AH, Dialogues and the Common Ground

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Speech Acts, Dialogues and the Common Ground

Michel PaquetteCollege de Maisonneuve

Email: [email protected]

Abstract

The formal semantics of speech acts, even in the clas-sical framework of illocutionary logic, requires consid-erations that go beyond individual speech activity andbeyond the interpretation of individual sentences. Weshow how the formal semantics of speech acts can beextended to take into account the social effects and in-

teractive aspects ofillocutionary activity. To illustrateour approach, we focus on the semantics of assertionsand descriptive discourse, contrasting the individual as-pect of speakers meaning and the epistemic effects ofassertion making. The approach presented in this pa-per generalizes to all other types of illocutionary acts,adding specific content to theconversational recordthatregisters the common ground of speakers and hearers asa dialogue unfolds.

Introduction

We presuppose the speech act theory of Searle and Van-derveken (FIL) found in (Searle and Vanderveken 1985). Inthis framework, the basic units of human communication are

speech acts and basic illocutionary acts of the form F(P)consist of an illocutionary force Fand a propositional con-tent P. Illocutionary logic provides a logico-philosophicalanalysis of each illocutionary force in terms of six compo-nents: an illocutionary point, the mode of achievement of anillocutionary point, propositional content, preparatory andsincerity conditions, and degree of strength. The formal se-mantics of elementary illocutionary acts is uniquely deter-mined by these components and by the propositional con-tent. It provides an analysis of the logical forms of speechacts. Illocutionary acts have propositional contents withoutbeing themselves reducible to sentences and propositions.In this framework, there are three distinct and irreduciblesemantic values:truth,successand satisfaction.

Vandervekens approach of pragmatic phenomena is notreductionist. To the contrary, Vanderveken has extendedthe same strategy to construct a theory of discourse (Van-derveken 2001) that explains the types of possible discur-sive goals that speakers can attempt to achieve by way ofconversing. The framework of this more recent work shows

Copyright c 2012, Association for the Advancement of ArtificialIntelligence (www.aaai.org). All rights reserved.

how the conversation types can be defined in terms of pre-viously defined concepts of illocutionary logic. As Searleand others have pointed out, it turns out that the basic usesof language are few in number. In fact they can be sepa-rated according to four possible directions of fit betweenwords and the world. Accordingly, there are only four ba-sic types of discourses. These are descriptive discourses,deliberative discourses, declarative discourses and expres-sivediscourses. Other discourse types can be generated withBoolean operations on the components of simpler discoursetypes.1

In previous papers, (Paquette 2002), (Paquette 2010), wehave contributed to this research program by extending itsscope in the direction of strategic interaction. Adding someassumptions and additional requirements to Vandervekenstheory, we formulated a representation of the speech act ac-count of purposeful communication in game theoretical se-mantics. We have described the basic components of the re-sulting logic of conversation. We have defined some of thekey notions in terms of Stalnakers and Bonannos epistemicmodels for games. More importantly, we have proposed that

a dialogue is successful in the sense of the illocutionary ac-count of dialogues if and only if (1) there is a solution to thecorresponding dialogue game in the form of a Nash equilib-rium (2) the participating agents are efficiency maximizersand (3) the participating agents are rational and cooperativewith respect to the internal goal of the dialogue. In our view,this equivalence paves the way that brings us from speechacts to the logic of games.

Speech acts and dialogical interaction

The approach taken in the present paper allows us to answerthose critics of speech act theory who claim that this frame-work is irrevocably individual bound rather than social andsentential rather than dialogical.2 We argue that these criti-cisms are no longer relevant. Indeed, we claim that that thespeech act approach can meet the challenge of the interac-tive turnwhich is now dominant in the study of dialogue and

1 Vanderveken, (Vanderveken 2001), III.3.2 See, for instance, Asher and Lascarides (Asher and Lascarides

2003), p.74.

