Justificatory and Explanatory Argumentation for Committing Agents
aa r X i v : . [ c s . A I] A p r Justificatory and Explanatory Argumentationfor Committing Agents
Ioan Alfred Letia and Adrian Groza Technical University of Cluj-NapocaDepartment of Computer ScienceBaritiu 28, RO-400391 Cluj-Napoca, Romania {letia,adrian}@cs-gw.utcluj.ro
Abstract.
In the interaction between agents we can have an explica-tive discourse, when communicating preferences or intentions, and a nor-mative discourse, when considering normative knowledge. For justifyingtheir actions our agents are endowed with a Justification and Explana-tion Logic (
JEL ), capable to cover both the justification for their com-mitments and explanations why they had to act in that way, due to thecurrent situation in the environment. Social commitments are used toformalise justificatory and explanatory patterns. The combination of ex-planation, justification, and commitments provides flexibility for definingseveral types of argumentative agents.
The institutional economics demands a clear account of a fuzzy world and istherefore in accordance [17] with the dictum attributed to Keynes: ”it is betterto be roughly right than precisely wrong”. As many multi-agent systems areorganized in some kind of institution, judging the behavior of agents in suchcontexts requires sometimes understanding of how their actions stand vis-a-visto the goals of the overall system.Habermas [17] proposed different types of discourses dealing with differentvalidity claims. In the interaction between agents we can thus have an explicativediscourse, when communicating knowledge, and a normative discourse, whenconsidering normative knowledge. For justifying their actions our agents areendowed with a Justification and Explanation Logic (
JEL ), capable to coverboth the justification for their commitments and explanations why they had toact in that way, due to the current situation in the environment. The distinctionbetween factual and normative knowledge is important in argumentative agentssince facts of various kinds might not provide agents with any choice, whilenorms are possible to be bent and eventually changed.The difference between explanation and justification has not been clearlydelimited in computational models of arguments. From this perspective, there isa gap between argumentation in the philosophy of science and computational-based argumentation. Given the idea that argumentation is a means to justifyclaims or to persuade other agents of these claims [10], there are two approacheshen defining what ”good argumentation” represents: i) argumentation able tojustify its target claims and ii) argumentation able to convince an audience.These two lines form the basis for investigating the contrast between justificatoryarguments and explanatory arguments .The philosophy of science distinguishes between explanatory reasons and nor-mative or justificatory reasons [12]. While explanations are reasons why eventsoccur, justifying reasons are ”considerations which count in favor” or ”explana-tions of ought facts”. Differently, in the computation models of arguments there isa blurred distinction between explanation-based argumentation and justification-based argumentation, as in [16], where explanations and evidence are used toconstruct justifications.In many practical domains the distinction between explanation and justifi-cation has pragmatic force. Many examples come from the legal domain, wherean illegal action can be explained, but in many cases the action is not justified.For instance, a theft can be explained by the loss of money because the personlost his job, but it does not have normative justificatory power. Another com-mon example is based on the well known lack of time explanatory pattern: ”Icould not finalize the task due to lack of time”, with its many instantiations: ”Icould not review the paper because I was at a conference during the deadline”or ”I could not finalize the article, because input data arrived too late”. In mostsituations, this explanation pattern does not have justificatory power at all. Inother words, something can explain a behavior but it cannot always justify it.In this paper we investigate the inter-living of explanations and justifica-tions in business-oriented situations. Current business interactions are affectedby postmodern ideas like post-structuralism and heterogeneity at different levels.In line with postructuralism, business commitments act as a flexible frameworkfor guiding business interactions, agents preferring soft law against the hard lawgovernance, whilst the idea of heterogeneity of individuals is reflected at the busi-ness policy level through the concept of heterogeneity of customers [20]. Considerthe contractual clause in which the debtor a promises to deliver an item to thecreditor b within a pre-agreed deadline. Not meeting the deadline, the agent a provides an explanation: ”I could not deliver the product because my supplier c has not delivered the parts yet”. This explanation provides the creditor b withsome insights on the current situation, but it does not have enough justificatorypower in order to justify the behavior of agent a for not delivering the item. Itmay be a case in which the supplier c has no normative obligation to deliver thecomponents of the product: either a commitment C ( s , a , pay , parts ) for deliver-ing the parts does not exist between a and the supplier c , or the agent a didnot pay the components in due time. Valid justifications should be normative,like: ”emergency situation forces me not to deliver the item”, where emergencyis a normative concept. Observe that the emergency justifier does not help thedebtor a to understand the situation. The agent can ask for further explanationsfor the conveyed justifier, but also for further normative justifications for it.The paper advances the state-of-the-art in logic of argumentation in threeways: i) proposing JEL for handling both justificatory and explanatory argu-ents; ii) introducing commitments as proof terms; and iii) formalising severaljustificatory and explanatory patterns. The remaining of the paper is organisedas follows: Section 2 extends justification logic [2] with explanatory capabilitiesand introduces commitments as proof terms. The expressivity of social commit-ments is exploited in section 3 to represent both justificatory and explanatorypatterns. Section 4 describes types of argumentative agents based on the combi-nation of justificatory and explanatory attitudes, whilst section 5 illustrates thedeveloped instrumentation through an illustrative scenario. We end the paperwith related work and conclusions.
The first part of this section extends the justification logic with explanatorycapabilities. The second part illustrates how the concept of commitments usedas proof terms can enact business dialogs.
