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Chapter 3 Dialogue Games

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In this chapter, we go through some relevant proposals in dialogue game frameworks for agent communication. We highlight the foundations and the structures of these frameworks. We also compare these proposals and discuss their limits. Our dialogue game protocol presented in Chapter 9 is an attempt to push these limits.

To communicate, agents using traditional agent communication protocols, like those proposed by FIPA, must follow the protocol sequences. Hence, these protocols are often unsuitable for autonomous agents. This is due to the inflexibility of these protocols and to the fact that there is no mechanism allowing agents to choose the communicative acts they will perform. To solve this problem, several proposals have been put forward using formal dialogue games. Formal dialogue games are abstract structures that can be composed to construct the whole dialogue. They involve interactions between two or more players, in which each player moves by making utterances according to a pre-defined set of rules. The rules typically define which locutions may or must be uttered in different circumstances, and they may also indicate when the dialogue terminates. As a joint activity, the dialogue requires the coordination of the participants’ actions. In this context, dialogue games are structures enabling agents to coordinate the dialogical activity.

Dialogue games have been studied in philosophy from at least the time of Aristotle (350 B.C) (van Emeren et al., 1996), and were extensively studied and practiced in medieval times (Spade, 1979). They differ from the games of Economic Game Theory, in that payoffs for winning or losing a game are not considered, and because there is no use of uncertainty measures such as probabilities, to model the possible moves of opponents. Dialogue games have been used in argumentation theory for the contextual analysis of fallacious reasoning, on the assumption that what may count as a logical fallacy in one context may not be so in another. The main proponents of this approach were Hamblin (1970, 1971) and MacKenzie (1979, 1990). All Hamblin’s games have as their purpose, "the exchange of information among the participants" and so may be considered as models of information-seeking dialogues.

Another strand of philosophy, led by Lorenzen (1960), has used formal dialogue games to provide a constructive proof-theory for statements in intuitionistic and classical logic. Here a speaker in a dialogue game treats a proposition in a logical language as a statement. This statement is subject to question and challenge by an opponent. The proponent of the statement must defend the statement against the opponent’s attack in pre-defined ways. In doing so, a proof (or disproof) of the statement is incrementally constructed. The precise rules of the dialogue game determine whether this proof corresponds to classical or intuitionistic logic.

Recently, dialogue games have been proposed as a basis for agent communication. Various dialogue game protocols have been developed. Applications have included frameworks for Walton and Krabbe’s analysis of dialogue types (Reed, 1998) (McBurney and Parsons, 2001, 2002), for negotiation protocols (Dastani et al., 2000), and for agent team-formation dialogues modeled as combination of information-seeking and persuasion dialogues (Dignum et al., 2000). Dialogue games have also been used for joint-intention-formation dialogues, modeled as persuasion dialogues possibly containing embedded negotiation dialogues (Dignum et al., 2001), for request for action (Maudet et al., 2002), and for inconsistent and biased information (Lebbink et al., 2004). In this chapter, we go through these proposals in some details.

The rest of this chapter is organized as follows. In Section 3.2, we summarize Reeds’ dialogue frames. In Section 3.3, we present Dastani et al.s’ negotiation protocols. In Section 3.4, we discuss the layer model of McBurney and Parsons. Maudet et al.’s DIAGAL language and Lebbink et al.s’ dialogue games will be presented in Sections 3.5 and 3.6. In Section 3.7 we review Dignum et al.s’ dialogue games. Finally, in Section 3.8, we compare and discuss these proposals.

Reed (1998) proposed the notion of dialogue frames as abstract exchange structures. This notion is used to explore the dialogue typology proposed in (Walton and Krabbe, 1995) and one of its important features, the concept of functional embedding. In these frames, persuasion, inquiry and information seeking are epistemic , negotiation is concerned with contracts , and deliberation with plans . Epistemic issues can be modeled by a BDI approach (Rao and Georgeff, 1991), or a propositional logic encompassing beliefs, values (such as those employed to evaluate issues during negotiation), rules, intentions, etc. The notion of contract is intended to abstract from the precise structure used to reach a deal. Plan refers to the abstract notion of a set of partially ordered contracts. The foundation of the model is a set of agents, A , a set of agent’s beliefs, B , a set of agent’s contracts, C , and a set of agent’s plans, P .