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discourse.3 In fact, as Baltag pointed out in (Baltag 2001),we must come to realize that the logic of communicationmust extend beyond individualspeech activity, and that suchis required by the logic of games and the logic of public an-nouncements.

In order to document the shared common ground in a con-versational context, we make use of the notion of a conversa-tional record.4 The conversational record is a public evolv-

ing representation of the state of a conversation. The pos-tulated elements of the conversational record complete theclauses required to define the success and satisfaction con-ditions of coherent and rational discourse.

Assertion: two views

We start by stating the received view. A proposition can beviewed as a way of dividing a set of possible worlds into twoparts: the ones that are ruled out by the truth of the propo-sition and the ones that are not. When an assertion is madeby the speaker the proposition asserted Psplits the set ofpossible worlds in two and the speaker asserts that the actualworld of the context of his assertion belongs to the subset ofthe set of possible worlds in which P is true. The speaker

represents a state of affairs as being actual.5 Under this anal-ysis, assertions are pretty much individual activities. Thisgoes hand in hand with the fact that the distinction betweenan illocutionary act and its perlocutionary effects is aimedat putting the speaker in command of his own sayings. Asis welI-known, perlocutionary effects are cancelable. So wecan say Dont be offended but it seems to me that what youjust said is completely silly. In speech act theory, the ex-istence of perlocutionary effects is acknowledged but theseeffects are not relevant to the conditions of success of asser-tions. A speaker can be successful in making an assertionindependently of any effect that his assertion may have onothers or on the outside world. The only requirement is thathe believes the propositional content, or, in other words, he

must have reasons for thinking that the propositional contentis true. Assertions are used to represent the world in a certainway, and the possibility of making a successful assertion isindependent of any side effects that the assertion may have.

In contradistinction with this semantics of assertions ad-vocated by speech act theory, there is an entirely differentapproach that has been flourishing in the last decades. Ac-cording to the interactive and dialogical picture of dialoguesand discourses, when people make assertions they are at-tempting to make other people believe what they say. In asocial setting, an assertion can be construed as a kind of up-date operator with respect to a given conversational record.The idea that the point of a meaningful assertion is the cre-ation of a belief goes back at least to Grice (Grice 1957).According to R. Thomason, this idea can be found in mostof the work in which planning is applied to discourse. Theview is also a basic tenet in Dynamic Epistemic Logic (DEL)

3 So it turns out that we,speech activists, can agree that one isindeed a lonely number. See J. van Benthem, (van Benthem 2002)and (van Benthem 2010).

4 We owe this notion to R. Thomason, (Thomason 1992).5 See Vanderveken, (Vanderveken 1990 91), p.117.

and Public Announcement Logic (PAL). These approacheshave shown that it is fruitful to think of speakers and hear-ers as interacting systems of beliefs. From the perspectiveof rational interaction, assertions can be viewed as attemptsto induce beliefs in others. Moreover, from a dynamic per-spective there is a close connection between assertion andthe update operator. This has been developed in DL, DELand PAL. One goal of asserting a proposition is to update

the conversational record with that proposition.

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We seem to be confronted with a fundamental incompat-ibility between the dynamical account of assertions and thesemantics of assertions of Searle and Vanderveken. In Searleand Vanderveken assertions have the words-to-world di-rection of fit since the point of assertions is to adjust thewords to correspond to the facts of the world. But underthe dynamical view mentioned above, the anticipated ef-fect of interacting with other belief systems and changingother peoples belief sets is the true purpose of making as-sertions. Assertions no longer have only the words to worlddirection of fit, they are also genuine attempts to change theworld. It may well be that the simplest countermeasure tothis problem is to acknowledge two different kinds of se-

mantic clauses, one semantic clause for the illocutionary actof assertion interpreted in isolation, another semantic kind ofsemantic clause for the interpretation of assertions in con-text. Here, we limit ourselves to underlining the difficultyand leave it as an open issue. We come to realize that theextension of speech act theory to dialogical interaction callsinto question the usual sharp separation between illocution-ary acts and their perlocutionary effects. Even the semanticsof assertions needs to be revisited and requires significantadjustments in a dynamic setting.

