An Argumentation-based Approach for Explaining Goal Selection in Intelligent Agents
Mariela Morveli-Espinoza, Cesar Augusto Tacla, Henrique Jasinski
AA N A RGUMENTATION - BASED A PPROACH FOR E XPLAINING G OAL S ELECTION IN I NTELLIGENT A GENTS
Mariela Morveli-Espinoza
Graduate Program in Electrical and Computer Engineering (CPGEI),Federal University of Technology - Paraná (UTFPR), Curitiba - Brazil [email protected]
Cesar Augusto Tacla
Graduate Program in Electrical and Computer Engineering (CPGEI),Federal University of Technology - Paraná (UTFPR), Curitiba - Brazil [email protected]
Henrique Jasisnki
Graduate Program in Electrical and Computer Engineering (CPGEI),Federal University of Technology - Paraná (UTFPR), Curitiba - Brazil [email protected] A BSTRACT
During the first step of practical reasoning, i.e. deliberation or goals selection, an intelligent agentgenerates a set of pursuable goals and then selects which of them he commits to achieve. ExplainableArtificial Intelligence (XAI) systems, including intelligent agents, must be able to explain theirinternal decisions. In the context of goals selection, agents should be able to explain the reasoningpath that leads them to select (or not) a certain goal. In this article, we use an argumentation-basedapproach for generating explanations about that reasoning path. Besides, we aim to enrich theexplanations with information about emerging conflicts during the selection process and how suchconflicts were resolved. We propose two types of explanations: the partial one and the completeone and a set of explanatory schemes to generate pseudo-natural explanations. Finally, we apply ourproposal to the cleaner world scenario. K eywords Goal selection · Explainable agents · Formal argumentation
Practical reasoning means reasoning directed towards actions, i.e. it is the process of figuring out what to do. Accordingto Wooldridge [1], practical reasoning involves two phases: (i) deliberation, which is concerned with deciding what stateof affairs an agent wants to achieve, thus, the outputs of deliberation phase are goals the agent intends to pursue, and (ii)means-ends reasoning, which is concerned with deciding how to achieve these states of affairs. The first phase is alsodecomposed in two parts: (i) firstly, the agent generates a set of pursuable goals , and (ii) secondly, the agent chooseswhich goals he will be committed to bring about. In this paper, we focus on the first phase, that is, goals selection.Given that an intelligent agent may generate multiple pursuable goals, some conflicts among these goals could arise, inthe sense that it is not possible to pursue them simultaneously. Thus, a rational agent selects a set of non-conflictinggoals based in a criterion or a set of criteria. There are many researches about identifying and resolving such conflict inorder to determine the set of pursued goals (e.g., [3][4][5][6][7]). However, to the best of our knowledge, none of these Pursuable goals are also known as desires and pursued goals as intentions. In this work, we consider that both are goals atdifferent stages of processing, like it was suggested in [2]. a r X i v : . [ c s . A I] S e p pproaches gives explanations about the reasoning path to determine the final set of pursued goals. Thus, the returnedoutcomes can be negatively affected due to the lack of clarity and explainability about their dynamics and rationality.In order to better understand the problem, consider the well-know “cleaner world” scenario, where a set of robots(intelligent agents) has the task of cleaning a dirty environment. The main goal of all the robots is to have theenvironment clean. Besides cleaning, the robots have other goals such as recharging their batteries or being fixed.Suppose that at a given moment one of the robots (let us call him BOB ) detects dirt in slot (5,5); hence, the goal “cleaning(5,5)” becomes pursuable. On the other hand,
BOB also auto-detects a technical defect; hence, the goal “be fixed” alsobecomes pursuable. Suppose that
BOB cannot commit to both goals at the same time because the plans adopted for eachgoal lead to an inconsistency. This means that only one of the goals will become pursued. Suppose that he decides tofix its technical defect instead of cleaning the perceived dirt. During the cleaning task or after the work is finished, therobot can be asked for an explanation about his decision. It is clear that it is important to endow the agents with theability of explaining their decisions, that is, to explain how and why a certain pursuable goal became (or not) a pursuedgoal.Thus, the research questions that are addressed in this paper are: (i) how to endow intelligent agents with the ability ofgenerating explanations about their goals selection process? and (ii) how to improve the informational quality of theexplanations?In addressing the