Contracts are composed of < issue , value > pairs. To make explicit the assumption that there is some basic result of a fulfilled contract, this result can be expressed as a conjunction of beliefs. Let us consider the example of a contract specifying that for agent a to receive information from agent b , a must pay b $10. The issue-value pairs are < Price , $10>, < Quality , High >. Plans can be constructed from contracts: a complete plan is a fully ordered set of contracts each of which is fully specified with respect to its result, r , its list of issue-value pairs, vn , and the settings of both issue and value in each value pair vi .

The set of dialogue types D is defined on the basis of the sets defined above (first paragraph of this section). Each type is a name-substrate pair:

Formally, a dialogue frame is defined as a tuple with four elements:

where is the type of this dialogue frame, is the set of beliefs, contracts or plans, is the topic of the dialogue frame, are the interlocutors, and refers to the i th utterance occurring in a dialogue between agents and in which is the originator of the utterance and An utterance is a pair in which is a statement (i.e. a well formed formula in the communication language), and the represent the arguments supporting that statement.

A dialogue frame is thus of a particular type, , and focuses on a particular topic. For example, for a persuasion dialogue, the topic focuses on a particular belief, and for a negotiation dialogue, the topic focuses on a contract. A dialogue frame is initiated by a propose-accept sequence that can be considered as meta-acts whose purpose is to open the frame. These meta-acts have an empty support The frame terminates with a characteristic utterance indicating acceptance or concession to the topic on the part of one of the agents.

Let us consider the following example of persuasion dialogue between two agents a and b .

In this example, agent a initiates the dialogue to persuade agent b that some third party, c , has information. The dialogue is open because agent b accepts it. Agent a supports its claim by citing d as its source. Agent b undercuts the argument by pointing out the unreliability of d , and with no further supports available, agent a retracts its assertion with a concede which terminates the dialogue frame.

Reed considers two kinds of game compositions, sequencing and embedding . Sequencing is the canonical ordering and embedding is captured within the model without further complications of the structures. Indeed, since propositions to enter a frame are moves like any others, they can be made within ongoing frames. When a new dialogue frame is proposed at turn i by a , and accepted by b at i +1 while a frame was open, Reed assumed that is just suspended ( is then embedded in ). When the frame terminates, resumes where it was stopped. Generally, the speaker who concedes in the embedding frame is not the speaker who resumes in the embedding frame.

Dastani, Hulstijn and der Torre (Dastani et al., 2000) proposed a methodology for constructing flexible negotiation protocols based on joint actions and dialogue games, following the work of (Hulstijn, 2000a, b). Negotiation is considered as a combination of joint actions represented by simple dialogue games from which larger interactions can be constructed. These dialogue games consist of initiatives followed by responses.

The key notion of these negotiation protocols is coherence. An utterance or move in a negotiation dialogue is coherent with the dialogue context, if (i) it fits a plan that might achieve the apparent goals of the agent, and (ii) it fits the current interaction rules. The information conveyed or requested by an utterance is called the semantic content . An utterance has a purpose: the communicative function . Each utterance is analyzed as a dialogue act which is characterized by a semantic content and a communicative function.

Negotiation dialogue games are sequences of moves. Each move corresponds to a type of utterance. Moves can be either initiatives or responses. Each initiative must be followed by an appropriate response, although there may be other exchanges first. For example, a clarification exchange may precede the answer to a question. The basic game structure is an exchange capturing that an initiative can be followed by either a positive or a negative response, or else a retry. For example, a proposal is an initiative, an acceptance is the corresponding positive response, a rejection is the negative response, and a counter-proposal is an example of a retry. An exchange is allowed, given that the coherence constraint on the semantic contents of the initiative and response is met. In other words, the response must address the initiative. Formally, an exchange between two agents, and about the content (the response content) is specified as follows:

is the shared dialogue context, is the initiative content, and is the retry content.

Games can be composed by sequencing or chaining. A sequential combination is specified as follows:

The recursive nature of the definition indicates that it is possible to combine as many games as requested. Like in the basic exchange, some coherence constraints are stated between the games’ topic. For instance, to be combined, games have to share a common subject matter. With regard to chaining composition, constraints require the last dialogue act (reactive) of the first game being the first (initiative) of the second game. Canonical examples of such chaining structures are question / answer / evaluation or proposal / counter-proposal. The difference between sequencing and chaining is that unlike chaining, sequencing does not impose any constraint about the relationship between the games.