In order to model justificatory and explanatory arguments we propose an ex-tended version of the Justification Logic (JL). Justification Logic combines ideasfrom epistemology and the mathematical theory of proofs. It provides an evidence-based foundation for the logic of knowledge, according to which ”F is known” isreplaced by ”F has an adequate justification”.Simply, instead of ”X is known” ( KX ) consider t : X , that is, ”X is knownfor the explicit reason t” [2]. Justification logic lacks this component of interpre-tation. It also lacks the capability to express explanation or partial justification.This section extends the justification logic with explanatory capabilities, by in-troducing the explanatory operator t ⊳ F , where t is an explanation for F . Definition 1.
The language of Justification and Explanation Logic
JEL con-tains proof terms t ∈ T and formulas F ∈ F t : = x | c | t · t | t + t | ! t | ? t | t ⋗ tF : = p | F ∨ F | ¬ F | t : F | t ⊳ F Proof terms t are abstract objects that have structure. They are built upfrom axiom constants c ∈ Cons , proof variables x ∈ Vars , and operators onjustifications and explanations · , +, !,?, ⋗ . The application operator · takes twoproof terms and constructs a new justification based on them. The sum operator+ concatenates the given proofs, whilst the unary operators ! and ? are used torequest for positive and negative proof terms for a formula in JEL . The operatorprecedence decreases as follows: ! , · , + , : , ⊳, ¬ , ∨ , and · , + are left associative, and: , ⊳ right associative. To express that t is not probative justification for supporting F one uses ¬ t : F . Parentheses are needed to express that ¬ t is a justificationfor F : ( ¬ t ) : F . Note that justification is used to support negated sentences too,as in t : ¬ F . Similar semantics applies for the explanation operator ⊳ . classical propositional axioms A F → ( t : F ∨ t ⊳ F ) (necessity) A s : ( F → G ) → ( t : F → ( s · t ) : G ) (j-application) A ′ s ⊳ ( F → G ) → ( t ⊳ F → ( s · t ) ⊳ G ) (e-application) A ′′ s : ( F → G ) → ( t ⊳ F → ( s · t ) ⊳ G ) (e-application) A ′′′ s ⊳ ( F → G ) → ( t : F → ( s · t ) ⊳ G ) (e-application) A s : F → ( s + t ) : F (j-sum) A t : F → ! t : ( t : F ) ∨ ! t ⊳ ( t : F ) (proof checker) A ′ t ⊳ F → ! t ⊳ ( t ⊳ F ) (explanation checker) A ¬ t : F → ? t : ( ¬ t : F ) ∨ ? t ⊳ ( ¬ t : F ) (negative proof checker) A ′ ¬ t ⊳ F → ? t ⊳ ( ¬ t ⊳ F ) (negative explanation checker) Fig. 1.
Axioms of
JEL . The axioms of
JEL are shown in figure 1, where axiom A forces all formulas F to have a justification or an explanation t . The compounds t : F or t ⊳ F represent a formula, which should have their own justification. This correspondsto the principle of inferential justification : for sentence F to be justified on thebasis of t one must justify t and justify that t makes F plausible. Constantsare used to stop the ad infinitum justification chain by representing a kind ofjustification that does not depend on other justifiers.The application axiom A takes a justifier s of an implication F → G and ajustifier t of its antecedent F , and produces a justification s · t of the consequent G . If at least one of the terms s , t represents an explanation, the formula G isconsidered only explained, but not justified (axioms A ′ , A ′′ , and A ′′′ ).The j-sum axiom says that if a formula F is justified by the justifier s , thanfor a new justifier t , the formula is still justified. Thus, justification reasoning ismonotonic, new justification not defeating the existing one. The correspondingaxiom for explanation is missing, leaving space for contradictory explanationsand non-monotonic explanatory reasoning. The rationality behind this is thatnorms are considered static at a given moment and assumed apriori known by theparticipants, whilst explanations are constructed dynamically during a dialog.Justifications and explanations are assumed to be verified. Based on axiom A , a justifier t for formula F can be further justified by the term ! t , but it canalso be explained. The axiom A ′ limits the possibility to justify an explanation,an explanation can only be further explained. The negative proof checker A forces agents to provide justifications or explanations why they are not ableto justify a particular formula F . Justifiers cannot be used to justify why theformula F is not explained by the explanandum t , as axiom A ′ states that onlyexplanans can be used. A proof term can be stronger than another one, givenby the operator ⋗ . One of the issues regards what sort of things can be a justifier. In a normativeframework regulated only by social commitments, a justifier can be represented xpression Informal Semantics C ( a , b , p , q ) : i F C is probative evidence for F for agent i . ¬ C ( a , b , p , q ) : i F C is not probative justification for F for agent i .( ¬ C ( a , b , p , q )) : i F The absence of C is a justification for F for agent i . C ( a , b , p , q ) : i ¬ F C ( a , b , p , q ) is evidence for ¬ F for the agent i . Table 1.
Commitment based justification in a multi-agent system. by such commitments. In the proposed approach, by restricting the acceptablejustifications and explanations to commitments, it means that the proof terms t in the JEL language represent commitments.The classical definition of a conditional commitment states that the debtor x promises to creditor y to bring about a particular formula P under the con-dition Q , encapsulated as C ( x , y , Q , P ). In multi-agent systems, a justificationaccepted as probative evidence for an agent may not meet the standard of prooffor another agent, which rejects it. To model this, we link the justification andexplanatory operators to the agent accepting the evidence. Thus, the construc-tion C ( a , b , p , q ) : i F says that commitment C is a probative justification foragent i regarding the sentence F (see table 1). A commitment may be pre-ferred to another one by the agent i when choosing an explanation, formalizedas ( C ≻ C ) ⊳ i F . If one of the terms in the commitment is not constrained inany aspect, “do not care” sign “ ” is used. Examples 1, 2, and 3 illustrate howthe JEL formalism is enacted in a commitment-based multi-agent setting.