first question, we will use arguments to generate and represent the explanations. At this point, itis important to mention that in this article, argumentation is used in two different ways. Firstly, argumentation willbe used in the goals selection process. The input to this process is a set of possible conflicting pursuable goals suchthat each one has a preference value and a set of plans that allow the agent to achieve them, and the output is a set ofpursued goals. We will base on the work of Morveli-Espinoza et al. [4] for this process. One important contributiongiven in [4] is the computational formalization of three forms of conflicts, namely terminal incompatibility, resourceincompatibility, and superfluity, which were conceptually defined in [2]. The identification of conflicts is done by usingplans, which are represented by instrumental arguments . These arguments are compared in order to determine the formof conflict that may exist between them. The set of instrumental arguments and the conflict relation between them makeup an Argumentation Framework (AF). Finally, in order to resolve the conflicts, an argumentation semantics is applied.This semantics is a function that takes as input an AF and returns those non-conflicting goals the agent will commit to.Secondly, argumentation is used in the process of explanation generation. The input to this process is the AF mentionedabove and the set of pursued goals and the output is a set of arguments that represent explanations. The argumentsconstructed in this part are not instrumental ones, that is, they do not represent plan but explanations. Regarding thesecond question, we will use the information in instrumental arguments for enriching explanations about the form(s) ofconflict that exists between two goals.Next section focuses on the knowledge representation and the argumentation process for goal selection. Section 3presents the argumentation process for generating explanations. Section 4 is devoted to the application of the proposalto the cleaner world scenario. Section 5 presents the main related work. Finally, Section 6 is devoted to conclusions andfuture work. In this section, we will present part of the results of the article of Morveli-Espinoza et al. [4], on which we will base toconstruct the explanations. Since we want to enrich the explanations, we will increase the informational capacity ofsome of the results.Firstly, let L be a first-order logical language used to represent the mental states of the agent, (cid:96) denotes classicalinference, and ≡ the logical equivalence. Let G be the set of pursuable goals, which are represented by ground atomsof L and B be the set of beliefs of the agent, which are represented by ground literals of L . In order to constructinstrumental arguments, other mental states are necessary (e.g. resources, actions, plan rules); however, they are notmeaningful in this article. Therefore, we will assume that the knowledge base (denoted by K ) of an agent includes suchmental states, besides his beliefs.According to Castelfranchi and Paglieri [2], three forms of incompatibility could emerge during the goals selection:terminal, due to resources, and superfluity . Morveli-Espinoza et al. [4] tackled the problems of identifying and An instrumental argument is structured like a tree where the nodes are planning rules whose premise is made of a set of sub-goals,resources, actions, and beliefs and its conclusion or claim is a goal, which is the goal achieved by executing the plan represented bythe instrumental argument. Literals are atoms or negation of atoms (the negation of an atom a is denoted ¬ a ). Hereafter, terminal incompatibility is denoted by t , resource incompatibility by r , and superfluity by s . G are evaluated. Considering that in their proposal each plan is represented by means of instrumentalarguments, as a result of the identification problem, they defined three AFs (one for each form of incompatibility) and ageneral AF that involves all of the instrumental arguments and attacks of the three forms of incompatibility. Definition 1 (Argumentation frameworks)
Let
ARG ins be the set of instrumental arguments that an agent can buildfrom K . A x -AF is a pair AF x = (cid:104) ARG x , R x (cid:105) (for x ∈ { t, r, s } ) where ARG x ⊆ ARG ins and R x is the binary relation R x ⊆ ARG ins × ARG ins that represents the attack between two arguments of
ARG ins , so that ( A, B ) ∈ R x denotes thatthe argument A attacks the argument B . Since we want to improve the informational quality of explanations, we modify the general AF proposed in [4] byadding a function that returns the form of incompatibility that exists between two instrumental arguments. Thus, anagent will not only be able to indicate that there is an incompatibility between two goals but he will be able to indicatethe form of incompatibility.
