Running Contracts with Defeasible Commitment

Running Contracts with Defeasible Commitment Ioan Alfred Letia1 and Adrian Groza1 Technical University of Cluj-Napoca Department of Computer Science Baritiu 28, RO-400391 Cluj-Napoca, Romania {letia,adrian}@cs-gw.utcluj.ro

Abstract. Real life contracts imply commitments which are active during their running window, with effects on both normal runs as well as in the case of exceptions. We have defined defeasible commitment machines (DCMs) to provide more flexibility. As an extension to the task dependency model for the supply chain we propose the commitment dependency network (CDN) to monitor contracts between members of the supply chain. The workings of the DCMs in the CDN is shown by a simple scenario with supplier, producer, and consumer Keywords: Multi-agent systems, Autonomous agents, Internet applications

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Introduction

Although contracts are a central mechanism for defining interactions between organizations, there is currently inadequate business support for using the information provided by these contracts. The current requirements of the supply chains [1] demand a more outward view on contract management for each entity within the chain. The emerging services science deals with such issues: 1) services contract specifications, cases, and models; 2) service level agreements; 3) automatic and semi-automatic services contract generation and management; 4) legal issues in services contract and operations; 5) decision support systems for contracts operations. Our work [2] belongs to the above trend, based on the temporalised normative positions in defeasible logic [3] using a special case of the nonmonotonic commitment machines [4]. In the supply chain context a contract breach can be propagated over the entire chain, with rules imposed by law that help agents to manage perturbations in the supply chain. Each agent has more than one way to respond to a perturbation, following remedies that are adequate for an efficient functionality of the supply chain: expectation damages, opportunity cost, reliance damages, and party designed damages [5]. The main contribution of this paper consists in showing how the defeasible commitment machines (DCMs) can be used within a commitment dependency network (CDN). In the next section we describe the temporalised normative positions that we use in section 3 to define DCMs and contracts. In the section 4 we show for a simple scenario how contracts are executed and the section 5 discusses how exceptions can be captured in our framework.

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Temporalised normative positions

We are using the temporalised normative positions as defined in [3]: A normative defeasible theory (NDL) is a structure (F , RK , RI , RZ , RO , ≻) where F is a finite set of facts, RK RI RZ RO are respectively a finite set of persistent or transient rules (strict, defeasible, and defeaters) for knowledge, intentions, actions, and obligations, and ≻ representing the superiority relation over the set of rules. A rule in NDL is characterized by three orthogonal attributes: strength, persistence, modality. As for modality, RK represents the agent’s theory of the world, RZ encodes its actions, RO the normative system or his obligations, while RI and the superiority relation capture the agent’s strategy or his policy. A persistent rule is a rule whose conclusion holds at all instants of time after the conclusion has been derived, unless a more powerful rule, according to the superiority relation, has derived the opposite conclusion, while A transient rule establishes the conclusion only for a specific instance of time [3]. Strict rules are rules in the classical sense, that is whenever the premises are indisputable, then so is the conclusion, while defeasible rules are rules that can be defeated by contrary evidence. Usually, sending the goods means the goods were delivered. In our defeasible inference, if we know that tho goods were sent then they reach the destination, unless there is other, not inferior rule, suggesting the contrary. Defeaters are rules that cannot be used to draw any conclusions, their only use is to prevent some conclusions, as in ”if the customer is a regular one and he has a short delay for paying, we might not ask for penalties”. This rule cannot be used to support a ”not penalty” conclusion, but it can prevent the derivation of the penalty conclusion. We use the following notation: →tX , ⇒tX and tX for transient rules (strict, defeasible respectively defeaters), →pX , ⇒pX and pX for persistent rules (strict, defeasible respectively defeaters), where X ∈ {K, I, Z, O} represents the modality. A conclusion in NDL is a tagged literal where +∆τX q : t means that q is τ definitely provable of modality X, at time t in N DL (fig. 1) and +∂X q : t: q means q is defeasible provable of modality X, at time t in N DL (fig. 2, 3). Similarly, −∆τX q : t: q which means that q is not definitely provable of modality τ X and −∂X q : t: q meaning q is not defeasibly provable of modality X. Here τ ∈ {t, p}, t stands for transient, while p for a persistent derivation. A strict rule r ∈ Rs is ∆X − applicable if r ∈ Rs,X ∀a : tk ∈ A(r) : ak : tk is ∆X − provable. A strict rule r ∈ Rs is ∆X − discarded if r ∈ Rs,X ∃ak : tk ∈ A(r) : ak : tk is ∆X − rejected. As regard conditions for ∂X − applicable and ∂X − discarded, we replace ∆ with ∂. The conditions for concluding whether a query is transient or persistent, definitely provable is shown in the figure 1. For the transient case, at step i + 1 one can assert that q is definitely transient provable if there is a strict transient rule r ∈ Rst with the consequent q and all the antecedents of r have been asserted to be definitely (transient or persistent) provable, in previous steps. For the persistent case, the persistence condition (3) allows us to reiterate literals definitely proved at previous times. For showing that q is not persistent definitely provable, in addition to the condition we have for the transient case, we have to assure that, for all instances of time before now the persistent property