McBurney and Parsons defined a model for a generic dialogue game protocol to represent combinations of dialogues according to the typology proposed by Walton and Krabbe (1995). This model is used in the development of a three-level hierarchical formalism for agent dialogues. The lowest level is the topic layer, the next level is the dialogue layer, and the highest level is the control layer. The topic layer defines the matters which may be discussed in the dialogue. These matters refer to real-world objects or to states of affairs.

In the dialogue layer, different dialogue games are modeled as classical dialectical systems [2] with the following components: (i) beginning rules , (ii) locution rules , (iii) combination rules , (iv) commitment rules , and (v) termination rules . Beginning rules define the circumstances under which the dialogue starts. Locution rules indicate which utterances are permitted. Typically, legal locutions allow participants to assert propositions, to question or contest prior assertions. They also allow agents to justify the propositions that they have asserted which have been subsequently questioned or contested. Combination rules define the dialogue contexts under which particular locutions are permitted or not. For instance, it may not be permitted for a participant to assert a proposition p and subsequently to assert the proposition again in the same dialogue, without in the meanwhile having retracted the former assertion. Commitment rules define the circumstances under which participants express commitment to a proposition. These rules are inspired by formal dialogue systems proposed by Hamblin (1970) that establish public sets of commitments, called commitment stores, for each participant. This notion will be detailed in Chapter 4. Termination rules define the circumstances under which the dialogue ends.

The selection of specific dialogue types and transition between these types is presented in the control layer. This layer is defined in terms of two components: a set of atomic dialogue types which include the dialogue types of Walton and Krabbe, and a set of control dialogues which are dialogues that have as their discussion subjects other dialogues rather than topics. These dialogues include beginning and termination dialogues.

In addition, McBurney and Parsons propose the following combinations of atomic or control dialogues:

Iteration : If G is a dialogue, then Gn is also a dialogue consisting of the n -fold repetition of G. Each dialogue starts after termination of the preceding dialogue.

Sequencing : If G and H are both dialogues, then G ; H is also a dialogue consisting of undertaking G until its closure and then immediately undertaking H .

Parallelization : If G and H are both dialogues, then G H is also a dialogue consisting of undertaking both G and H simultaneously until termination.

Embedding : If G and H are both dialogues, then G [ H | ] is also a dialogue consisting of undertaking G until a sequence of legal locutions of G has been executed, and then switching immediately to dialogue H which is undertaken until its termination, whereupon dialogue G resumes from where it was interrupted.

Testing : If p is a well formed formula, then < p > is a control dialogue testing p truth status. When p is found to be false, the current active dialogue ends.

Maudet and Chaib-draa (2002) proposed an agent communication language DIAGAL (DIAlogue Game based Agent Language) by adapting the Maudet’s work (2001) to the communication between software agents. An implementation of this language as a dialogue game simulator is described in (Labrie et al., 2003). In the model proposed by the authors, dialogue games are handled through a contextualization game which aims at defining how games are opened, combined, and closed during the conversation. This model adopts a strict commitment-based approach within the game structure. This approach proposed by (Singh, 1998) and (Colombetti, 2000) will be discussed in detail in Chapter 4.

In DIAGAL, games are bilateral structures capturing the different commitments created during the dialogue (Chaib-draa et al., 2005). These games are defined by entry conditions , success conditions , exit conditions , and dialogue rules . Entry conditions define conditions which must be fulfilled at the beginning of the game. Success conditions are conditions which indicate whether the game terminates successfully or not. Exit conditions define the goal of the participants when they are engaged in the game. Dialogue rules indicate the permitted communicative acts that participating agents can perform. In their formulation, the authors use sanctions penalizing agents that will not follow the expected dialogical behavior as described in the dialogue rules.

Maudet, Chaib-draa, and Labrie (Maudet et al., 2002) used DIAGAL to model the request for action proposed by Winograd and Flores (1986) as a composition of different basic games. These compositions which can have conditions and effects are:

Sequencing : denoted g 1 ; g 2, which means that g2 starts immediately after termination of g1 .

Conditions game g 1 is closed.

Effects termination of game g 1 involves entering g 2.

