Implicit Communication in a Joint Action

Ross A. KnepperDepartment of Computer

ScienceCornell UniversityIthaca, NY, USA

rak@cs.cornell.edu

Christoforos I.Mavrogiannis

Sibley School of Mechanicaland Aerospace Engineering

Cornell UniversityIthaca, NY, USA

cm694@cornell.eduJulia Proft

Department of ComputerScience

Cornell UniversityIthaca, NY, USA

jproft@cs.cornell.edu

Claire LiangDepartment of Computer

ScienceCornell UniversityIthaca, NY, USA

cyl48@cornell.edu

ABSTRACTRobots must be cognizant of how their actions will be in-terpreted in context. Actions performed in the context ofa joint activity comprise two aspects: functional and com-municative. The functional component achieves the goalof the action, whereas its communicative component, whenpresent, expresses some information to the actor’s partnersin the joint activity. The interpretation of such communi-cation requires leveraging information that is public to allparticipants, known as common ground. Much of humancommunication is performed through this implicit mecha-nism, and humans cannot help but infer some meaning –whether or not it was intended by the actor – from mostactions. We present a framework for robots to utilize thiscommunicative channel on top of normal functional actionsto work more effectively with human partners. We considerthe role of the actor and the observer, both individually andjointly, in implicit communication, as well as the effects oftiming. We also show how the framework maps onto vari-ous modes of action, including natural language and motion.We consider these modes of action in various human-robotinteraction domains, including social navigation and collab-orative assembly.

1. INTRODUCTIONAn important domain for human-robot interaction involves

collaboration on a joint activity, such as collaborative fur-niture assembly (Figure 1). A great deal of attention hasbeen paid to what actions to perform [1, 16, 17, 27] andwhen to perform them [9, 13, 35] in order to complete acooperative task. Often underappreciated, however, is theimplicit communication that occurs as a result of an ac-

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DOI: http://dx.doi.org/10.1145/2909824.3020226

Figure 1: Robots that collaborate with humans,such as in an assembly task [22], must consider thecorrectness of both the functional and communica-tive aspects of their actions.

tion situated in context. We call behaviors that implicitlycommunicate information communicative actions. Humansare adept at drawing inference from observed actions andcommon ground – in fact, they instinctively perform thisinference, thus reading additional meaning about the in-tent of an action [8], and many people treat informationgleaned implicitly through inference as though it had beenstated outright. We argue that to be successful in a jointactivity with humans, robots must be cognizant of implicitcommunication because humans will inevitably use it andexpect robots to comprehend its meaning. We further arguethat if a robot fails to attend to a human’s interpretation ofits own actions through the implicit communication mecha-nism, then people will perceive the robot’s purely functionalactions as sending random implicit signals, sowing confusion.

Implicit communication is identified by various terms indiffering contexts. In robot motion, including reaching [10]and social navigation [29], it has been termed legibility. Inlinguistics, it has been termed conversational implicature [15],for which we provide a primer in Sec. 5.1.1. In natural lan-guage generation for HRI, it has been called inverse seman-

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tics [22]. In each of these cases, the meaning is extractedby leveraging common ground. The goal of this paper is tounify these separate works by explicating a common math-ematical framework that underlies all of them.

Extending an earlier workshop paper [20], we contribute:

• a unifying mathematical framework describing how andwhy people implicitly communicate information on topof functional behaviors,• formal expressions for encoding and decoding commu-

nicative actions, and• collected example applications to illustrate the theory.

2. WHY IMPLICITLY COMMUNICATE?Humans are able to express a multitude of ideas “in code”,

by means other than explicit natural language statements.Motivations for implicit communication include efficiency,tact, group cohesion, and social bonding. In this section,we give examples of several categories of implicit communi-cation. Message categories include expressing intent, coor-dinating plans, and conveying information. Broadly, thesecategories all fulfill the role of setting expectations, and weconsider each separately.

Social navigation is among the most superficial forms ofinteraction, yet it is rife with implicit communication. Insocial navigation, the objective is to avoid collision with co-inhabitants of the space and reach one’s destination. Com-bined, these objectives comprise the navigator’s intent. Col-lision avoidance without intent expression is only the barestdefinition of correct navigation – it alone would not be judgedas competent behavior by fellow pedestrians [31]. Compe-tence demands that we convey our intended trajectory tonearby observers. We trust in return that they will conveytheir intent to us. Such intent-expressive actions minimizethe global uncertainty about future motions of the agents(humans or robots) in the scene, leading to smooth and sta-ble motion. We borrow from Barbalet [2] the definition oftrust as “the confidence that another’s actions will corre-spond with one’s expectations.” In the absence of socialtrust, people begin to behave defensively, and the efficiencyof motion drops globally in response.