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+∆tX : If P (i + 1) = +∆tX q : t then q : t ∈ F , or t ∃r ∈ Rs,X [q : t] r is ∆X − applicable +∆pX : If P (i + 1) = +∆pX q : t then q : t ∈ F , or p ∃r ∈ Rs,X [q : t] r is ∆X − applicable or ′ ∃t ∈ Γ : t′ < t and +∆pX q : t′ ∈ P (1..i). Fig. 1. Transient and persistent definitely proof for modality X

has not been proved. According to the above conditions, in order to prove that q is definitely provable at time t we have to show that q is either transient, or persistent definitely provable [3]. Defeasible derivations have an argumentation like structure [3]: firstly, we choose a supported rule having the conclusions q we want to prove, secondly we consider all the possible counterarguments against q, and finally we rebut all the above counterarguments showing that, either some of their premises do not hold, or the rule used for its derivation is weaker than the rule supporting initial conclusion q. A goal q which is not definitely provable is defeasible transient provable if we can find a strict or defeasible transient rule for which all its antecedents are defeasible provable, ¬q is not definitely provable and for each rule having ¬q as a consequent we can find an antecedent which does not satisfy the defeasible provable condition (in figure 2). t t q : t then : If P (i + 1) = +∂X +∂X (1) +∆X q : t ∈ P (1..i) or (2)−∆X ¬q : t ∈ P (1..i) and (2.1) ∃r ∈ Rsd,X [q : t]: r is ∂X -applicable and (2.2) ∀s ∈ R[¬q : t]: s is ∂X -discarded or ∃w ∈ R(q : t) : w is ∂X -applicable or w ≻ s

Fig. 2. Transient defeasible proof for modality X.

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Defeasible commitment machines

Commitment machines were proposed as a formalism for declarative specification of protocols. From a technical point of view, a contract is just a protocol binding different parties to their commitments by specifying the type of services agreed upon, the obligations, and the remedies in case of breach. In our approach we represent contracts as defeasible commitment machines (DCM). A DCM is a theory in normative defeasible logic (NDL) consisting of two parts. The first

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p t +∂X : If P (i + 1) = +∂X q : t then p (1) +∆X q : t ∈ P (1..i) or (2)−∆X ¬q : t ∈ P (1..i), and p (2.1) ∃r ∈ Rsd,X [q : t]: r is ∂X -applicable, and (2.2) ∀s ∈ R[¬q : t]: either s is ∂X -discarded or ∃w ∈ R(q : t): w is ∂X -applicable or w ≻ s; or p (3) ∃t′ ∈ Γ : t′ < t and +∂X q : t′ ∈ P (1..i) and ′ (3.1) ∀s ∈ R[¬q : t”], t < t” ≤ t,, s is ∂X -discarded, or ∃w ∈ R(q : t”): w is ∂X -applicable and w ≻ s.