Definition 2 (General Argumentation Framework)
Let
ARG ins be a set of instrumental arguments that an agent canbuild from K . A general AF is a tuple AF gen = (cid:104) ARG ins , R gen , f _ INCOMP (cid:105) , where R gen = R t ∪ R r ∪ R s and f _ INCOMP : R gen → { t,r,s } . Example 1
Recall the cleaner world scenario that was presented in Introduction where agent
BOB has two pursuablegoals, which can be expressed as clean (5 , and be ( f ixed ) in language L . Consider that there are two instrumentalarguments whose claim is clean (5 , , namely A that has a sub-argument E whose claim is pickup (5 , and C thathas a sub-argument D whose claim is mop (5 , . Besides, there are two instrumental arguments whose claim is be ( f ixed ) , namely B that has a sub-argument H whose claim is be ( in _ workshop ) and F that does not have anysub-argument.Recall also that terminal incompatibility was also exemplified. In order to exemplify the other forms of incompatibilityand generate the general AF for this scenario, consider the following situations: • BOB has 90 units of battery. He needs 60 units for achieving C , he needs 70 units for achieving A , heneeds 30 units for achieving B , and he does not need battery for achieving F because the mechanic cango to his position. We can notice that there is a conflict between A and B and consequently between theirsub-arguments. • As can be noticed, there are two instrumental arguments whose claim is clean (5 , and two instrumentalarguments whose plan is be ( f ixed ) . It would be redundant to perform more than one plan to achieve the samegoal, this means that arguments with the same claim are conflicting due to superfluity. This conflict is alsoextended to their sub-arguments.We can now generate the general AF for the cleaner world scenario: AF gen = (cid:104){ A, B, C, D, E,F, H } , R gen , f _ INCOMP (cid:105) where R t = { ( A, B ) , ( B, A ) , ( E, B ) , ( B, E ) , ( E, H ) , ( H, E ) , ( A, H ) , ( H, A ) , ( C, B ) , ( B, C ) , ( D, B ) , ( B, D ) , ( D, H ) , ( H, D ) , ( C, H ) , ( H, C ) } , R r = { ( A, B ) , ( B, A ) , ( E, B ) , ( B, E ) , ( A, H ) , ( H, A ) , ( E, H ) , ( H, E ) } , and R s = { ( C, A ) , ( A, C ) , ( E, D ) , ( D, E ) , ( C, E ) , ( E, C ) , ( A, D ) , ( D, A ) , ( F, B ) , ( B, F ) , ( F, H ) , ( H, F ) } . Figure 1 shows the graph representation. So far, we have referred to instrumental arguments – which represent plans – however, since the selection is at goalslevel, it is necessary to generate an AF where arguments represent goals. In order to generate this framework, it isnecessary to define when two goals attack each other. This definition is based on the general attack relation R gen ,which includes the three kinds of attacks that may exist between arguments. Thus, a goal g attacks another goal g (cid:48) whenall the instrumental arguments for g (that is, the plans that allow to achieve g ) have a general attack relation with all theinstrumental arguments for g (cid:48) . This attack relation between goals is captured by the binary relation RG ⊆ G × G . Wedenote with ( g, g (cid:48) ) the attack relation between goals g and g (cid:48) . In other words, if ( g, g (cid:48) ) ∈ RG means that goal g attacksgoal g (cid:48) . Definition 3 (Attack between goals)
Let AF gen = (cid:104) ARG ins , R gen , f _ INCOMP (cid:105) be a general AF, g, g (cid:48) ∈ G be twopursuable goals, ARG _ INS ( g ) , ARG _ INS ( g (cid:48) ) ⊆ ARG ins be the set of arguments for g and g (cid:48) , respectively. Goal g attacks goal g (cid:48) when ∀ A ∈ ARG _ INS ( g ) and ∀ A (cid:48) ∈ ARG _ INS ( g (cid:48) ) it holds that ( A, A (cid:48) ) ∈ R gen or ( A (cid:48) , A ) ∈ R gen . For further information about how instrumental arguments are built, the reader is referred to [4]. ARG _ INS ( g ) denotes all the instrumental arguments that represent plans that allow to achieve g . C F clean(5,5)clean(5,5) mop(5,5)pickup(5,5)be(fixed)
BED H (5,5)(5,5) be(fixed)be(in_workshop)
Figure 1: (Obtained from [8])
The general AF for the cleaner world scenario. The nodes represent the argumentsand the arrows represent the attacks between the arguments. The text next to each node indicates the claim of eachinstrumental argument.Once the attack relation between two goals was defined, it is also important to determine the forms of incompatibility thatexist between any two conflicting goals. The function
INCOMP _ G ( g, g (cid:48) ) will return the set of forms of incompatibilitybetween goals g and g (cid:48) . Thus, if ( g, g (cid:48) ) ∈ RG , then ∀ ( A, A (cid:48) ) ∈ R gen and ∀ ( A (cid:48) , A ) ∈ R gen where A ∈ ARG _ INS ( g ) and A (cid:48) ∈ ARG _ INS ( g (cid:48) ) , INCOMP _ G ( g, g (cid:48) ) = (cid:83) f _ INCOMP (( A, A (cid:48) )) ∪ f _ INCOMP (( A (cid:48) , A )) . We can now define an AFwhere arguments represent goals. Definition 4 (Goals AF)
An argumentation-like framework for dealing with incompatibility between goals is a tuple
GAF = (cid:104) G , RG , INCOMP _ G , PREF (cid:105) , where: (i) G is a set of pursuable goals, (ii) RG ⊆ G × G , (iii) INCOMP _ G : RG → { t,r,s } , and (iv) PREF : G → (0 , is a function that returns the preference value of a given goal such that 1stands for the maximum value. Hitherto, we have considered that all attacks are symmetrical. However, as can be noticed goals have a preference value,which indicates how valuable each goal is for the agent. Therefore, depending on this preference value, some attacksmay be considered successful. This means that the symmetry of the relation attack may be broken.