The logic of games

There are two different ways to connect games and logic.The first way is to use some tools from game theory to inter-pret logic. This approach goes back at least to C. S. Peirce 7

but is better known is association with a form of model-theoretic technique whereby logical formulas, or more gen-erally structures are interpreted as games (e.g. Ehrenfeucht-Frass, Hintikkas IF-logics). The key idea is that the logicgames approach is concerned with the study of games thatare played with logic. Game-theoretic semantics, for in-stance, belongs to this lively tradition and this is what isfalls under the concept of logic games. The other categoryof work is the study of gamesusinglogics, usually as a com-bination of modal, epistemic, temporal and dynamic logics.This approach is what is referred to as game logics. Thissecond category of work, entirely different from the first,has been expanding rapidly in the last two decades. It is con-cerned with the development of logics that are appropriate toexpress game-theoretic notions and reformulate a large part

6Alternatively, in van Benthems logical dynamics, updating islike relativization to a model.

7Peirce observed that thinking is a dialogue with signs as itsmatter much in the way that the game of chess has the chessmenfor its matter. Quoted from Peirce, 1966, MS 298, p.6 quoted byPietarinen (Pietarinen 2003).

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of game theory in terms of modal logics. The survey paperby Wiebe van der Hoek and Marc Pauly (van der Hoek andPauly 2006) is a good introduction to the field. In the presentwork, we refer only to logics that belong to the second cate-gory, game logics, or, perhaps less confusingly, the logic ofgames.

New insights in dialogue game theory

In our own earlier attempt to bridge the gap between thespeech act theory of dialogues propounded in (Vanderveken2001), we used as the target formal framework the epistemiclogic models proposed by Stalnaker in (Stalnaker 1997) and(Stalnaker 1999). In this setting, we were able to formulatea game-theoretic interpretation of the notion of intelligentdialogue, distinguish between cooperative and strategic as-pects of goal-oriented dialogical activity and establish byway of an informal argument that the notion of success fora dialogue is equivalent to the notion of Nash equilibrium 8.The role of efficiency and rationality in dialogical interac-tion came to be highlighted. It was shown that key conceptsof game theory could be applied to dialogical interaction.It became apparent that a formal dialogue game could be

defined as a (partial) description of a sequence of interde-pendent Bayesian decision problems. Some critics seem tohave understood our earlier efforts (Paquette 2002) and (Pa-quette 2010) as merely providing an interpretation of game-theoretical concepts in terms of some vague program forbuilding a pragmatics of dialogue. Our complaint is that ourcritics seem to have entirely missed the point that there re-ally exists a detailed logical account of intelligent dialogue,namely Vanderveken (Vanderveken 2001), that we were try-ing to extend and represent within the framework of an epis-temic logic interpretation of game-theoretic concepts. Thiscrucial fact is what makes the enterprise worthwhile, at oncedifficult and promising.

There were significant shortcomings in our earlier at-

tempts that needed to be addressed. First, Stalnakers epis-temic models for games are formulated for games in normal(strategic) form. When a game is presented in this form, thepayoff matrix is entirely laid out and the sequential natureof the interaction is obliterated. When a game is presentedin extensive form, the sequential structure of the moves isrevealed. Following Fudenberg and Tirole9, we believe thatgame theorists use the concept of game in extensive form tomodel dynamic situations in which players make sequentialchoice. On the other hand, it is sometimes said that thereis no important theoretical difference between games in nor-mal form and games in extensive forms. Indeed, it is possibleto reformulate a game in normal form into a game in exten-sive form.10 So, one could argue that the dynamical appear-

ance of a game tree is merely a feature of the presentation of8A comparable account can be found in Parikh (Parikh 2001)

and (Parikh 2010). One significant difference is that Parikhs ap-proach is based on situation semantics.