Fig. 3. Persistent defeasible proof for modality X.

one captures the representation of commitments and the operations on them in NDL (section 3.2) as a contract independent theory, while the second is contract dependent and includes rules describing specific contractual clauses (section 3.3). 3.1

Standard commitments

Reasoning formally assumes that the contracts have a formal semantics. We base our semantics on the notion of commitment where the clauses of the contract can be seen as an exchange and manipulation of commitments. The first step in processing a contract consists in representing it in a logical form by translating clauses into facts, definitions, or normative rules. The contracts contain commitments which capture the obligations from one party to another. Realistic approaches attach deadlines to commitments in order to detect their breach or satisfaction. A base-level commitment C(x, y, p : tmaturity ) : tissue binds a debtor x to a creditor y for fulfilling the proposition p until the deadline tmaturity . A conditional commitment CC(x, y, q : t′maturity , p : tmaturity ) : tissue denotes that if a condition q is brought about at t′maturity , then the commitment C(x, y, p : tmaturity ) : tissue will hold. For instance, in the conditional commitment CC(s, b, pay(Pc ) : tmaturity , deliver(gi ) : tmaturity + 3) : tissue the agent s (representing the seller agent or the debtor) assumes the obligation to the b agent (representing the buyer or the creditor) to deliver the item g i in three days after the buyer has paid the price Pc . A commitment may be in one of the following states: active (between tissue and tmaturity and ¬breach), violated (tmaturity ≤ tcurrent and the commitment was not discharged or released) or performed (if the debtor executes it until tmaturity ). The operations for the manipulations of commitments [6] are: – Create(x, C) : tissue - the debtor x signs the commitment C at time tissue (can only be performed by the C’s debtor x); – Cancel(x, C) : tbreach - the debtor x will no longer satisfy its obligation (usually1 , this can only be performed by C’s debtor x); 1

The current practice in law decommits an agent from his obligations in some special situations (i.e. the creditor has lost his rights). Hence, the normative agent that monitors the market can also cancel some commitments.

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– Release(y, C) : tx - releases C’s debtor x from commitment C (performed by the creditor y); – Assign(y, z, C) : tx - replaces arbitrarily y with z as C’s creditor (performed by the creditor y); – Delegate(x, z, C) : tx - replaces x with z as C’s debtor (performed by the debtor x); – Discharge(x, C) : tx - C’s debtor x fulfills the commitment. These operations cannot be carried out arbitrarily. They are subject to rules that govern the electronic market and which set the power of agents within that market [4]. An agent has power when an action of that agent determines a normative effect. For instance, the agents must have the power to delegate or assign a commitment, otherwise, their operations have no normative consequence. 3.2

Commitments in the normative defeasible logic

We adapted the task dependency network model [1, 5] used in the analysis of the supply chain as follows. A commitment dependency network (CDN) is a graph (V,E) with vertices V = C∪A, where: G = the set of commitments, A = S∪P ∪C the set of agents, S = the set of suppliers, P = the set of producers, C = the set of consumers, and a set of edges E connecting agents with their input and output commitments. An output commitment for a agent is a commitment in which a is the debtor. An input commitment for a agent is a commitment in which a is the creditor. With each agent a we associate an input set Ia and an output set Oa : Ia = {c ∈ C|hc, ai ∈ E} containing all the commitments where a is creditor and Oa = {c ∈ C|ha, ci ∈ E} containing all the commitments where a is debtor. Agent a is a supplier if Ia = 0, a consumer if Oa = 0, and a producer in all other cases. Such a multi-party commitments network is satisfiable if all the commitments may be discharged [7]. Following the steps in [4], we have defined [2] the defeasible commitment machines (DCM) using the normative defeasible logic instead of the causal logic with the goal to increase the flexibility of the commitments. Commitments in NDL are declared to be persistent knowledge: →pK C(x, y, p) : ti , →pK CC(x, y, q, p) : ti . The rules from fig. 4 capture the meaning of the operations, where tm stands for tmaturity , representing the deadline attached to the commitment. Being persistent, the conclusions remain valid until a more powerful derivation retracts them (for instance r2 ≻ r1 ). For the life-cycle of a commitment, cancellation means an exception which appears in contract execution (rules r3 and r4 . Generally, cancellation is compensated by activating another commitment or contrary-toduty obligation. The debtor may propose another commitment which is more profitable for both partners in the light of some arising opportunities on the market or it just recognizes his incapacity to accomplish the task. The sooner it notifies, the less the damages may be. In some situations, a commitment may be active even after it is breached [6]. We permit this by defining rule r3 as defeasible. Therefore, a normative agent can block the derivation of that conclusion in order to force the execution of a specific commitment. The same reason is valid