Definition 5 (Successful attack) Let g, g (cid:48) ∈ G be two goals, we say that g successfully attacks g (cid:48) when ( g, g (cid:48) ) ∈ RG and PREF ( g ) > PREF ( g (cid:48) ) .Let us denote with GAF sc = (cid:104) G , RG sc , INCOMP _ G , PREF (cid:105) the AF that results after considering the successful attacks.
The next step is to determine the set of goals that can be achieved without conflicts, which can also be called acceptablegoals and in this article, they can be explicitly called pursued goals. With this aim, it has to be applied an argumentationsemantics. Morveli-Espinoza et al. did an analysis about which semantics is more adequate for this problem. Theyreached to the conclusion that the best semantics is based on conflict-free sets, on which a function is applied. Next wepresent the definition given in [4] applied to the Goals AF.
Definition 6 (Semantics)
Given a
GAF sc = (cid:104) G , RG sc , INCOMP _ G , PREF (cid:105) . Let S CF be a set of conflict-free setscalculated from GAF sc . MAX _ UTIL : S CF → S CF determines the set acceptable goals. This function takes as input aset of conflict-free sets and returns those with the maximum utility for the agent in terms of preference value.Let G (cid:48) ⊆ G be the set of goals returned by MAX _ UTIL . This means that G (cid:48) is the set of goals the agent can commit to,which are called pursued goals or intentions. Regarding the function for determining acceptable goals, there may be many ways to make the calculations; for example,one way of characterizing
MAX _ UTIL is by summing up the preference value of all the goals in an extension. Anotherway may be by summing up the preference value of just the main goals without considering sub-goals. We will use thefirst characterization in our scenario. In other works (e.g., [9] [10]), it is called a defeat relation. xample 2 Consider the general AF of Example 1, the agent generates:
GAF sc = (cid:104){ clean (5 , , pickup (5 , ,mop (5 , , be ( in _ workshop ) , be ( f ixed ) } , { ( mop (5 , , pickup (5 , , ( clean (5 , , be ( in _ workshop )) , ( mop (5 , ,be ( in _ workshop )) , ( pickup (5 , , be ( in _ workshop )) } , INCOMP _ G , PREF (cid:105) . Figure 2 shows this GAF, the preferencevalues of each goal, and the form of incompatibilities that exists between pairs of goals. clean(5,5)mop(5,5) be(in_workshop
PREF: 0.75PREF: 0.8 PREF: 0.6 t pickup(5,5) be(fixed)in_workshop) PREF: 0.75 PREF: 0.6 st,r t,r
Figure 2: GAF for the cleaner world scenario. The text next to each arrow indicates the form of incompatibility.
From
GAF sc , the number of conflict-free extensions is: | S CF | = 14 . After applying MAX _ UTIL , theextension with the highest preference is: { clean (5 , , mop (5 , , be ( f ixed ) } . This means that G (cid:48) = { clean (5 , , mop (5 , , be ( f ixed ) } are compatible goals that can be achieved together without conflicts. In this section, we present explanatory arguments and the process for generating explanations for a goal become pursuedor not.First of all, let us present the types of questions that can be answered: • WHY ( g ) : it is required an explanation to justify why a goal g became pursued . • WHY _ NOT ( g ) : it is required an explanation to justify why a goal g did not become pursued. As a result of the above section, we obtain a Goals Argumentation Framework (GAF) and a set of pursued goals. Recallthat in a GAF, the arguments represent goals; hence, in order to generate an explanation from a GAF, it is necessaryto generate beliefs and rules – that reflect the knowledge contained in it – from which, explanatory arguments canbe constructed. Before presenting the beliefs and rules, let us present some functions that will be necessary for thegeneration of beliefs: • COMPS ( GAF sc ) = { g | (cid:64) ( g, g (cid:48) ) ∈ RG sc (or ( g (cid:48) , g ) ∈ RG sc ) , where g, g (cid:48) ∈ G } . This function returns theset of goals without conflicting relations. • EVAL _ PREF ( GAF sc ) = { ( g, g (cid:48) ) | ( g, g (cid:48) ) ∈ RG sc and ( g (cid:48) , g ) (cid:54)∈ RG sc } . This function returns all the pairs ofgoals in RG (cid:48) that represent non-symmetrical relations between goals. When the relation is not symmetrical, itmeans that one of the goals is preferred to the other.Using these functions, the set of beliefs generated from a GAF sc = (cid:104) G , RG sc , INCOMP _ G , PREF (cid:105) are the following: • ∀ g ∈ COMPS ( GAF sc ) generate a belief ¬ incomp ( g ) • ∀ ( g, g (cid:48) ) ∈ EVAL _ PREF ( GAF sc ) , if PREF ( g ) > PREF ( g (cid:48) ) , then generate pref ( g, g (cid:48) ) and ¬ pref ( g (cid:48) , g ) . • ∀ ( g, g (cid:48) ) ∈ ( RG sc \ EVAL _ PREF ( GAF sc )) generate a belief eq _ pref ( g, g (cid:48) ) . These beliefs are created forthose pairs of goals with equal preference. • ∀ ( g, g (cid:48) ) ∈ RG sc generate a belief incompat ( g, g (cid:48) , ls ) where ls = INCOMP _ G ( g, g (cid:48) ) • ∀ g ∈ G (cid:48) generate a belief max _ util ( g ) • ∀ g ∈ G \ G (cid:48) generate a belief ¬ max _ util ( g ) In order to better deal with goals, we map each goal to a constant in L . B of the agent. These beliefs are necessary fortriggering any of the following rules: • r ¬ incomp ( x ) → pursued ( x ) • r incompat ( x, y, ls ) ∧ pref ( x, y ) → pursued ( x ) • r incompat ( x, y, ls ) ∧ ¬ pref ( y, x ) → ¬ pursued ( y ) • r incompat ( x, y, ls ) ∧ eq _ pref ( x, y ) → pursued ( x ) • r max _ util ( x ) → pursued ( x ) • r ¬ max _ util ( x ) → ¬ pursued ( x ) Let
E R = { r , r , r , r , r , r } be the set of rules necessary for constructing explanatory arguments. Definition 7 (Explanatory argument)
Let B , E R , and g ∈ G be the set of beliefs, set of rules, and a goal of an agent,respectively. An explanatory argument constructed from B and E R for determining the status of g is a pair A = (cid:104) S , h (cid:105) such that (i) S ⊆ B ∪ E R , (ii) h ∈ { pursued ( g ) , ¬ pursued ( g ) } , (iii) S (cid:96) h , and (iv) S is consistent and minimal forthe set inclusion .Let ARG exp be the set of explanatory arguments that can be built from B and E R . We call S the support of an argument A (denoted by SUPPORT ( A ) ) and h its claim (denoted by CLAIM ( A ) ). We can notice that rules in
E R can generate conflicting arguments because they have inconsistent conclusions. Thus,we need to define the concept of attack. In this context, the attack that can exist between two explanatory arguments isthe well-known rebuttal [12], where two explanatory arguments support contradictory claims. Formally:
Definition 8 (Rebuttal)
Let (cid:104) S , h (cid:105) and (cid:104) S (cid:48) , h (cid:48) (cid:105) be two explanatory arguments. (cid:104) S , h (cid:105) rebuts (cid:104) S (cid:48) , h (cid:48) (cid:105) iff h ≡ ¬ h (cid:48) . Rebuttal attack has a symmetric nature, this means that two arguments rebut each other, that is, they mutually attack.Recall that the semantics for determining the set of pursued goals is based on conflict-free sets and on a function basedon the preference value of the goals. This function is decisive in the selection of the extension that includes the goalsthe agent can commit to. Thus, it is natural to believe that arguments related to such function are stronger than otherarguments. This difference in the strength of arguments turns out in a defeat relation between them, which breaks thepreviously mentioned symmetry.
Definition 9 (Defeat Relation - D ) Let
E R be the set of rules and A = (cid:104) S , h (cid:105) and B = (cid:104) S (cid:48) , h (cid:48) (cid:105) be two explanatoryarguments such that A rebuts B and vice versa. A defeats B iff r ∈ S (or r ∈ S ).We denote with ( A, B ) the defeat relation between A and B . In other words, if ( A, B ) ∈ D , it means that A defeats B . Once we have defined arguments and the defeat relation, we can generate the AF. It is important to make it clear that adifferent AF is generated for each goal.