Example 1 (Distributed Application).
Assume the commitment C ( a , b , , F ) isagent’s b justification for F and the conditional commitment C ( b , c , F , G ) rep-resents a justification for agent c regarding the formula F → G . Accordingto axiom A , the application operator builds a justification for G of the form C ( b , c , F , G ) · C ( a , b , , F ) : b G . Notice that the commitment aggregation isbased on the view of agent b . C ( b , c , F , G ) : cF → G → ( C ( a , b , , F ) : b → C ( b , c , F , G ) · C ( a , b , , F ) : b G )Not being omniscient, agents are not aware of all the consequences from theircommitments. When used by the same agent, the proof checker operator acts asa positive introspection function, helping agents to be aware of the justificationof their own commitments. Given a commitment C justifying the formula F , theagent i can inspect its own commitment store to further justify the formula C : i F by enacting the application of the proof checker operator on itself: ! C : i C : i F .Consequently, given the commitment C an agent can construct a justificationfor it based on other commitments. Example 2 (Positive Introspection).
Because agent a has promised agent b todeliver the item , given by C ( a , b , ⊤ , item ), this is the justification of agent a egarding the commitment C ( b , c , parts , pay ) with agent c , in which agent b hasto pay the components provided by agent c . Given the right associativity of thejustificatory operator :, parenthesis are introduced only for clarity: C ( a , b , ⊤ , item ) : a [ C ( b , c , parts , pay ) : a Item ]. Example 3 (Explaining a Justification).
Although a hotel specifies in the com-mitment that check-in is at time 14, usually there is no problem if the guestarrives at 12. The situation in which the guest is not served, is often not justifiedby personnel with the commitment itself (the active contractual relation) butby other valid justifiers such as: ”no clean rooms at the moment”. The customercan explain the situation to himself by the reduced number of staff, which canbe further explained by the economical policy of the hotel, with the followingchain of reasoning. economicalPolicy ⊳ guest reducedStaff ⊳ guest ( ¬ CleanedRooms ) : hotel ¬ CheckIn
Justifying the impossibility to check-in by the existing contractual commitmentleads to a different chain of reasoning. increaseProfit ⊳ guest C ( hotel , guest , pay , checkIn
14) : hotel ¬ CheckIn
Given the recurrent nature of business interactions, in common situationsbusiness agents convey the same justificatory and explanatory schemes. Thefollowing section formalizes two justificatory and two explanatory patterns.
An explanation involves discovering the meaning of an event in a particularcontext, such that an explanandum is explained by a coherent set of explanans .The explanation aims to understanding the explanandum by indicating whatcauses it. An explanation answers to why questions or to contrastive why P ratherthan X questions when the opponent requests an explanation for proponentpreferences.The theory of justification advocates the idea that justification is a normativeactivity, where a concept is defined as normative if it depends on norms. Thething that justifies a proposition is called justifier . Justifiers act as a vehiclebetween beliefs and knowledge, as the definition of knowledge as justified truebelief suggests. Supplementary to explanans, a justifier should be legitimate byobjective factors such as social structures, normative frameworks, or abstractrationality.To synthesize the differences, a justification acts in a more normative frame-work, whilst an explanation works in a social context. An explanation implies the ustification from gratuitous promise + GPIntent : Stressing out that no one has forced the debtor to commit.Context : The creditor or other agent perform actions based on the promise.Pattern : C ( a , b , ⊤ , P ) : c FVariants : b=c, a=c, F=PExample : Grandfather promises to his nephew to pay for a trip.Based on it, the father buys a new bag for his son.
JEL : C ( grandfather , nephew , ⊤ , PayTrip ) : father
NewBag
Fig. 2.
Commitment-based justificatory promise. existence of an audience which understands the claim and its explanans, whilstjustification is in relation only with an objective world of true beliefs. The aboveobservations are used to differentiate between two classes of business dialogs:justification patterns and explanatory patterns.
Commitment-based justification patterns are constructed in terms of the inten-tion of the agent which provides the justification, the context in which theyare usually used, the formal representation of the pattern, within specific cases.An example is illustrated by informal text and its representation in
JEL . Allcommitment-based justification patterns of the general form C ( a , b , P , Q ) : c F may be questioned by a common set of critical questions. – CQ : If c = b , which is the relationship between the agent c and b ? – CQ : If F = P , which is the link between the formulas F and P ? – CQ : Is there a stronger commitment which does not justify F ?Specific attacking options for each justification pattern are added at the end ofthe pattern. Gratuitous Promise.
In a gratuitous promise the debtor x promises the cred-itor y to bring about P , without requesting anything: C ( x , y , ⊤ , P ). This mayserve as enough justification for agent y for the achievement of P , given by C ( x , y , ⊤ , P ) : y P (figure 2). The debtor is the one affected by the violation ofthe commitment. In case the agent enacting the gratuitous promise is not thecreditor, one continuation path regards the relationship between the proponentof the justification and the creditor. In the example from figure 2, in case CQ is risen, the relation between father and son can be legally justified.For the CQ attack, the justification stands only if there is an evident connec-tion between the promise P and the action F . Note that the particular variant C ( a , b , ⊤ , P ) : b P avoids the above two attacks. Assuming that in sequent step, ustification from request + RIntent : Justifying actions based on the directive conveyed by anormative empowered agent.Context : The creditor or other agent act on request from other agent.Pattern : C ( a , b , P , ⊤ ) : c FVariants : b=c, a=c, F=P, ¬ PExample : During driving lessons, the instructor requests the student to stopthe car. Consequently, the next student’s action is to signal right.
