some other m-goal.

M(M) {F, T} S SSM(M)

SSM 1(S) \ M = MS-TERMINATE terminate(S)

M-comm to a-goal Last, we describe the rules in which one or more a-goals support a maintenance commitment.

AD-CONSIDER: Suppose a m-comm S is in the conditional state. Then the debtor of S considers one or more a-goals to detach S. Let ω = V i succ(Gi), where Gi GAS(S), and Φ = {Gj} is a set of new goals such that V j succ(Gj) ω |= ant(S).

S(S) = C ω |= ant(S) AD-CONSIDER consider(Φ)

AD-TERMINATE: Suppose a m-comm S is expired or terminated. Then terminate each a-goal supporting S that is not supporting some other m-comm S .

S(S) {E, T} G GAS(S) GAS 1(G) \ S =

AD-TERMINATE terminate(G)

6 Results on Coherence and Convergence We prove repeated convergence of traces under two assumptions. First, action fairness means that all agents act towards achieving their commitments and goals. Hence, all a-goals eventually reach a terminal state, either positive (e.g., Satisfied) or negative (e.g., Failed); and no m-goals remain indefinitely in a response state, i.e., Active. Second, for convergence we cannot have forever-cycling commitments or goals. TSY define cycling in the achievement case; the next two definitions provide a definition in the maintenance case. Definition 10. Let S = S(x, y, p, q) be a m-comm and τ be a trace of states S0, S1, . . . . Suppose S(S) = σ in some state Si and in some subsequent state Sj, where j > i. If τ contains infinite pairs of Si, Sj , Sj = S, then we say that S is cycling on τ. Definition 11. Let M = M(x, m, s, f) be a m-goal and τ be a trace of states S0, S1, . . . . Suppose G(G) = σ in some state Si and in some subsequent state Sj, where j > i. If τ contains infinite pairs of Si, Sj , Sj = A, then we say that G is cycling on τ.

Results focusing on one agent These theorems relate one agent s (s-) commitments and (aand m-) goals. The first theorem says that a m-comm does not remain in Sustain infinitely long on a trace. The second says that the trace sustains a coherent configuration. Theorem 1. Let S = S(x, y, l, m, d) be an m-comm and τ be a trace of states S0, S1, . . . . Suppose in state Sc that S(S) = B. Then a state Sh, h > c such that S(S) = B. Theorem 2. Let τ = S0, S1, . . . be a trace. Then for any state Si in τ, if Si is not coherent, there is a subsequent state Sj, j > i, in τ such that Sj is coherent.

Results focusing on many agents These theorems concern the m-comms in a multiagent system. They state that the agents together maintain their m-goals and commitments in a rational way. Theorem 3. Suppose agent x in a multiagent system M has a m-goal M = M(x, m, s, f). Then the agents in M create minimal sets of m-comms, m-goals, and a-goals necessary to maintain the condition m. Theorem 4. Suppose agent x in a multiagent system M has a m-comm S = S(x, y, l, m, d). Then the agents in M create minimal sets of m-goals and a-comms and a-goals necessary to maintain the condition m.

7 Applying the Theory We illustrate the value of integrated reasoning over maintenance commitments and goals with the aerospace aftermarket scenario of Figure 1. Due to space, we apply our approach to a portion of the scenario, and compact a few steps by combining goal consideration (Null to Inactive) and activation (Inactive to Active). Table 2 shows a possible progression of the operator and manufacturer configurations. In Step 1, the operator employs C-CREATE rule to create an a-comm to the manufacturer to paying if the latter maintains the engine: C = C(OPER, MFR, S, maint paid), where S = S(MFR, OPER, , engine running, expiry). In Step 2, MFR employs DETACH rule (TSY) to create m-comm S, which detaches a-comm C. In Step 3, MFR employs MCONSIDER rule to consider and activate the m-goal M = M(MFR, engine running, expiry, engine dead). In Step 4, OPER pays (main paid) OPER, which satisfies commitment C (TSY). In Step 5, suppose the engine fails and stops running. This causes the m-goal M to transition to Active and m-comm S to transition to Sustain. In Step 6, MFR employs A-CONSIDER to consider and activate a goal R=G(MFR, engine running, engine dead) to restore the engine. In Step 7, MFR fixes the engine, which satisfies R and causes M to transition to Monitoring, and S to Sustain.