Definition 10 (Explanatory Argumentation Framework)
Let g ∈ G be a pursuable goal. An Explanatory AF for g isa pair X AF g = (cid:104) ARG gexp , D g (cid:105) where: • ARG gexp ⊆ ARG exp such that ∀ A ∈ ARG gexp , CLAIM ( A ) = pursued ( g ) or CLAIM ( A ) = ¬ pursued ( g ) . • D g ⊆ ARG gexp × ARG gexp is a binary relation that captures the defeat relation between arguments in
ARG gexp . The next step is to evaluate the arguments that make part of the AF. This evaluation is important because it determinesthe set of non-conflicting arguments, which in turn determines if a goal becomes pursued or not. Recall that forobtaining such set, an argumentation semantics has to be applied. Unlike the semantics for goals selection, in this casewe can use any of the semantics defined in literature. Next, the main semantics introduced by Dung [13] are recalled . Definition 11 (Semantics)
Let
X AF g = (cid:104) ARG gexp , D g (cid:105) be an explanatory AF and E ⊆ ARG gexp : • E is conflict-free if ∀ A, B ∈ E , ( A, B ) / ∈ D g Minimal means that there is no S (cid:48) ⊂ S such that S (cid:96) h and consistent means that it is not the case that S (cid:96) pursued ( g ) and S (cid:96) ¬ pursued ( g ) [11]. It is not the scope of this article to study the most adequate semantics for this context or the way to select an extension whenmore than one is returned by a semantics. E defends A iff ∀ B ∈ ARG gexp , if ( B, A ) ∈ D g , then ∃ C ∈ E s.t. ( C, B ) ∈ D g . • E is admissible iff it is conflict-free and defends all its elements. • A conflict-free E is a complete extension iff we have E = { A | E defends A } . • E is a preferred extension iff it is a maximal (w.r.t. the set inclusion) complete extension. • E is a grounded extension iff is a minimal (w.r.t. set inclusion) complete extension. • E is a stable extension iff E is conflict-free and ∀ A ∈ ARG gexp , ∃ B ∈ E such that ( B, A ) ∈ D g . Finally, a goal g becomes pursued when ∃ A ∈ E such that CLAIM ( A ) = pursued ( g ) . In this article, an explanation is made up of a set of explanatory arguments that justify the fact that a pursuable goalbecomes (or not) pursued. Recall that there is a different explanatory AF for each pursuable goal. Thus, we can say thatan explanation for a given goal g is given by the explanatory AF generated for it, that is X AF g . Besides, if g ∈ G (cid:48) ,the explanation is required by using WHY ( g ) ; otherwise, the explanation is required by using WHY _ NOT ( g ) . Finally, wecan differentiate between partial and complete explanations depending on the set of explanatory arguments that areemployed for the justification: • A complete explanation for g is: CE g = X AF g • A partial explanation for g is: P E g = E , where E is an extension obtained by applying a semantics to X AF g .We can now present the steps for generating explanations. Given a GAF sc = (cid:104) G , RG sc , INCOMP _ G , PREF (cid:105) and a set ofpursued goals G (cid:48) , the steps for generating an explanation for a goal g ∈ G are:1. From GAF sc generate the respective beliefs and add to B
2. Trigger the rules in
E R that can be unified with the beliefs of B
3. Construct explanatory arguments based on the rules and beliefs of the two previous items4. ∀ g ∈ G do(a) Generate the respective explanatory AF (that is, X AF g ) with the arguments whose claim is pursued ( g ) or ¬ pursued ( g ) and the defeat relation(b) Calculate the extension E from X AF g Like it was done in [14], in this sub-section we present a pseudo-natural language for improving the understanding ofthe explanations when the agents are interacting with human users. Thus, we propose a set of explanatory schemes , onefor each rule in
E R . This means that depending on which rule an argument was constructed, the explanation scheme isdifferent. In this first version of the scheme, we will generate explanatory sentences only for partial explanations.Recall that goals are mapped to constants of L , in order to improve the natural language let NAME ( g ) denote the originalpredicate of a given goal g . Besides, let RULE ( A ) denote which of the rules in E R was employed in order to construct A . Definition 12 (Explanatory Schemes)
Let A = (cid:104) S , h (cid:105) be an explanatory argument. An explanatory scheme exp _ sch for A is: • If RULE ( A ) = r ¬ incomp ( x ) → pursued ( x ) , then exp _ sch = (cid:104) NAME ( x ) has no incompatibility, so it became pursued. (cid:105)• If RULE ( A ) = r incompat ( x, y, ls ) ∧ pref ( x, y ) → pursued ( x ) , then exp _ sch = (cid:104) NAME ( x ) and NAME ( y ) have the following conflicts: ls . Since NAME ( x ) is more preferable than NAME ( y ) , NAME ( x ) became pursued. (cid:105) Underlined characters represent the variables of the schemes, which depend on the variables of rules. If RULE ( A ) = r incompat ( x, y, ls ) ∧ ¬ pref ( y, x ) → ¬ pursued ( y ) , then exp _ sch = (cid:104) NAME ( x ) and NAME ( y ) have the following conflicts: ls . Since NAME ( y ) is less preferable than NAME ( x ) , NAME ( y ) did not become pursued. (cid:105)• If RULE ( A ) = r incompat ( x, y, ls ) ∧ eq _ pref ( x, y ) → pursued ( x ) , then exp _ sch = (cid:104) NAME ( x ) and NAME ( y ) have the following conflicts: ls . Since NAME ( x ) and NAME ( y ) have thesame preference value, NAME ( x ) became pursued. (cid:105)• If RULE ( A ) = r max _ util ( x ) → pursued ( x ) , then exp _ sch = (cid:104) Since