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r1 : Create(x, y, p : tm ) : tissue →pK C(x, y, p : tm ) : tissue r2 : Discharge(x, y, p : tm ) : tperf →pK ¬C(x, y, p : tm ) : tperf r3 : Cancel(x, y, p : tm ) : tbreach ⇒pK ¬C(x, y, p : tm ) : tbreach r4 : Cancel(x, y, p : tm ) : tbreach ⇒pK C(x, y, contrary to duty : t′m ) : tbreach r5 : Release(x, y, p : tm ) : trelease →pK ¬C(x, y, p : tm ) : trelease r6 : Delegate(x, y, p : tm , z) : tdelegate ⇒pK ¬C(x, y, p : tm ) : tdelegate r7 : Delegate(x, y, p : tm , z) : tdelegate ⇒pK C(z, y, p : tm ) : tdelegate r8 : Assign(x, y, p : tm , z) : tassign ⇒pK ¬C(x, y, p : tm ) : tassign r9 : Assign(x, y, p : tm , z) : tassign ⇒pK C(x, z, p : tm ) : tassign r10 : CCreate(x, y, q : tm , p : tm + τ ) : tissue →pK CC(x, y, q : tm , p : tm + τ ) : tissue r11 : CDischarge(x, y, q : tm , p : t : m + τ ) : tperf →pK ¬CC(x, y, q : tm , p : tm + τ ) : tperf r12 : CDischarge(x, y, q : tm , p : t : m + τ ) : tperf →pK C(x, y, p : tm + τ ) : tperf r13 : tcurrent > tm ∧ C(x, y, p : tm ) : tm ⇒pK ¬C(x, y, p : tm ) : tm r14 : tcurrent > tm ∧ C(x, y, p : tm ) : tm ⇒pK C(x, y, contrary to duty : t′m ) : tm r2 ≻ r1 , r3 ≻ r1 , r5 ≻ r1 , r6 ≻ r1 , r8 ≻ r1 , r11 > r10

Fig. 4. Defeasible commitment machine

for the rules r13 and r14 when the debtor does not execute its commitment until the deadline tm . However, a commitment cannot be active after it is satisfied (rule r2 ). Note that the operations assign and delegate are defeasible, because the agents need special power to execute them. 3.3

Contract specification in the normative defeasible logic

The rules in the figure 5 use the DCM for representing a specific contract between two agents, expressing actions that spread over more instances of time (i.e rules r24 , r28 , r31 ). For instance, the rule r24 says that the seller agent starts the action SendGoods at time tx , but the items reach the destination only after two days, when the fluent goods becomes true. The same rules are also defeasible, meaning that if an unpredictable event appears (i.e. an accident), their consequent fluents may be retracted. The execution of the contract may start from any state, because there is no specific order of actions. This can be useful for the supply chain, where long time business relationships suppose that the first steps in contract negotiation are no longer needed.

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Running the contracts

In the simple scenario of figure 6 the supplier A commits to deliver the item g1 no later than the deadline tm . The producer B commits to pay the item in maximum 3 days after receiving it, and also, it commits to deliver g2 until t′m . The consumer C commits to pay no later than 2 days after obtaining the product. The commitment dependency network specifies which commitments are in force in a particular instance of time. The picture illustrates the t1 instant

Running Contracts with Defeasible Commitment r18 r19 r20 r21 r22 r23 r24 r25 r26 r27 r28 r29 r30 r31 r32

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: SendRequest : tx →pK request : tx : SendOf f er : tx →pK of f er : tx : SendOf f er : tx →tZ CCreate(M, C, acceptC : tm , goods : tm + 2) : tx : SendAccept : tx →pK accept : tx : accept : tx ∧ CC(M, C, acceptC : tm , goods : tm + 3) : tx →tZ CDischarge(M, C, acceptC : tm , goods : tm + 3) : tx : SendAccept : tx →tZ CCreate(C, M, goods : tm , pay : tm + 2) : tx : SendGoods : tx ⇒pK goods : tx + 2 : SendGoods : tx →tZ CCreate(M, C, pay : tm , receipt : tm + 1) : tx : goods : tx ∧ CC(C, M, goods : tm , pay : tm + 2) : tx →tZ CDischarge(C, M, goods : tm , pay : tm + 2) : tx : goods : tx ∧ C(M, C, goods : tm ) →tZ Discharge(M, C, goods : tm ) : tx : SendP ayment : tx →pK pay : tx + 1 : pay : tx ∧ CC(M, C, pay : tm , receipt : tm + 1) : tx →tZ CDischarge(M, C, goods : tm , pay : tm + 2) : tx : pay : tx ∧ C(C, M, payC : tm ) : tx →tZ Discharge(C, M, payC : tm ) : tx : SendReceipt : tx ⇒pK receipt : tx + 1 : receipt : tx ∧ C(M, C, receipt : tm ) : tx →tZ Discharge(M, C, receipt : tm ) : tx