8 Related Work This paper draws on Telang, Singh, and Yorke-Smith s (2019) study of a-comms and a-goals. That work does not consider maintenance of either construct. M-goals are handled by, for instance Duff, Thangarajah, and Harland (2014), who do not consider commitments. The developments we provide to handle maintenance of commitments are non-trivial, including

Step Rule OPER Action OPER State MFR Action MFR State

1 C-CREATE Sec 5.2 create(C) CA CA 2 DETACH TSY CD, SD create(S) CD, SD 3 M-CONSIDER Sec 5.2 CD, SD activate(M) M M, CD, SD 4 Life cycle TSY maint paid CS, SD M M, CS, SD 5 Life cycle Figures 2, 3 engine running, SB engine running, M A, SB 6 A-CONSIDER Sec 5.2 engine running, SB activate(R) engine running, RA, M A, SB 7 Life cycle Figures 2, 3 engine running, SD engine running engine running, RS, M M, SD

Table 2: Progression of configurations in an aerospace scenario. C = C(OPER, MFR, S, maint paid), S = S(MFR, OPER, , engine running, expiry), M = M(MFR, engine running, expiry, engine dead) R = G(MFR, engine running, engine dead)

new definitions of support functions, closure and coherence, and new life cycle rules and theorems. Other differences from TSY are that we handle suspension operationally rather than with life cycle states and practical rules, which reduces the complexity of our model. The theorems, naturally, are unique to the presence of maintenance constructs. The few works that address m-comms reduce them to acomms albeit with more complex formulae. However, such a representation is inadequate because it does not capture potentially repeated interventions by the debtor to re-establish m should it fail. Further, these works do not study the life cycle of m-comms, nor the connection to goals. Mallya, Yolum, and Singh (2003) write maintenance commitments as achievement commitments for temporal formulae of the form always m . Chesani et al. (2013) define commitments with universally quantified properties during a time interval. They employ a Reactive Event Calculus framework, which supports greater temporal expressiveness than ours. Their formulation does not have an explicit notion of m-commitment, having only a limited maintenance life cycle. We anticipate that an approach such as ours could be developed for their technical framework. Chopra and Singh (2015) define a commitmentspecification language, Cupid, that is first-order and maps to event expressions using relational algebra. Cupid can capture commitments of the form of for each insurance claim, I will provide a payment but does not capture maintenance in that it handles only the achievement of the consequent: it does not handle a consequent being forever or repeatedly made true. G unay, Winikoff, and Yolum (2015) propose a framework to enable agents to create a commitment protocol dynamically. Such an approach to agent interaction provides for runtime coordination between agents goals. The framework admits achievement commitments. Determining whether an agent keeps to its (achievement) commitments is known as monitoring (Dastani, van der Torre, and Yorke-Smith 2017). The act of monitoring has a maintenance-like ongoing nature. Extending the approach of, e.g., Kafalı and Torroni (2018) to understand monitoring and responding to failures is future work, as is handling disputes between agents as to the facts (Telang et al. 2015) and their effects on coherence. Criado, Black, and Luck (2016) discuss a notion of coherence where they seek to identify consistent sets of norms. They formulate coherence as constraint satisfaction where an agent can compute preferences across its norms with respect

to its cognitive state. In a somewhat similar approach, Desai, Narendra, and Singh (2008) evaluate sets of commitments, viewed as contracts, from the perspective of the preferences of the participants. In contrast to these approaches, we seek not to evaluate coherence but to show how each agent is individually coherent and how, linked through their commitments, the agents are collectively coherent over time. Al-Saqqar, Bentahar, and Sultan (2016) develop a logic that considers both agents knowledge and commitments. In contrast, we develop an operational semantics relating achievement and maintenance goals and commitments.

9 Conclusion

This paper studies the dynamic relationships between a rational agent s cognitive state (i.e., beliefs and goals) and its social state (i.e., commitments). First-class maintenance commitments are a powerful new type of social commitments that enable richer relationships than otherwise possible, thereby supporting expanded forms of collaboration. By formalizing the concept of a maintenance commitment, we defined an operational semantics based on life cycle rules and practical rules. Further, by motivating an extended notion of coherence, we proved that a system of rational agents following the practical rules will have coherence between the achievement and maintenance goals and commitments. We proposed a set of practical rules that captures certain intuitions and leads to coherence results. One can conceive of alternative sets of such rules: our methodology is generic. Future work is, first, to allow explicit representation of time in commitments, as indicated by Chesani et al. (2013); Fornara and Colombetti (2009). Particularly interesting is how temporally qualified propositions interact with the nature of maintenance commitments. Second, our approach assumes propositional goals and commitments: a future direction is to consider enhanced representations that involve decidable fragments of first-order logic. Another interesting future direction is to consider maintenance as an essential component of norms broadly, not only commitments. Such an approach would be an enabler of a new theory of resilient norms that maintain their coherence with each other and the cognitive constructs, supporting both probabilistic reasoning about norms (Cranefield et al. 2016) and new verification techniques (Drawel et al. 2020).

Acknowledgments We thank the anonymous reviewers for their suggestions. MPS thanks the US National Science Foundation (grant IIS1908374) for support. NYS was partially supported by TAILOR, a project funded by EU Horizon 2020 research and innovation programme under GA No 952215.

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