NAME ( x ) belonged to the set of goals that maximize the utility, it became pursued. (cid:105)• If RULE ( A ) = r ¬ max _ util ( x ) → ¬ pursued ( x ) , then exp _ sch = (cid:104) Since
NAME ( x ) did not belong to the set of goals that maximizes the utility, it did not becomepursued. (cid:105) Let us consider the
GAF sc = (cid:104) G , RG sc , INCOMP _ G , PREF (cid:105) presented in Example 2, whose graph is depicted in Figure2. Recall also that G (cid:48) = { clean (5 , , mop (5 , , be ( f ixed ) } .Firstly, we map the goals in G into constants of L in the following manner: g = clean (5 , , g = pickup (5 , , g = mop (5 , , g = be ( in _ workshop ) , and g = be ( f ixed ) . We will also map the beliefs and rules to constants in L .We can now follow the steps to generate the explanations:
1. Generate beliefs - b : ¬ incomp ( g ) b : ¬ max _ util ( g ) - b : incompat ( g , g , ‘ s ’ ) b : pref ( g , g ) - b : incompat ( g , g , ‘ t ’ ) b : ¬ pref ( g , g ) - b : incompat ( g , g , ‘ t, r ’ ) b : pref ( g , g ) - b : incompat ( g , g , ‘ t, r ’ ) b : ¬ pref ( g , g ) - b : max _ util ( g ) b : pref ( g , g ) - b : max _ util ( g ) b : ¬ pref ( g , g ) - b : max _ util ( g ) b : pref ( g , g ) - b : ¬ max _ util ( g ) b : ¬ pref ( g , g )
2. Trigger rules - r : ¬ incomp ( g ) → pursued ( g ) - r : incompat ( g , g , ‘ s ’ ) ∧ pref ( g , g ) → pursued ( g ) - r : incompat ( g , g , ‘ s ’ ) ∧ ¬ pref ( g , g ) → ¬ pursued ( g ) - r : incompat ( g , g , ‘ t ’ ) ∧ pref ( g , g ) → pursued ( g ) - r : incompat ( g , g , ‘ t ’ ) ∧ ¬ pref ( g , g ) → ¬ pursued ( g ) - r : incompat ( g , g , ‘ t, r ’ ) ∧ pref ( g , g ) → pursued ( g ) - r : incompat ( g , g , ‘ t, r ’ ) ∧ ¬ pref ( g , g ) → ¬ pursued ( g ) - r : incompat ( g , g , ‘ t, r ’ ) ∧ pref ( g , g ) → pursued ( g ) - r : incompat ( g , g , ‘ t, r ’ ) ∧ ¬ pref ( g , g ) → ¬ pursued ( g ) - r : max _ util ( g ) → pursued ( g ) - r : max _ util ( g ) → pursued ( g ) - r : max _ util ( g ) → pursued ( g ) - r : ¬ max _ util ( g ) → ¬ pursued ( g ) - r : ¬ max _ util ( g ) → ¬ pursued ( g )
3. Construct explanatory arguments - A = (cid:104){ b , r } , pursued ( g ) }(cid:105) - A = (cid:104){ b , b , r } , pursued ( g ) }(cid:105) - A = (cid:104){ b , b , r } , ¬ pursued ( g ) }(cid:105) - A = (cid:104){ b , b , r } , pursued ( g ) }(cid:105) - A = (cid:104){ b , b , r } , ¬ pursued ( g ) }(cid:105) - A = (cid:104){ b , b , r } , pursued ( g ) }(cid:105) - A = (cid:104){ b , b , r } , ¬ pursued ( g ) }(cid:105) - A = (cid:104){ b , b , r } , pursued ( g ) }(cid:105) - A = (cid:104){ b , b , r } , ¬ pursued ( g ) }(cid:105) - A = (cid:104){ b , r } , pursued ( g ) }(cid:105) A = (cid:104){ b , r } , pursued ( g ) } (cid:105) - A = (cid:104){ b , r } , pursued ( g ) }(cid:105) - A = (cid:104){ b , r } , ¬ pursued ( g ) }(cid:105) - A = (cid:104){ b , r } , ¬ pursued ( g ) }(cid:105)
4. For each goal, generate an explanatory AF and extension - For g : X AF g = (cid:104){ A , A } , {}(cid:105) , E = { A , A } - For g : X AF g = (cid:104){ A , A , A } , { ( A , A ) , ( A , A ) }(cid:105) , E = { A , A } - For g : X AF g = (cid:104){ A , A , A } , {}(cid:105) , E = { A , A , A } - For g : X AF g = (cid:104){ A , A , A , A } , {}(cid:105) , E = { A , A , A , A } - For g : X AF g = (cid:104){ A , A } , {}(cid:105) , E = { A , A } Thus, the – partial or complete – explanations for justifying the status of each goal were generated. Next, we present thequery, set of arguments of the partial explanation, and the explanatory sentences for the status of each goal: • For the query
WHY ( g ) , we have P E = { A , A } , which can be written:* clean (5 , and be ( in _ workshop ) have the following conflicts: ‘ t, r ’. Since clean (5 , is more preferablethan be ( in _ workshop ) , clean (5 , became pursued * Since clean (5 , belonged to the set of goals that maximizes the utility, it became pursued • For the query
WHY _ NOT ( g ) , we have P E = { A , A } , which can be written:* mop (5 , and pickup (5 , have the following conflicts: ‘ s ’. Since pickup (5 , is less preferable than mop (5 , , pickup (5 , did not become pursued * Since pickup (5 , did not belong to the set of goals that maximizes the utility, it did not become pursued • For the query