Fig. 5. Contracts in the normative defeasible logic

C(A, B, g1 : tm ) : t1 C(B, C, g2 : t′m ) : t1

✓ ✞ ☎ A ✝ ✆ ✻ ✒

✓ ✏ ✞ ❄☎ B ✝ ✆ ✻ ✑ ✒

✏ ✞ ❄☎ C ✝ ✆ ✑

CC(B, A, g1 : tm , Pc : tm + 2) : t1 CC(C, B, g2 : t′m , Pc′ : t′m + 3) : t1

Fig. 6. Commitment dependency network: supplier A, producer B, consumer C.

of time from the figure 7, which traces the scenario by focusing on the relevant instances of time. At time t0 the consumer C notifies the agent B that he intends to buy the item g2 paying for it the price Pc′ in 2 days after the shipment was made. Consequently, producer B asks the supplier A for delivering the item g1 at the price Pc . At time t1 the A agent commits to deliver its output item, and so the agent B. At time t2 A agent executes the action SendGoods(g1 ). Observe, it is a transient derivation. Otherwise, the agent will send the item g1 at every instant of time, until o more powerful rule eventually blocks the operation. According to rule r25 , the consequence of the operation is the commitment →pK CC(A, B, Pc : tm , receipt : tm + 1) : t2 . At time t4 , according to rule r24 , the items arrive (⇒pK g1 : t4 ) and the B agent pays the price Pc for them. Observe, it is a defeasible derivation which can be defeated by an unpredictable event. The fluent

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t0 B : →tZ Create(B, A, g1 : tn , Pc : tn + 3) : t0 C : →tZ Create(C, B, g2 : t′n , Pc′ : t′n + 2) : t0 ′ ′ ⇒p DCM : ⇒p K CC(C, B, g2 : tn , Pc : tn + 2) : t0 K CC(B, A, g1 : tn , Pc : tn + 3) : t0 t1 A : →tZ Create(A, B, g1 : tm ) : t1 B: →tZ Create(B, C, g2 : t′m ) : t1 ′ DCM ⇒p ⇒p K C(A, B, g1 : tm ) : t1 K C(B, C, g2 : tm , ) : t1 CC(B, A, g1 : tn , Pc : tn + 3) : t1 CC(C, B, g2 : t′n , Pc′ : tn + 2) : t1 t2 A : →tZ SendGoods(g1 ) : t2 DCM : →p K CC(A, B, Pc : tm , receipt : tm + 1) : t2 CC(B, A, g1 : tn , Pc : tn + 3) : t2 CC(C, B, g2 : t′n , Pc′ : tn + 2) : t2 C(A, B, g1 : tm ) : t2 C(B, C, g2 : t′m , ) : t2 t3 DCM : CC(A, B, Pc : tm , receipt : tm + 1) : t3 CC(B, A, g1 : tn , Pc : tn + 3) : t3 CC(C, B, g2 : t′n , Pc′ : tn + 2) : t3 C(A, B, g1 : tm ) : t3 ′ C(B, C, g2 : tm , ) : t3 t4 B : →tZ SendP ay(Pc ) : t4 DCM : ⇒p →p K g1 : t4 K C(B, A, Pc : t7 ) : t4 CC(A, B, Pc : tm , receipt : tm + 1) : t4 CC(C, B, g2 : t′n , Pc′ : tn + 2) : t4 ′ C(B, C, g2 : tm , ) : t4 . . . t9 B : →tZ SendReceipt(receipt′ ) : t9 ′ DCM : ⇒p → C(B, C, receipt′ : t′10 ) : t9 K Pc : t9 g2 : t9 receipt : t9 Pc : t9 g1 : t9 ′ t10 DCM : ⇒p Pc′ : t10 K receipt : t10 g2 : t10 receipt : t10 Pc : t10 g1 : t10