Choice : denoted g 1 | g 2, which means that participants play either g 1 or g 2 non-deterministically. This combination has no specific conditions nor consequences.

Pre-sequencing : denoted g 2 g 1, which means that g2 is opened while g1 is proposed.

Conditions game g 1 is proposed.

Effects successful termination of game g 1 involves entering game g 2.

These pre-sequencing games are used to ensure that entry conditions of a forthcoming game are actually established.

Embedding : denoted g 1 < g 2, which means that g 1 is now opened while g2 was already opened. This means that g 2 is suspended and one must return to it after the termination of g 1.

Conditions game g 1 is open.

Effects Commitments of the embedding games are considered proprietary over those of the embedding game.

Flores, Pasquier, and Chaib-draa (2004) proposed a conversational semantics for DIAGAL using social commitments. This semantics defines the meaning of messages on the basis of their use as coordinating devices advancing conversations. This semantics captures the evolution of conversations using the state of social commitments and the state of activities in which agents participate. According to the authors, a commitment could be either accepted or rejected according to whether or not agents are engaged in it. If accepted, a commitment is active, violated or fulfilled. If rejected, it is either inactive or cancelled. Commitments can move between states through four transition types: adoption, where an active commitment becomes accepted; violation and fulfillment, where an active commitment becomes violated or fulfilled, respectively; and discharge, where an accepted commitment becomes cancelled.

In this semantics, the meaning of communicative acts is defined through four levels: compositional level , conversational level , commitment state level , and joint activity level . Compositional level deals with message classification. Definitions at this level identify messages based on the type and identity of their components. Conversational level indicates the significance of messages once they are uttered. This significance is given taking into account the fact that messages as part of conversations seeking agreement to advance the state of commitments. Commitment state level refines the definitions of messages according to the shared state of the commitment being manipulated. Joint activity level refers to the meaning given to messages when they are used as part of joint activities. Definitions at this level are given in terms of the type of actions the commitments bring about, and in terms of the roles that interacting agents play in these actions.

Lebbink, Witteman and Meyer (Lebbink et al., 2004) proposed dialogue games in which coherent conversational sequences with inconsistent and biased beliefs are described at the speech act level. A belief is called "biased" when more evidence exists to believe than to disbelieve something or vice versa . In the former, the belief is said to be biased true , and in the latter, the belief is said to be biased false . A special case of a biased belief is when an agent has evidence to believe a statement but it also has an equal amount of evidence to believe the contrary. In such a situation, an agent’s belief is considered inconsistent from an epistemic perspective.

The authors present these biased and inconsistent beliefs with bilattice structures (Fitting, 1991) that are constructed from two complete lattices and A complete lattice is a structure such that is a non empty set ordered according to and for all , there is a greatest lower bound and a least upper bound of A bilattice is an algebraic structure that formalizes an intuitive space of generalized truth-values with two lattice orderings and . The intuition is that provides evidence for believing a statement and provides evidence for disbelieving a statement. A bilattice has at least four truth-values: t , f , u , and i . Truth-value t represents full evidence for believing and no evidence for disbelieving. Opposite to t is truth-value f that represents no evidence for believing but maximal evidence for disbelieving. Truth-values t and f correspond to the true and false values of classical logic. In truth-value u neither evidence for believing nor for disbelieving exists. In truth value i both maximal evidence for believing and for disbelieving exist.

In addition, the authors define a multi-valued logic in order to describe dialogue games in which agents can communicate about their cognitive states. Whereas in classical logic terms are assigned a truth value true or false , in multi-valued logic, new truth-values can be captured to represent epistemic attitudes. These truth-values can represent unknown information and inconsistent and biased information. A language of multi-valued logic is defined in order to formalize two types of sentences: atomic sentences and conditional sentences . Atomic sentences consist of a propositional formula taken from an ontology . Conditional sentences resemble the conditionals of classical logic.

In the dialogue games proposed by the authors, communicative acts are utterances used by agents to manifest parts of their cognitive states. Three communicative acts are used: questions , statements of belief and statements of ignorance . A question is a request for a belief addition, that is, an agent a asks an agent b whether it may add a sentence to its beliefs. In a statement of belief, an agent a states to an agent b that a given sentence is part of its beliefs and that b may add this to its beliefs. A belief statement can be an approval of a request for a belief addition. This request can also be denied, which is in effect a statement of ignorance, that is, an agent a states to an agent b that it is ignorant about a given sentence.