Coordination among team-mates engaged in a joint activ-ity requires setting expectations of future actions. Considerthe simple example of Steve and Cathy assembling furni-ture together, in which a number of screws must be insertedand tightened. Steve might pick up the screwdriver, whichachieves the functional objective of readying Steve to tightenscrews. In context, the action also implies that Cathy shouldgather screws for insertion in order to help. Since Steveis cooperative, Cathy knows that once she begins to insertscrews, Steve will fulfill his implicit promise to tighten them.

Beyond forecasting actions, team-mates might also try toconvey information about their capabilities. Human inter-actional expectations are broadly governed by a common setof human functional and social capabilities, whereas humansare largely uninformed about a robot’s true capabilities.Therefore, robots will likely find themselves being judgedaccording to the wrong standards. Although humans showpatience for robots that fail under the right conditions, arobot that seldom works as expected will likely not remainin use, even if the failure is one of expectations rather thancapabilities. Properly setting expectations allows humanteam-mates to avoid being disappointed by robots [5, 23,25].

3. FRAMEWORKIn this section, we describe a framework for implicit com-

munication, modeled as a single-shot act.

3.1 DefinitionsIn coordinated activities, Clark [6] distinguishes among

several related concepts. A joint activity engages a groupof two or more agents in acting together toward a commongoal. Examples include a marriage ceremony, a classroomlecture, and a football game. Within the context of a jointactivity, participants perform joint actions, which continu-ously unfold over some period of time. A specialization isthe joint act, which is a one-shot joint action. For example,in the joint activity of playing golf, yelling “fore!” is a jointact by which the speaker warns any listeners of a waywardflying ball (their avoidance response, in contrast, is an indi-vidual act, performed without consideration of how it willaffect the group). The fact of an act being joint or individ-ual is purely a matter of the mental state of the involvedagent(s).

Participation in a joint action may be asymmetric – forexample, speech is a joint action involving a speaker andlistener. Note that the listener actively participates by com-prehending and back-channeling (nodding, saying “uh-huh”,etc.). Knowledge comprises information believed by an agentto be true and is collected into a set of facts, each withassociated confidence. Compulsory asymmetry occurs in ajoint act or action when one individual, the actor, sharesknowledge with one or more observers. Thus, an importantaspect of the joint action is to communicate information.Frequently, an actor embeds information implicitly in anotherwise purely functional action as part of the joint activ-ity to perform implicit communication.

Any communicative action will be perceived by an ob-server with a certain level of surprisal, which is an encodingof how probable the observer believes the action to be giventhe context. As Hohwy [19] states, surprisal is a decliningfunction of probability: the higher an observer’s surprisal,the more improbable the observer believes the action to bein the given context; the lower an observer’s surprisal, themore probable the observer believes the action to be in thegiven context. Common-sense knowledge and a shared un-derstanding of the context allows an actor to gauge howsurprising her action will be to an observer, which in turnshapes her choice of action depending on the informationshe would like to convey. In the remainder of this sec-tion, we show that greater surprisal corresponds with a morestrongly-conveyed message (i.e. the action is more meaning-ful).

3.2 FoundationsThe interplay of two sets is at the core of the framework.A comprises all possible actions, whereasM is composed ofall possible facts about the world.

In the course of a joint activity, an agent performs a se-ries of actions (including single-shot acts) a1, a2, . . . , an ∈ A.Each action accomplishes both functional and communica-tive goals to varying degrees. Let Af ⊆ A be the set of(possibly many) different ways of accomplishing the func-tional goal of the action. Thus, Af can be thought of as asubgoal of the shared goal of the joint activity.

An agent Q performs actions in a context MQ comprisinga set of facts m1,m2, · · · ∈MQ ⊂M that capture informa-tion about the individuals’ knowledge. Only by leveragingthis context can implicit communication occur. MQ ex-

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presses Q’s beliefs about the world, including the state his-tory of all agents in the joint activity, the observable scene,properties of objects within it, and common-sense knowl-edge. An individual fact m ∈ MQ can have an associatedconfidence, thus allowing facts in MQ to be added, removed,or changed following the observation of an action.MQ is divided into several components. Knowledge that

all participants in an interaction know they all share is publicknowledge, Mpub, also called common ground. Other knowl-edge is not known to be public; agent Q’s private knowledgeis denoted MQpriv. Q may be aware that a subset of the other

agents know fact m ∈ MQpriv. It is even possible that everyagent in a joint activity privately knows m. In both cases,m /∈ Mpub unless all agents are all aware that m is sharedby all. Q’s total knowledge MQ is equal to Mpub ∪MQpriv.