WHY ( g ) , we have P E = { A , A , A } , which can be written:* mop (5 , and pickup (5 , have the following conflicts: ‘ s ’. Since mop (5 , is more preferable than pickup (5 , , mop (5 , became pursued * mop (5 , and be ( in _ workshop ) have the following conflicts: ‘ t ’. Since mop (5 , is more preferable than be ( in _ workshop ) , mop (5 , became pursued * Since mop (5 , belonged to the set of goals that maximizes the utility, it became pursued • For the query
WHY _ NOT ( g ) , we have P E = { A , A , A , A } , which can be written:* mop (5 , and be ( in _ workshop ) have the following conflicts: ‘ t ’. Since be ( in _ workshop ) is less preferablethan mop (5 , , be ( in _ workshop ) did not become pursued * clean (5 , and be ( in _ workshop ) have the following conflicts: ‘ t, r ’. Since be ( in _ workshop ) is lesspreferable than clean (5 , , be ( in _ workshop ) did not become pursued * pickup (5 , and be ( in _ workshop ) have the following conflicts: ‘ t, r ’. Since be ( in _ workshop ) is lesspreferable than pickup (5 , , be ( in _ workshop ) did not become pursued * Since be ( in _ workshop ) did not belong to the set of goals that maximizes the utility, it did not becomepursued • For the query
WHY ( g ) , we have P E = { A , A } , which can be written:* be _ f ixed has no incompatibility, so it became pursued * Since be _ f ixed belonged to the set of goals that maximizes the utility, it became pursued For all the queries, except
WHY _ NOT ( g ) , the complete explanation is the same. In the case of WHY _ NOT ( g ) , thecomplete explanation includes the attack relations between some of the arguments of its explanatory AF.We are also working in a simulator – called ArgAgent – for generating explanations. In it first version, just partialexplanations are generated. Figure 3 shows the explanation for query WHY ( g ) . Since XAI is a recently emerged domain in Artificial Intelligence, there are few reviews about the works in this area.In [15], Anjomshoae et al. make a Systematic Literature Review about goal-driven XAI, i.e., explainable agency forrobots and agents. Their results show that 22% of the platforms and architectures have not explicitly indicate their Available at: https://github.com/henriquermonteiro/BBGP-Agent-Simulator/
WHY ( g ) . Obtained by using the simulator ArgAgent.method for generating explanations, 18% of papers relied on ad-hoc methods, 9% implemented their explanations inBDI architecture.Some works relied on the BDI model are the following. In [16] and [17], Broekens et al. and Harbers et al.,respectively, focus on generating explanations for humans about how their goals were achieved. Unlike our proposal,their explanations do not focus on the goals selection. Langley et al. [18] focus on settings in which an agent receivesinstructions, performs them, and then describes and explains its decisions and actions afterwards.Sassoon et al. [19] propose an approach of explainable argumentation based on argumentation schemes andargumentation-based dialogues. In this approach, an agent provides explanations to patients (human users) abouttheir treatments. In this case, argumentation is applied in a different way than in our proposal and with other focus,they generate explanations for information seeking and persuasion. Finally, Morveli-Espinoza et al. [20] propose anargumentation-based approach for generating explanations about the intention formation process, that is, since a goal isa desire until it becomes an intention; however, the generated explanations about goals selection are not detailed andthey do not present a pseudo-natural language. In this article, we presented an argumentation-based approach for generating explanations about the goals selectionprocess, that is, giving reasons to justify the transition of a set of goals from being pursuable (desires) to pursued(intentions). Such reasons are related to the conflicts that may exist between pursuable goals and how that conflicts wereresolved. In the first part of the approach, argumentation was employed to deal with conflicts and in the second part itwas employed to generate explanations. In order to improve the informational quality of explanations, we extended theresults presented in [21]. Thus, explanations also include the form of incompatibility that exists between goals. Besides,we proposed a pseudo-natural language that is a first step to generate explanations for human users. Therefore, ourproposal is able generate explanations for both intelligent agents and human-users.As future work, we aim to further improve the informational quality of explanations by allowing information seekingabout the exact point of conflict between two instrumental arguments (or plans) and information about the force of thearguments. The pseudo-natural language was only applied to partial explanations, we plan to extend such language inorder to support complete explanations.
Acknowledgment
This work is partially founded by CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior).
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