A dialogue game is formalized by, first, defining the agent’s cognitive state as a set of multi-valued theories, second, by defining the dialogue rules, and last, by defining update rules. As a motivation to participate in a dialogue game, agents have the incentive to reduce an imbalanced desire and belief state (Grice, 1975). There is an imbalance in the agents’ belief and desire state, when these agents do not believe a proposition but they do desire to believe it. In such case, it is said that the agent is interested to add the proposition to its beliefs. For example, two roles of questions are distinguished. The first role is to reduce the imbalance between an agent’s desire and belief, that is, the question is about a sentence the agent itself is interested to believe. The second role is to reduce an imbalanced desire and belief state of another agent, that is, the question is about a sentence another agent is interested to believe. Dialogue rules define which communicative acts are applicable in a dialogue game. For example, a question from an agent a to an agent b is applicable when a is interested in a sentence and this sentence is sensible , that is, it is not part of b ’s ignorance as a is aware of. In addition, the question must be fresh , that is, a is not allowed to pose a question for the same information more than once. Update rules prescribe the cognitive state of both the sending and the receiving agent after the information in a communicative act is accepted by both agents. For example, if an agent a has uttered a belief statement to an agent b , agent b believes the underlying sentence, b is aware that a believes the sentence, and a is aware that b believes the sentence. In fact, Dialogue rules and update rules describe pre and post conditions on agent’s cognitive state.

The dialogue game protocols presented in the work of Dignum, Duin-Keplicz and Verburgge (2000, 2001) are intended to enable agents to form teams and to agree on joint intentions. They present a theory for agents that are able to discuss the team formation and to adopt joint intentions and subsequently work as team members until the collective goal has been fulfilled. For both protocols, the authors assume that one agent, an initiator or proponent , seeks to persuade others ( opponents ) to join a team, and that another initiator (possibly the same agent) seeks, after the team formation, to persuade team members to adopt a group belief or intention. They present structured dialogues, with an emphasis on persuasion, which can be shown to lead to the required team formation and joint intentions. The dialogue games are formally specified using modal logics and speech acts. The team-formation dialogue is modeled as information-seeking dialogue followed by a persuasion, while the joint-intentions-formation dialogue is modeled as a persuasion dialogue, which may include embedded negotiation dialogues. For the persuasion dialogue, the authors adapt the rigorous persuasion dialogue game of Walton and Krabbe (1995).

The protocol for joint intention formation dialogues includes seven locutions: statement , question , challenge , challenge with statement , question-with-statement and final remarks . The statements associated with challenges and questions may be concessions made by the speaker. The protocol for team formation dialogues may also use the same set of locutions. The authors assume the participating agents have a belief-desire-intention architecture (BDI) and vest the locutions with a private axiomatic semantics, the locutions being defined in terms of their impacts on agent mental states.

For team formation by dialogue, the authors postulate that agent architecture should contain a number of specific modules. The heart of the system is the reasoning module. When realizing the consecutive stages leading ultimately to team formation, interaction with the planning , communication and social reasoning modules is necessary. All these modules contain a number of specific reasoning rules. Each rule refers to a specific aspect of the reasoning process.

The first task of the initiator in the team formation protocol is to form a partial plan for the achievement of the overall goal. For this reason, it determines which agents might be most suited to form the team. In order to determine this match, the initiator tries to find out the properties of the agents, being interested in three aspects, namely their abilities , opportunities , and their willingness . The initiator has to form beliefs about these aspects of the individual agents. Thus, it may first investigate the willingness of particular agents, and on this basis ask the interested ones about their abilities and opportunities. The questions in this stage form part of an information seeking dialogue game. To establish a collective intention within the team, agents start a persuasion dialogue consisting of three main stages: information exchange, rigorous persuasion, and completion.

In this section, we compare and discuss the dialogue game frameworks presented in this chapter using the following factors: the formal language used for the specification, the dialogue types supported by the framework, the architecture of the participating agents, the purpose of the proposal, the mechanism, if any, used in the framework for the decision making process, and the computational issues. Table 3.1summarizes this comparison.