Fig. 7. Trace of running the contracts in DCM

g1 : t4 fires the rule r25 . Hence the conditional commitment is discharged and applying rule r12 a base-level commitment is created (→pK C(B, A, Pc : t7 ) : t4 ). At time t10 one can see that all the fluents had become true: the goods g1 and g2 were delivered, the amounts Pc and Pc′ were paid and both receipts were send, meaning that the system has reached a desirable state [8]. The goal of executing a contract does not consist in performing certain sequences of actions, but to reach a desirable state. Observe that not all the possible commitments from section 3.3 had been activated by the agents. For instance, no one had used the acceptC commitment. Such situations often arise when the agents are running long time business relationships and they do no initiate their interactions from a start state. This is an argument for using our framework, for the supply chain context. Note also that there are not any base-level commitments, so the system is in a final state. In a final state, the interactions may end. But, the interaction can continue from such a state by activating any of the commitments of the contract. A well-formed contract is one in which bot final and undesirable states 2 do not occur at the same time. In the supply chain, the majority of actions are repetitive. Our approach captures easily such a requirement. The agents have only to derive persistently and defeasibly their actions (i.e. ⇒pZ SendGoods : tx ). We introduce defeasible logic to permit agents to manage perturbations in the supply chain. In case a 2

States in which at least one fluent is not true.

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perturbation appears, they can rebut the above rule by activating a stronger one which specifies more or less items to deliver. Therefore, the perturbation is managed with minimum effort, only by changing the superiority relation over the set of rules.

5

Exceptions

An exception represents a deviation from the normal flow of contract execution. It can be an opportunity, a breach, or an unpredictable sequence of operations. Expected exceptions can be captured by defining a preference structure over the runs within the commitments dependency network [9]. Having the superiority relation from defeasible logic, we can easily define such a structure in our framework. In our view, unexpected exceptions can be managed in two ways: by introducing exceptions patterns or, when there is no domain dependent information, by applying principles of contract law. Contracts can be more or less elaborate. Therefore, different levels of contracts exist. Using well-defined exceptions patterns, one can generate more robust contracts. Moreover, it is considered that 80% of actual judicial cases follow the same classes of exceptions patterns. We can provide a taxonomy of template contracts and a taxonomy of exceptions. When there are no explicit contrary-to-duty rules and no dependent domain information, the solution is to apply principles of contract law in order to compute the remedy, such as expectation damages, reliance damages, and opportunity costs. The amount of expectation damages must place the victim in the same position as if the actual contract had been performed. The amount of reliance damages must place the victim in the same position as if no contract had been signed. The amount of opportunity-cost damages must place the victim in the same position as if the best alternative contract had been performed [10, 5]. By tracking the life cycle of the commitments within a CDN one can detect and anticipate exceptions in contract execution, and therefore design proactive agents for such a market. An active base-level commitment represents a hard constraint for the debtor agent, while proposing a conditional commitment denotes a more risk-averse attitude. Moreover, inner commitments are permitted in a defeasible commitment machine. This opens the possibility of designing agents with different levels of risk attitude [5].

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Related work and conclusions

Nonmonotonic commitment machines have been defined [4] using causal logic, while in DCMs deadlines have been attached to commitments, which represents a more realistic approach. Moreover, in our view, defeasible logic is more suitable than causal logic in capturing exceptions. Contracts have been already represented with defeasible logic and RuleML [11], but, by introducing DCMs between members of the supply chain, we offer a more flexible solution for contract monitoring. Capturing exceptions in the commitment machines of [9] is

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not performed with deadlines, needed for detecting the breach of a contractual clause. Exceptions in a semantic perspective [12] have used courteous logic which is a subset of defeasible logic. Commitments between a network of agents have also been analyzed [7], but without time constraints. The main contribution of this paper consists in introducing DCMs in the execution of contracts, to obtain two main advantages. On the one hand, agents can reason with incomplete information. Therefore, contracts represented as DCMs are more elaboration tolerant [4]. Also, this property of nonmonotonic logics permits, in our case, to model confidential contractual clauses. On the other hand, our long term research goal is to manage exceptions in contract execution. We argue that using DCMs and the expressiveness of defeasible logic it is easier to catch both expected and unexpected exceptions. The novelty regarding commitments consists in attaching deadlines to each commitment by using the temporalised normative defeasible logic [3].

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