JEL : C ( instructor , student , StopCar , ⊤ ) : student SignalRightCQ : Is the request legitimate?
Fig. 3.
Commitment-based justificatory patterns. the nephew informed that he has no bag for the trip, the grandfather reacts byassuring his nephew that he will pay both for the trip and buy a new bag. Fromthe father’s perspective, the newly stronger commitment acts as a justificationfor the opposite conclusion ¬ NewBag : C ( grandfather , nephew , ⊤ , PayTrip ∧ NewBag ) : father ¬ NewBag
The promise made by the creditor can justify future actions of the creditoritself. For instance the grandfather starts saving money due to its gratuitouspromise: C ( grandfather , nephew , ⊤ , PayTrip ) : grandfather
SaveMoney . Directives.
In a fact request the debtor does not promise anything, it onlyrequests the precondition q to be satisfied, given by C ( a , b , q , ⊤ ) (figure 3). Theadditional critical question CQ regards the normative rightness of the directive.For instance, there is no obligation for the agent b to meet the request or, if thereis indeed a power relationship between the creditor and the debtor, it may nothave jurisdiction in the context of the sentence q requested. In the example offigure 3, the requested action of stopping the car is legitimate by the relationshipbetween the instructor and the student. If the requested act is negated, thecommitment represents a taboo or an interdiction. Example 4 (Justification from Interdiction). ”I can not sell you cigarettes be-cause the law interdicts to sell them to the minors” will be formalized in
JEL as C ( na , , ¬ SellCigarMinor , ⊤ ) : me ¬ C ( me , you , Pay , SellCigar ) : me ¬ Sell
Here the law is personalized by the normative agent na . According to contractlaw, when exposing an item for selling, an open offer is created. The sellercommits to sell the item in case of acceptance, which usually occurs by pay-ment: C ( seller , buyer , Pay , Sell ). The exact representation captures this when xplanation from cognitive consistency + CCIntent : Explaining actions based on the goals that an agent is following.Context : The debtor commits itself to achieve a particular sentence.Pattern : C ( a , a , Q , P ) ⊳ c FVariant : a=c, Q = ⊤ Example : Tom cannot join the party because he wants to learn for the exam.
JEL : C ( tom , tom , ⊤ , Learn ) ⊳ jim ¬ JoinPartyCQ : Is the debtor aware of his commitments?
Fig. 4.
Explanation for preferred commitment. the agent me justifies his refuse to sell, because he is not committed to do so,which is further justified by the normative interdiction to sell cigarettes to theminors.The two justificatory patterns introduced above are not exhaustive in termsof basic justificatory schemes. However, by combining such basic patterns onecan increase the expressivity of the justifiers. Firstly, by composing a gratuitouspromise with a fact Q treated as a condition, a unilateral contract UL is obtained: C ( a , b , ⊤ , P ) ◦ q Q = C ( a , b , Q , P ). The same UL pattern can also be obtainedby composing a request with a fact P treated as a promise: C ( a , b , Q , ⊤ ) ◦ p P = C ( a , b , Q , P ).Secondly, when the term used for composition is a commitment itself a higherorder commitment [13] is constructed. In this line, justification from bilateralcontract BC is formalized as C ( a , b , C ( b , a , ⊤ , pay ) , deliver ). Here, both partiesmake promises: the agent a commits to deliver the item if the agent b promisesto pay. The pattern is a composition between a unilateral contract and a justifi-cation from request pattern. The composition is applied on the requested actionwhich represents a commitment itself: C ( a , b , Q , P ) ◦ q C ( b , a , ⊤ , Q ). For thegiven example, the justifier is constructed as follows: BC = C ( a , b , , deliver ) ◦ q C ( b , a , ⊤ , pay ). The justification from promise to commit pattern is a composi-tion of two gratuitous promises, applied on the fourth term of the commitment: C ( a , b , ⊤ , ) ◦ p C ( a , c , ⊤ , pay ) = C ( a , b , ⊤ , C ( a , c , ⊤ , deliver )), where agent a promises agent b that he will commit to agent c to deliver the item. Explanation patterns are not rooted in an objective normative frame, havinga subjective component. Explanatory schemes can be viewed as providing sub-jective reasons, with a more flexible relation between explainers and what isexplained.
Public goals.
Consider the situation in which the agent commits itself to bringabout r : C ( a , a , ⊤ , r ). It is on the edge between social semantics and mentalistic xplanation from preferred commitment + PCIntent : Explaining choice between two commitments.Context : The debtor is committed with different strengths to creditors.Pattern : C ( a , b , P , Q ) ≻ C ( a , c , P ′ , Q ′ ) ⊳ d FVariants : a=d, b=d, c=dExample : The agent a promised his boss to attend at a late meeting. He alsopromised his wife to take the child from the school if he has time.Aware of the constraint, the wife decides to go to the school herself.
JEL : C ( a , boss , ⊤ , Meeting ) ≻ C ( a , wife , Time , TakeChild ) ⊳ wife GoSchoolCQ : Is it not possible to achieve the both commitments?CQ : Is the preference relation explained by the cognitive consistencyproperty of the agent d?
Fig. 5.
Commitment-based explanatory preference. semantics of communicative agents (figure 4). The commitment belongs to thesocial semantics because it is public, and points toward the mentalistic approachbecause it represents a goal of the agent. Assuming sincere agents, the attackoption CQ questions the possibility that the agent may not be aware of all itscommitments. Explanation from preference.