Finally, the distribution P(a|M) describes the likelihoodthat a specific agent may next perform action a in the spe-cific context M . Even if we restrict the scope of a to actionsthat accomplish a particular goal, there may be a set of pos-sible actions (Af ⊆ A) to choose among. Some of theseactions will be preferred over others for reasons of efficiency,simplicity, or custom.

Posit that the following common understandings are agreedupon by all participants in the joint activity:

• the set of alternative actions Af that would accomplisha functional goal• the common ground context model Mpub

• the action distribution P(a|M) (for plausible M ⊂M)

3.3 Implicit Communication CriteriaThe goal of agent Q is to perform an action a ∈ Af that

satisfies functional goals while also communicating fact m ∈MQpriv. However, it is not always possible to communicatean arbitrary fact m implicitly, nor is it always possible tocommunicate implicitly via an action a.

The key idea is for the actor Q and observer R to lever-age the common understandings in order to achieve implicitcommunication. Q selects an action that is surprising toR, i.e. perceived by R as improbable in the given context.However, R does not treat the improbable a as a fluke –rather, it triggers her to seek an explanation in the form ofa previously-unknown fact m that resolves the surprise. ForR to correctly interpret Q’s intended meaning, we proposethat action a and fact m must meet four implicit communi-cation criteria:

1. ∃a, a′ ∈ Af : a 6= a′

2. P(a|Mpub) < P(a′|Mpub)− ε3. P(a|Mpub) < P(a|m,Mpub)− ε4. ∀m ∈M\Mpub∪{m} : P(m|a,Mpub) < P(m|a,Mpub)−ε

The ε term incorporates variation caused by personal pref-erence and noise. The strength of a given implicit commu-nication is measured as the largest possible ε satisfying thecriteria above. Criteria 1–2 govern the actor’s generation ofimplicit communication, whereas criteria 3–4 govern the ob-server’s ability to correctly interpret the intended meaning.We speak of the fact m as the meaning of the action becauseit explains Q’s choice of action. We next provide additionalinsight into each of the criteria.

Criterion 1 requires that there must be at least two fea-sible, distinct actions that accomplish the functional goal,but preferably there are many more. An example of Afthat violates this criterion is placing a telephone call. Ne-glecting timing and caller ID, there is only one way to make

somebody’s telephone ring, leaving no room for a surprisingchoice of action.

Criterion 2 triggers the observer to search for an explana-tion of why the actor chose action a over the more obviouschoice, a′. This criterion fails in situations where there doesnot exist an action a that is a priori substantially less prob-able than others. An example situation that violates it isone’s first time visiting a clown convention, where normally-improbable actions are expected and hence unsurprising.

Criterion 3 requires that the fact m will be easy for theobserver to verify as an explanation of a. That is, a is unsur-prising when m is known. A well-known historical violationof this criterion was John Hinckley, Jr.’s attempted assas-sination of President Ronald Reagan in order to gain thefavor of actress Jodie Foster – it is unclear how shooting thepresident is intended to convey infatuation.

Criterion 4 states that no other inferred meaning m isequally or more likely than the intended explanation m.There are many example violations of this criterion in theform of hand gestures that take different meanings acrosscultures and geographies. One case in point is a gesture thatvariously signifies a Satanic association, infidelity, and a col-lege football team in Texas. All three forms have famouslybeen used by politicians. Only by understanding each indi-vidual actor’s Mpub at the time he made the gesture can wedisambiguate among the three meanings.

3.4 Understanding and GenerationSuppose that an agent Q hopes to convey some informa-

tion, m ∈ MQpriv, to agent R without resorting to disclosingit explicitly. Q selects an action a consistent with the im-plicit communication criteria, and R determines a to be animprobable action given what he knows. R, believing Qto be rational, hypothesizes that there must be some un-known factor m that explains seeing Q perform a. R thussearches over a set of plausible facts M and chooses m to bethe fact with the highest posterior probability given a andMpub. Maximizing this probability minimizes the surprisalthat resulted from Q performing a, which in turn causes ato become increasingly stronger evidence for R’s hypothe-sis [19]. Hence, upon seeing a, R proceeds to infer

m← argmaxm∈M

P(m|a,Mpub), (1)

and thus R concludes that m ∈ MQpriv, i.e. Q believes m tobe true. Using Bayes’ rule, we can re-express (1) as

m←argmaxm∈M

P(a|m,Mpub)P(m|Mpub)

P(a|Mpub)

=argmaxm∈M

P(a|m,Mpub)P(m|Mpub).