9(Fudenberg and Tirole 1998), p. 67.10Every extensive-form game has an equivalent normal-form

game. But the transformation to normal form may resultin an expo-nential blowup in the size of the representation, making it compu-tationally impractical. ((Shoham and Leyton-Brown 2009), p. 35).

the game and that the difference is merely notational. This,however, definitely ceases to be true when a game in exten-sive form is interpreted in a multi-modal logic incorporat-ing temporal logic and dynamic operations. Under such ananalysis, the sequential nature of a game becomes apparentwhereas it is obliterated in the normal form where the gameis characterized by its payoff matrix. As Brandenburger haspointed out, with the epistemic interpretation of games, a

game can no longer be identified with its payoff matrix. Theepistemic program in game theory aims to provide a method-ical construction of game theory from its most basic ingre-dients. These are the concepts of rationality and irrational-ity, belief and knowledge about such matters, iterated beliefsabout beliefs, and iterated knowledge about knowledge. Theformal methods of this program rely on epistemic and multi-modal logics. These new approaches have convinced us thatthere was some gain to be made by building new bridgesfrom the speech act theory of dialogues towards the newerlogics of games.

A further reason to go beyond the basic epistemic logicfor games is to seek refinements or other solution conceptsthan Nash equilibrium to represent the notion of success in

a dialogue game. A refinement of Nash equilibrium is avail-able in the modal logic interpretation of games proposed byHarrenstein et al. in (Harrenstein et al. 2004). It correspondsto the notion of a Nash equilibrium being subgame perfect.This raises the question as to whether this notion is relevantin the analysis of dialogical interaction and if new facts canbe systematized in the new framework.

The notion of a subgame can be viewed as the cuttingoff of some initial segment from a game tree which yieldsanother game in extensive form. This yields the notion ofa subgame perfect Nash equilibrium which is an extensionof the backwards induction method designed for extensiveform games. The notion of a proper subgame is defined asa subset of the nodes of the game starting with an initial

node and including all its successors that preserves all in-formation sets of the game and over which a new game isdefined by the restriction of the original game elements suchas moves, payoffs, information sets, etc. A strategy profile issaid to be asubgame perfect Nash equilibriumif it is a Nashequilibrium, and for every proper subgame, the restriction ofthose strategies to the subgame is also a Nash equilibrium.This solution concept is applicable in the case of structureddialogues that contain embedded dialogues.

The third reason to go beyond the basic epistemic mod-els in our investigation has to do with keeping up with re-cent developments in the field. It has become increasinglyclear that we need to reap the benefits of recent develop-ments in dynamic logic to further our own research program

on the logic of dialogue. Indeed we need to bring our re-search closer to the kernel of new logics that have yieldedan impressive amount of knowledge linking various kinds ofmodal logics and numerous concepts of game theory, com-munication and rational interaction.

The relevance of game theory to the analysis of agentcommunication can hardly be doubted. Consider the follow-ing question, formulated by G. Bonanno in the context of alecture on the epistemic foundations of game theory : What

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strategies can be chosen by rational players who know thestructure of the game and the preferences of their opponentsand who recognize each others rationality and knowledge?It seems clear that this question has immediate resonanceand application in the analysis of rational discursive interac-tion and that it is immediately relevant to the logic analysisof rational verbal interaction. Indeed, Bonannos questionaptly describes the predicament of participants in any type

of rational verbal interaction.

Games in extensive form

We consider finite games in extensive form with perfect in-formation. In a game with perfect information, no two nodeshave the same information state. That is, whenever a playermoves, he knows the past moves of all other players and (andthe moves of chance if such a player is included), as well asis own past moves.11. As usual, a (pure) strategy for a gameconsists of a complete plan for a player i that specifies howto play that game. Strategy profiles, denoted by , combinestrategies, one for each player. A strategy profile determinesfor each node a unique outcome, though not necessarily foreach node the same one.