The preference relation usually has a strongsubjective component, making it a candidate for explanatory arguments ratherthan justificatory ones. In our example (figure 5), C ( a , boss , ⊤ , Meeting ) is a gra-tuitous commitment, whilst C ( a , wife , Time , TakeChild ) is a unilateral contract.The gratuitous promise representing a stronger promise compared to a unilateralcontract, the preference relation can be deduced based on the strength of eachtype of commitment.
An argument is a pair h t , F i where t is the chain of justifiersor explanans and F the conclusion such that t justifies or explains H and t isminimal. We distinguish between explanatory arguments and justificatary arguments . Definition 3.
A justificatary argument is supported by justifiers only. An expli-catary argument contains at least one supporting explanandum.
A fact can be supported at the same time by several explanatory or justificatoryarguments. efinition 4 (Conflict among arguments).
In the case of an undercuttingargument, its conclusion attacks one justifier or explanation in the support ofanother argument. In the case of rebuttals, the justified formulas contradict eachother directly.
There are two types of interrogative requests: request for explanation andrequest for justification.
Definition 5 (Request for justification).
Agent a requests agent b to provideits justification why t is agent its justification for F : C ( a , b , ! t : b t : i F , ⊤ ) . The general case reflects the situation when the agents a , b and i are different. Example 5 (Request for justification).
Consider that the judge agent requeststhe lawyer agent to legally support the belief of the victim v that selfDefense isa justification for useGun , expressed as: C ( judge , lawyer , ! selfDefense : lawyer selfDefense : v UseGun , ⊤ )Note that the justification ! selfDefense is requested to be constructed from theperspective of the lawyer agent. The expressivity of the language allows to ask thelawyer to present the victim’s justification regarding the sentence selfDefense : v UseGun , given by C ( judge , lawyer , ! selfDefense : v selfDefense : v UseGun , ⊤ ).When b = i , the agent b is requested to justify itself. When a = b , theagent a requests itself to identify or construct a justification supporting why t is accepted by the agent i as valid justifier for F . Not being omniscient, in JEL , the agents are not assumed to be aware of all the justifications that canbe built from their knowledge base. Only an explicit constructed justification isconsidered, which makes sense for the agent to interrogate its own knowledgebase to identify a valid justification. Similarly, when a = b = i , the same agentis applying itself to the task of justifying its own sentences. Definition 6 (Request for explanation).
Agent a requests agent b to explainwhy t is the justification of i for F : C ( a , b , ! t ⊳ j t : i F , ⊤ ) . Similarly, agent arequests agent b to further explain why t is the explanation of agent i for F :C ( a , b , ! t ⊳ j t ⊳ i F , ⊤ ) . Notice that one cannot justify an explanation, but an explanation can berequested both for a justifier and for another explanation. The combinationof the above explicatory/justificatory patterns in dialogs helps the parties tounderstand normative-based decisions.
Strength of Justification.
The strength of a justification depends on the com-mitment used as evidence and the formula needed to be justified. The strongerthe commitment used as a justification term, the stronger the justification. roposition 1.
The commitment C ( a , b , q , p ) is stronger than C ( a , b , q ′ , p ′ ) ifthe debtor promises more and requests less.Example 6 (Strength of justification). ”The supplier s commits to deliver moreitems faster to the retailer r ” is stronger than ”The supplier commits to deliverthe items earlier if he receives the payment earlier”: C ( s , r , ⊤ , MoreItems ∧ FasterDeliv ) ⋗ C ( s , r , PayEarlier , FasterDeliv )In the particular case of no promised action ( p = ⊤ ), the same semanticsworks for defining stronger requests. Thus, the request pattern C ( a , b , p , ⊤ ) isstronger or more specific than C ( a , b , p ∨ q , ⊤ ). This can be used during ne-gotiation dialogs, where the less stronger request allows more options for therequester and introduces higher flexibility in the system. Example 7.
The request to pay either by credit card or by wire transfer isstronger to the wire transfer option, formalized as: C ( bank , a , card ∨ wired , ⊤ ) ⋗ C ( bank , a , wired , ⊤ ). Proposition 2.
A fact p is stronger than the commitment created to bring aboutthat p, given by p ⋗ C ( , , , p ) .Example 8. ”I commit to deliver the item after you confirm the order” is strongerthen ”I commit to deliver the item if you have promised me to confirm the order”: C ( me , you , Confirm , Deliver ) ⋗ C ( me , you , C ( me , you , ⊤ , Confirm ) , Deliver ).A preference relation succ on commitments can be defined based on thestrength of the commitment.
Proposition 3.
The creditor prefers stronger commitments, whilst the debtorprefers weaker commitments when explaining the formula F . If C ( a , b , P , Q ) ⋗ C ( a , b , P ′ , Q ′ ) then we have the following.C ( a , b , P , Q ) ≻ C ( a , b , P ′ , Q ′ ) ⊲ a F and C ( a , b , P ′ , Q ′ ) ≻ C ( a , b , P , Q ) ⊲ b F Conflict Resolution. In JEL all arguments are considered to have justificationsor explanations. When deciding between two conflicting formula, the strongerjustified formula will be preferred by the debtor, because the stronger commit-ment provides more guarantees for the promised action. If C ( a , b , p , q ) : b F and C ( a , b , ⊤ , q ∧ r ) : b ¬ F , the F formula would be accepted. In case the justificationshave the same strength, JEL forces the agents to provide further justificationson request.
Definition 7 (Preference-based conflict resolution).