Different logics are used to specify the dialogue game frameworks presented in this chapter. Modal and multi-valued logics are used to formalize and reason about agents’ mental states. Nonmonotonic logic is used to formalize arguments that agents use to support their communicative acts. Other formal languages are also used to describe some elements such as the dialogue frames (Reed, 1998) and the contextualization game (Maudet and Chaib-draa, 2002). Lebbink et al. use a specific algebraic language to represent inconsistent information that is a part of the agent’s cognitive state.

All the dialogue game proposals, with the exception of Maudet et al.’s framework and Lebbink et al.s’ dialogue games, are based on the dialogue typology proposed by Walton and Krabbe. Reeds’ dialogue frames and the layer model of McBurney and Parsons are defined to represent all the types according to this dialogue typology and the combination of these different types. Hence, these frameworks are more general than the other frameworks defined for specific dialogues. Maudet et al.’s DIAGAL is specified by four basic games: Request game, Offer game, Inform game, and Ask game. Although the combination of these games can describe different dialogue types, the authors do not specify these types. Lebbink et al.’s proposal does not use any philosophical foundation, but focuses on inconsistent dialogues without taking into account the goal of the dialogue.

Dastani et al. and McBurney and Parsons do not make assumptions concerning the internal architecture of agents. Consequently, it is not clear how these frameworks can be implemented and how agents establish the link between their mental states and their locutions during a dialogue. Reed does not specify a specific architecture, but only supposes that agents have epistemic issues, whose referent could equally be modeled by a BDI architecture or a propositional logic. On the other hand, Maudet and his colleagues propose an architecture in which each agent has a private agenda containing its commitments. Using this agenda, agents can follow the action effects on each move, i.e. check the creation, cancellation, fulfillment ... of commitments. In addition, agents can use a shared action board representing the actions which were played during the dialogue. This board is represented as a history of the performed actions. In Lebbink et al.’s framework, agents have a cognitive state consisting of a set of mental constructs: beliefs, desires and ignorance. These constructs can be private or manifested (communicated explicitly). Dignum and his colleagues propose an architecture in which agents have beliefs, intentions and goals. In addition, agents can reason about these states and about other agents.

Reed’s dialogue frames do not specify the rules that govern the performance of communicative acts but only an abstract form of these acts. Consequently, the formalism is descriptive and not generative. The purpose of Reed’s work is to analyze conversation, but cannot be used to help agents to take part in these conversations. Although the dialogue games proposed by Maudet et al. and by Lebbink et al. specify dialogue rules and update rules, these two formalisms do not specify how agents can generate dialogues. The reason is that they do not specify the decision making process enabling agents to decide, at a given moment, about the next communicative act to be performed. Dastani et al. propose a methodology to construct protocols by specifying some combination rules. However, because this methodology does not provide any decision making process, it does not specify how agents can use these protocols in an autonomy way. On the other hand, McBurney and Parsons’s model and Dignum et al.s’ dialogue games are defined for generating dialogues. The layer model is equipped with an argumentation theory that provides a decision making process and agents can reason about their locutions using dialogue layer rules. In the team formation dialogues, agents can also reason about their locutions. However, this reasoning mechanism is not clearly specified.

With the exception of the proposals of MacBurney and Parsons, and Maudet and his colleagues, there is no computational analysis in the other proposals. However, McBurney and Parsons propose only an operational semantics in order to achieve the objective of automating dialogues; they do not provide any implementation or complexity analysis. Operational semantics indicates how the states of a system change as a result of execution of the commands in a programming language. In dialogue games, the commands are the moves, and the states are the dialogue states which can be described by the different commitments. On the other hand, Maudet et al. provide a dialogue game simulator, but the computational complexity of the implemented dialogue games is not studied.

As a conclusion, the dialogue game frameworks discussed in this chapter have two main limitations. The first limitation is related to the link between private mental states, public or manifested states and the decision making process. This link is extremely important to generate dialogues and enable agents to participate flexibly in conversations. The second limitation is related to the computational issues. For example, complexity, termination and correctness of dialogue game algorithms should be analyzed when developing these algorithms. In addition, verifying whether agents respect or not these dialogue games protocols is another relevant issue to be addressed.

[2] The notion of the dialectical system will be discussed in Chapter 4, Section 4.4.2.

© Jamal Bentahar, 2005