In order to determine whether a strategy is a best responsefor a player, the player needs to know the strategies that theother players adopt so best response for a player is relativeto a strategy profile. Assuming that play commences at theroot node, a strategy profile is said to contain a best responsefor playerik, ifik cannot increase his payoff by playing an-other strategy available to him when the other players stickto their strategies as specified in . A strategy profile is aNash-equilibrium if none of the players can increase his pay-off by unilaterally playing another strategy. Equivalently, aNash equilibrium could be characterized as a strategy profilewhich contains a best response strategy for each player. 12

Conversational record

The conversational record is a public evolving representa-tion of the state of a conversation. In order to account forthe common ground that is being structured as a conversa-tion unfolds, it is necessary to associate with each step ina dialogue game an updated conversational record. An ex-tensive game can be understood as a process in which thehistory of the game is taken into account. From this perspec-tive, the model must take into account the individual actionsof the players and stepwise progression through successivestates are part of the definition of the game. Under such afine grained analysis, we look at more than the set of achiev-able outcomes which is usually the only aspect that mattersin classical game theory. The conversational record registersthe successive moves of the participants and the informa-tion that these moves make public. It takes the form of astructured set containing shared knowledge at a given mo-ment in a dialogue. The moves in a dialogue are taken tobe speech acts that can be simple or complex. Accordingly,the basic layer of the conversational record will contain the

11The definition is taken from (Meyerson 1991), p.45.12A formal treatment of the modal logic of games in extensive

forms canbe expoundedalong thelines of (Harrenstein et al.2002).

ordered list of speech acts that have been performed up toa given state. In the abstract model, it is convenient to sup-pose that the participants in a conversation satisfy a condi-tion known asperfect recall. This is for the sake of simplic-ity. Of course, we know that real people often need to bereminded of what was said at an earlier stage of a conver-sation. From this simplifying assumption arises no concep-tual difficulty. In addition to the list of previously performed

speech acts, the conversation record must contain a set ofpropositions encoding the common knowledge of the partic-ipants to some of depth of iteration. These propositions aresuch that player a knows that player b knows that player aknows etc. This scheme is the definition of common knowl-edge. This component is required in order that the conversa-tional record can be the repository from which the epistemicstates of the players can be construed. A third componentof the conversational record comprises a fair amount of se-mantic information that can be derived from the semanticsof speech acts. This is the semantic information that the par-ticipants must possess in order to understand the type of dis-course to which they are participating. Here, the semanticclauses that delineate the conditions of success for a type of

discourse play a crucial role in explaining the coordinationof the participants to a given dialogue. Following the theoryset forth in (Vanderveken 2001), our analysis is restricted tothe types of dialogue that possess an internal discursive goal,that is, dialogues that possess reachable endings that can beattained merely by making the appropriate discursive acts.This can only be possible if a shared minimal understand-ing of the discursive goals and subgoals is shared amongthe participants. Finally, the theory of success and satisfac-tion for rational dialogues demands that the most generalrequirements of coordinated behavior be satisfied. The firstof these requirements consists in the common belief in ra-tionality by which participants in a conversation expect ofeach other that they will attempt to achieve their goals and

take the appropriate means to achieve their goals. The sec-ond requirement is that there should be common knowledgeamong the participants of the prevailing norms of efficiencythat define cooperation; it must also be common knowledgethat the participants are committed to these norms.

Conclusion

The analysis of rational interaction using game theory andmodal logics is currently pursued in many different re-search communities and, accordingly, in many different for-mal frameworks. Our aim was to show how the classical the-ory of speech acts could be extended to make a contributionin this research program. Of course, the idea that the movesof players in a game yields a model for interaction in dis-course is not new. Our aim was to show in what ways theclassical framework of speech act theory might be devel-oped and find its place among the promising new treatmentsof dialogical interaction.

Acknowledgment

The research for this paper was supported by the governmentof Quebec through its funding agency FQRSC; Grant num-

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ber 2011-CH-137532. The views, findings, conclusions orrecommendations expressed in this material are those of theauthor and do not necessarily reflect the views of the fundingagency.

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AH, Dialogues and the Common Ground