Note that the prior P(m|Mpub) serves to prevent “conspir-acy theories” that would otherwise result when noise getsmistakenly interpreted as signal. That is, the fact beingcommunicated must have a reasonably likely prior proba-bility. For example, if Bob looks up at the night sky andsees a star twinkling, he is unlikely to attribute it to a UFO,given that the prior probability of discovering intelligent ex-traterrestrial life is small and that there is a more plausibleexplanation rooted in turbulence of the atmosphere.

Next, we turn to the generation problem. The structure ofthe generation problem is identical to understanding, exceptthat we now search over actions instead of facts,

a← argmaxa∈Af

P(m|a,Mpub). (2)

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Predictable

Legible

a∈Af

P(a|Mpub)

aa'

{

{(a) A likely action such as a′ is termed predictable, whereaswe say that an unlikely action a is legible. See Section 5.2.1for a full discussion of predictability and legibility. Sincea is rarely observed in context Mpub, the observer infersthat it probably was selected specifically to send a mes-sage.

a∈Af

P(a|m,Mpub)

P(a|Mpub)

aa'

(b) By performing legible action a, an agent implicatesthe new fact m because knowledge of that fact changesthe shape of the distribution, causing a to become apredictable action.

Figure 2: These plots illustrate the inference mechanism described in Section 3.4 and its effect on P(a|Mpub).Among the set of actions a ∈ Af that accomplish a task, each can be assigned a likelihood of being observedin context. Actions with high likelihoods of P (a|Mpub) are deemed predictable, low ones legible.

Applying Bayes’ rule again, we can re-express (2) as

a←argmaxa∈Af

P(a|m,Mpub)P(m|Mpub)

P(a|Mpub)

=argmaxa∈Af

P(a|m,Mpub)

P(a|Mpub).

The resulting expression selects the action for which con-tributing m to the common ground boosts P(a|Mpub) by thegreatest amount. See Figure 2 for an illustration.

We expand on these ideas and provide examples in Sec-tion 5, but first we broaden our discussion to include implicitcommunication occurring over time and in service of jointgoals.

4. ACHIEVING JOINT GOALSIn a joint activity, rational agents interact with each other

and make decisions towards achieving joint goals. Thesegoals could range from completing a collaborative assemblytask to smoothly avoiding each other while navigating in ahallway. Relying only on implicit communication to achievejoint goals requires the establishment and reinforcement oftrust. Implicit communication leverages trust to influencethe observer’s belief and converge to a consensus that isbeneficial for the accomplishment of a joint goal. In thissection we state our model for trust and propose an index formonitoring its evolution in order to inform decision making.

4.1 TrustOrdinarily, participants in a joint activity act rationally

and cooperate to achieve shared goals [18]. This policy for-bids deception and supports the assumption that the com-mon understandings (Section 3.2) are shared by all partic-ipants. Given the great diversity of knowledge and experi-ence among people, however, this assumption is perhaps toostrong to apply universally.

In particular, during interactions with strangers, we maybe unfamiliar with one another’s judgments regarding Af ,Mpub, and P(a|Mpub). If we define trust as confidence inanother agent’s future actions [2], then it is natural for oneagent to restrict their trust of another based on the limits of

common understandings among the individuals, even whenall agents behave rationally.

Another obstacle to trust is discrepant beliefs about facts.We allow facts about the beliefs of others to enter Mpub.Thus, it can simultaneously be part of the common groundthat G believes mG and that H believes mH, even if mG

and mH conflict. G and H are then free to leverage eitherof these facts in the generation and understanding of im-plicit communications between them. Epistemic logic [11]provides tools for representing and analyzing such scenar-ios. Each conflicting fact introduces additional uncertaintyinto the communication process because the observer mustinfer which fact the actor premised the communication upon.Thus, trust degrades with the number of discrepancies amongbeliefs within a joint activity. Beyond some limit, implicitcommunication becomes impossible.