If F attacks F ′ andF ′ attacks F and c n ⊲ c n − ⊲ ... c i ⊲ c j ⊲ .... ⊲ c ⊲ F and c ′ n ⊲ c ′ n − ⊲ ... c ′ i +1 ⊲ c ′ i ⊲ .... : c ′ ⊲ F ′ , F is preferred to F ′ if there is a chain of explanansc ⊲ ... c k so that equalStrength ( c k , c ′ k ) ∀ k ∈ [1 , i ] and c i +1 ≻ c ′ i +1 . .2 Argumentative Agents Combining commitments with justification and explanation logic provides flexi-bility for defining several types of argumentative agents.Firstly, regarding the logical framework, in the simplest approach, three typesof agents can be formalized: The less demanding agent requires only explanationsin order to accept a formula, given by the axiom t ⊳ i F → F . A rigorous agentwill accept only normative justified formulas: t : i F → F . The most demandingone requests both explanation and justification before accepting a sentence: t ⊳ i F ∧ s : i F → F . Aggregation of these components can lead for instance to a caution agent, which accepts a formula F if it has a valid justification and novalid explanation supporting the opposite conclusion ¬ F , formalized as: t : i F ∧ ( ¬ s ) ⊳ i ¬ F → F In a more elaborate agent system, the existing theories of justification (foun-dationalism, infinitism, internalism, externalism [12]) and explanation (causal,teleological) [15]) can be exploited to define the corresponding agent type. Eachtheory requires different amount and type of evidence before a formula can beconsidered justified or explained. For a foundationalist agent, the existence of abasic justificatory pattern would be enough for accepting the supported formula.Starting from the infinitism theory, a n-type credulous agent accepts a formula ifits justification chain has at least length n . An internalist agent should be ableto justify a sentence only through its own commitments, whilst for an externalist agent, third party commitments can be used as justifiers.Secondly, regarding the commitment patterns, agents can convey or acceptas valid justifiers only commitments meeting a strength threshold. By compos-ing the basic gratuitous promise and request justificatory patterns, one obtainshigher order patterns having different degrees of strength. Table 2 illustratespossible composed patterns that may justify that the payment will be made.By promising to deliver an item and only requesting a promise for payment,the pattern GP + ( R ◦ q GP ) is the weakest one, when justifying the formula Pay . Only an agent having a low justification standard as scintilla of justifica-tion would accept this pattern as valid justification. A little bit stronger justi-fication is given by the pattern GP + R where a promise for delivering and arequest for paying do exist. The agent a should have the reasonable justification proof standard to accept this justifier. In the bilateral contract UC ◦ q GP thepromise to pay representing a precondition for delivering, gives preponderence ofjustification for the agent a to consider it as a valid justifier. The pattern UC meets the convincing justification standard of proof of the agent a , whilst themost attractive pattern for the agent a is UC ◦ p GP , where it promises to deliverthe item only after the payment is finalized. This justifier should meet the mostskeptical standard of proof of an agent, which is behind any reasonable doubt .Thirdly, with respect to the explanatory component, the cognitive consistentpattern is used by sincere agents. Such an agent is committed to itself to bringabout the items that he promised to perform. It comes with several flavors: An wholehearted agent x would try to bring about p if he promised to do so, no attern Justifier Meaning GP + ( R ◦ q GP ) C ( a , b , ⊤ , deliver )+ a commits to deliver the item and C ( a , b , C ( b , a , ⊤ , pay ) , ⊤ ) : a Pay requests b to commit to pay for it. GP + R C ( a , b , ⊤ , deliver )+ a commits to deliver the item C ( a , b , pay , ⊤ ) : a Pay and requests b to pay for it. UC ◦ q GP C ( a , b , C ( b , a , ⊤ , pay ) , deliver ) : a Pay a commits to deliver the itemif b commits a to pay for it. UC C ( a , b , pay , deliver ) : a Pay a commits to deliver the itemin case b pays for it. UC ◦ p GP C ( a , b , pay , C ( a , b , ⊤ , deliver )) : a Pay a will commit to deliver the item if b pays. Table 2.
Composed patterns with varying degrees of strength. matter who its partner is and no matter if its partner has already performedor not the requested action: C ( x , x , C ( x , , , p ) , p ). Some agents can manifestsincerity only to some partner y : C ( x , x , C ( x , y , , p ) , p ). Here, if the agent x iscommitted to the particular agent y than he is committed to itself to bring about p . Re-assurance can be provided to its partner: “If I have promised you to bringabout p I will.”, given by C ( me , you , C ( me , you , , p ) , p ) or to a supervisor: “Iam committed to my boss to keep my promises to all agents which do not have toperform something in exchange.”, formalized as C ( me , boss , C ( me , , ⊤ , p ) , p ).Quite differently, for a diffident agent x , even he has promised to bring about p this is not conclusive for itself that P will hold, given by ¬ C ( x , y , ⊤ , P ) : x P .Depending on the justification provided for this sentence, it can be: i) the agentsimply does not trust its capabilities to accomplish the task; ii) the agent isaware of some stronger commitment that may block the execution of P ; or iii)he is not committed to itself to satisfy its own promises and it is aware of this. s s t ana Commitment Store: C ( t , a , pay , trip ) C ( t , t , flight ∧ acc , trip ) C ( s , t , pay , acc ) C ( s , t , C ( t , s , ⊤ , pay ) , flight ) C ( na , t , ¬ trip ∧ pay , C ( t , , ⊤ , pay )) C ( na , , ¬ EUcitizen , visa ) C ( na , , swiss , ¬ visa ) Fig. 6.
Commitment store in the running scenario.
Consider the scenario in which the agent a wants to book a trip to Valenciafrom the tourism agency c . The company has contracts for flights with the aircompany s and for accommodation with the business entity s (figure 6). Thegent t promises agent a to deliver the trip after he pays for it, representedby the UC pattern C ( t , a , pay , trip ). The capabilities of the agent t are repre-sented by the CC explanatory pattern C ( t , t , flight ∧ acc , trip ) in which, if hemanages to book the flight and accommodation, he can deliver the requestedtrip for his client. The tourism agency is aware of the unilateral contract fromthe accommodation company s , given by C ( s , t , pay , acc ), and also of the bi-lateral contract issued by s : C ( s , t , C ( t , s , ⊤ , pay ) , flight ). Here, the s agentwill provide plane tickets if the partner agent t promises to pay the amount pay .Given the location of the agent t within the European Community, it is doingbusiness under the jurisdiction of the corresponding normative agent na . Follow-ing the contract law, the normative agent na requests to all its business entitiesunder its umbrella that an open offer accepted by a client should be honored, oth-erwise the breaching agent should return the money and also pay penalties. Thecomposition between a unilateral contract and a gratuitous promise UC ◦ p GP is used to model this: C ( na , t , ¬ trip ∧ pay , C ( t , client , ⊤ , pay ))Here, if the client pays the amount pay and he does not receive the trip, thetourism company is committed to pay the amount pay = pay + penalty to theclient.Assume that the tourism agency is an internalist 1-type credulous agent witha convincing justification standard of proof. The client a is externalist, cautious agent having the preponderance of evidence justification standard.The agent a commences the dialog by requesting justification j guarantyingthe trip in case he pays, given by the R pattern: C ( a , t , j : t Trip , ⊤ )Being an internalist agent, the tourism company t can guarantee the trip basedonly on its contractual clauses with the suppliers s and s :[ C ( s , t , pay , acc ) + C ( s , t , C ( t , s , ⊤ , pay ) , flight )] : t Trip
We note the compound justifier above with J , such that J : t Trip . The firstterm in J is a UC, whilst the second commitment represents a BC. Both termssatisfying the proof standard of agent a , the compound justifier J will meetthe justification standard of agent a . Being an externalist agent, the client canaccept the justification of the agent t as valid:[ C ( s , t , pay , acc ) + C ( s , t , C ( t , s , ⊤ , pay ) , flight )] : a Trip
Note that in this line of justification, the agent t releases some private informa-tion like the values pay and pay .Being a cautious agent, the client should check if there are explanationssupporting the opposite conclusion ¬ Trip . Firstly, it requests explanans why J offers enough justification for the formula Trip : C ( a , t , ! J ⊳ t J : t Trip , ⊤ )sing the CC explanation pattern, the tourism agency explains based on itsbusiness practice that plane tickets and accommodation are enough to providethe requested trip: C ( t , t , acc ∧ flight , trip ) ⊳ t J : t Trip
Consider that the agent a is aware of the regulation requesting visa for nonEU citizens, formalized as C ( na , , ¬ EUcitizen , visa ). This is the main concernof the agent a for rebutting the Trip formula. C ( na , , ¬ EUcitizen , visa ) : a J : a ¬ Trip
We note the above justification chain with J ′ such that J ′ : a ¬ Trip . At thismoment the tourism agency may request explanations to agent a regarding hisconcern: C ( t , a , ! J ′ ⊳ a J ′ : a ¬ Trip , ⊤ )The agent a can provide the explanation that he is not an EU citizen. Thishelps agent t to figure out the case, but being a 1-type cautious agent it needs ajustification to accept the formula ¬ EUcitizen . Such a justification is requestedthrough: C ( t , a , J ′′ : a ¬ EUcitizen , ⊤ )One option would be to object the request by activating the critical question CQ of the R pattern, considering that the agent t is not legitimate to askfor such justifications. The other option is to provide an ID card or passportacting as a justification: swissPassport : a ¬ EUcitizen . A fact being strongerthat a commitment according to proposition 2, it satisfies the preponderance ofjustification standard of the t agent. Note that it may represent a constant inthe justificatory logic framework.Knowing that Swiss citizens do not need a visa for traveling in Europe, thecommitment C ( na , , swiss , ¬ visa ) undercuts the a ′ s justifier supporting ¬ Trip formula: C ( na , , swiss , ¬ visa ) : t ¬ J ′ : a ¬ Trip
We note the above justifier with J ′′′ such that J ′′′ : t ¬ J ′ : a ¬ Trip . J ′′′ com-mitment refers to the agent t too, which is under the normative framework ofthe agent na . Therefore, it can be used by the internalist agent t to constructsjustifications. Being cautious, the agent a needs a supplementary explanation,requested with: C ( a , t , ! J ′′′ ⊳ t J ′′′ : t ¬ J ′ : a ¬ Trip , ⊤ )The EU preferring to encourage traveling across Europe from safe countries,rather then imposing unnecessary security constraints, explains why a visa isnot required:[ C ( na , na , ⊤ , encourageTravel ) ≻ C ( na , , ¬ EUcitizen , visa )] ⊳ t J ′′′ : t ¬ J ′ : a ¬ Trip
Having both a justification and an explanation, the agent a accepts that hisvisa concerns are defeated. Consequently, given the accepted valid justification J for the trip, and no valid explanation for ¬ Trip , the agent accepts the
Trip formula.
Discussion and Related Work
Justification Logic and Argumentation.
In the proposed approach we apply thejustification logic mechanism to an argumentation context. The connection be-tween explanation, justification, and argumentation is best evidenced in scenar-ios where understanding is the focus (eg. learning). One reason is that the con-structivist approach needed in understanding is employed by justification logic.Justification Logic treats justification as the primary object, whilst the claim issecondary. Quite the opposite, nonjustificational criticism works towards attack-ing claims themselves, which is closer to classical approach in the argumentationtheory. The proof checker operator of JL promotes reflective communication ordeliberation on justificatory and explanatory knowledge.The constants in JL can be mapped to prima facie arguments, which do notrequire any sort of justification, whilst standard arguments should be supportedby justification chains. The framework of
JEL assures that all arguments aresupported through a chain starting from prima facie arguments only.The proposed framework applies the JL formalism to a multi-agent system.Differently from existing approaches [21,14], we introduce the explanatory oper-ator and force the justifiers to be social commitments. Particular to the classicalapproaches in JL [7], the explanatory operator introduces non-monotonic rea-soning in the JL framework. One of the advantages that commitments bringin this justification logic landscape, is that there are more possibilities to definecommunicative acts between agents: like requests or promises between conveyingagent a and receiving agent b . Argumentation Dialogs.
In the dialog typology of Walton and Krabbe [19], in-formation seeking and inquiry dialogs implies a search for a true answer to somefactual question [5]. In this respect, justification and explanation are subtypesof such dialogs. In the Habermas discourse theory [9], the classification includesexplicative, theoretical, and moral discourses, where explicative discourses aimat increasing comprehensibility, whilst theoretical discourses try to discover thetruth.A first step towards integrated argumentation reasoning with explanatoryreasoning is made in [4], where the distinction between argumentation and ex-planation does not come from the statical structure or mode of reasoning (oftenabductive for explanation, mostly deductive in argumentation), but rather frombroader dialogical context. Justifying reasons appear in two classes: epistemicreasons and practical reasons, treated as arguments [1]. Epistemic justifications(or theoretical reasons) are based only on beliefs and are used to justify beliefs.Practical justifications are constructed from beliefs and preferences and used tojustify options or actions.Compared to argumentation schemes, which aim to capture domain indepen-dent argumentation patterns, our proposal is more business oriented. We try toconstruct basic argumentation blocks used in negotiation and business processmonitoring. This represents a step towards developing an argumentation patternlanguage directly applied on business process modeling languages.ased on the content of explanation, rule-based systems exploit four types ofexplanations: (i) trace , which shows the line of reasoning supporting the conclu-sion, (ii) justification , describing the rationale behind each reasoning step, (iii) control or strategic explanations, which bears out the problem solving strategyor control behavior of the system, and (iv) terminological , providing definitionalinformation [23]. Justification-type explanations seems to give rise to more pos-itive user perceptions of a knowledge-based system than trace and strategic ex-planations [22]. Many knowledge-based systems address the issue of presentinguser-adapted explanations [23].Explanation types depend on domain knowledge. Within the social domain,folk psychological explanations are conveyed, in the physical domain both naiveand sophisticated theories, whilst in the religious domain explanatory standardsprevail. In our case, the main goal of seeking explanation in the business domainis to increase the ability to make predictions and to understand normative-baseddecisions. Social Commitments.
Explanation and justification are treated here as socialconstructs. Commitments have been used within an argumentation frameworkin [3], where argumentation relations as defend, attack, or justify are definedbetween two commitments. In our case, the strength relation is inferred basedon the commitment pattern, whilst the preference relation depends on the agentsrole in the commitment, as creditors or debtors. In both approaches, the agentsshould be able to justify their commitments.The expressivity arising from combining commitments have been exploitedfor representing business patterns [6,18] or legal contracts [13]. The large amountof work on commitments deals with modeling business patterns, which has beenproved satisfactory for real life business protocols. Often, a dialog occurs in whichthe creditor requests for justifiers or performance, whilst the debtor provides therequested justification or explanation in order to re-activate the commitment orto find an alternative solution.Defining commitment-based protocols is easier due to the closed word as-sumptions when designing a protocol. This is not the case in argumentationwhere agents may convey in an open world different types of justifications andexplanations. That is why an argumentation process is needed on top of thecommitments in order to assure the flexibility encountered in real life businessinteractions.
The main goal of our study has been to propose a technical instrumentation forhandling both justificatory and explanatory arguments. The first contributionregards the setting of some basis of exploiting in computational models of argu-ments the differences between justification and explanation, as already stressedout in the philosophy of science.s a second contribution, the
JEL is developed to cover both justifiers andexplanans, in the line of using logic in argumentation as envisaged by Gab-bay [8]. Introducing commitments enhances the capability of agents to reasonover justifications and explanations of the other agents.A third contribution regards the formalization of justificatory and explana-tory commitment-based patterns. The individual actions are taking place withina framework of interdependent social commitments. We consider agents as placedin various networks of commitment relations with other agents, where social in-fluences formulate the justification behind agents decisions [11]. The main benefithere regards the flexibility to construct a large variety of higher order patterns.Using together
JEL with commitments provides opportunities for definingseveral types of argumentative agents. Activating specific axioms in
JEL , rigor-ous or cautios agents can be formalized. The justification standard of each agentis defined based on the strength relation between compound commitments.As future work we will be investigating the role of critical questions in block-ing justifications and explanations.
Acknowledgements
We are grateful to the anonymous reviewers for their useful comments. AdrianGroza is supported by the Sectoral Operational Programme Human ResourcesDevelopment 2007-2013 of the Romanian Ministry of Labour, Family and SocialProtection through the Financial Agreement POSDRU/89/1.5/S/62557.