4.2 ConsensusIn a joint activity, agents take actions with functional ef-

fects (which contribute to reaching the joint goal) but alsowith communicative effects. One category of communica-tion, conveying intentions, serves to convey a preference ordesire regarding a joint strategy S for accomplishing thegoal. The joint strategy can be thought of as the sequence ofsubgoals of the joint activity, A0

f , A1f , . . . , A

nf , and is drawn

from the set of all possible strategies S.A consensus for each subgoal in the joint strategy may

unfold gradually or abruptly during the course of the jointactivity. As the agents act, the public knowledge Mpub is up-dated along with the agents’ beliefs regarding the emergingstrategy P(S|Mpub). Under the assumption of rationality,as formulated in our trust model (Section 4.1), a group ofcompetent agents taking actions bearing implicit communi-cation signals will be able to achieve consensus over the jointstrategy S. This essentially means that P(S|Mpub) (whichwe assume is shared by all agents) will converge to a dis-tribution that clearly indicates the emerging joint strategy.The entropy of this distribution is a measure of that conver-gence.

4.3 ReceptivityIn many joint activities, time and timing are critical at-

tributes of an action. Timing itself often conveys mean-

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ing, which we therefore consider as an attribute of an actiona ∈ Af . Another important aspect of timing is its rolein choosing whether (and when) to implicitly communicate.Participants in a joint activity are not equally receptive atall times to certain forms of implicit communication, partic-ularly with regard to consensus over the joint strategy.

When participants in a joint activity lack consensus abouta joint strategy, they cannot coordinate effectively to achieveshared goals. Rational agents therefore strive to reach con-sensus as early in a joint activity as possible in order tomaximize coordination efficiency. Consequently, the bulkof implicit communication for consensus should occur to-wards the beginning of the joint activity. As a joint strategyS∗ emerges and consensus is reached, the agents might fa-vor more predictable, less communicative actions, or theymight utilize the implicit communication channel for otherpurposes. More generally, the implicit consensus formationaspect of joint actions may wax and wane according to thegroup need. Consequently, there arises the need for mon-itoring (1) the state of consensus P(S|Mpub) and also (2)how receptive the group of agents is to the communicativesignals being transmitted.

We formalize this monitoring process by introducing a Re-ceptivity score, as

Receptivity = −∑S∈S

P(S|Mpub) log(P(S|Mpub)) (3)

which is the information entropy of the distribution overjoint strategies, given the common ground, P(S|Mpub). Re-call that common ground includes the action history withina joint activity. Intuitively, receptivity measures the willing-ness of individuals in a group to update their beliefs aboutthe joint strategy, inversely proportionate with clarity. SinceMpub is sequentially updated over time, receptivity reflectsthe way the agents incorporate observed communicative sig-nals into their own actions. The lower a receptivity scoregets, the closer the agents are to a consensus over a jointstrategy S∗. To avoid second-guessing a settled joint strat-egy, an observer suppresses strategy changes of a larger mag-nitude than the current receptivity level.

A consequence of a decline in receptivity is that agentscan be less expressive when it drops, since other agents willlikely ignore the inputs. In a scene with engaged competentagents, receptivity is expected to decrease rapidly, signifyinga consensus in the joint activity. This decrease will influencethe balance between the functional and communicative as-pect of actions taken, shifting the focus of decision makingtowards the functional component. Beyond some thresholddrop in receptivity, agents have become sufficiently certainabout the consensus strategy S∗ that they may even ignoretheir partners using civil inattention [21] to reinforce thepreviously agreed strategy. This behavior involves physi-cally looking away, “so as to express that [one] does notconstitute a target of special curiosity or design” [12]. Atthis point, only a major modification in the strategy willpenetrate an agent’s civil inattention.

5. CASE STUDIESIn lieu of generating new experimental results, which would

apply to a single domain and communication modality, wepresent examples of how implicit communication has beenmodeled and enforced by several communities in various col-laborative contexts and discuss how their frameworks alignwith our unifying framework for implicit communication.

5.1 Implicit Communication through NaturalLanguage

Speech acts are among the richest functional actions inwhich to embed implicit communication.

5.1.1 ImplicatureIn this section, we give a brief background on conversa-

tional implicature. We seek to draw parallels between im-plicature and other methods of implicit communication ofinterest in robotics. Implicature comes from pragmatics,the linguistics subfield that studies the usage of language incontext. Basic meaning that is expressed and understood bya speech act is achieved by entailment – that is, ideas thatlogically and unavoidably follow from the words chosen bya speaker.

With implicature, in contrast, the speaker implicates (i.e.implies or suggests) an idea without explicitly stating it. Itis a frequent phenomenon in English, first described by Grice[15]. Consider this example from Lappin and Fox [24]:

Ann: Do you sell paste?Bill: I sell rubber cement. (a)implicature: Bill does not sell paste. (m)

A test for conversational implicature in particular is whetherit is cancelable – that is, does there exist some phrase that,when appended to the sentence, cancels the meaning of theimplicature? From the above example, a phrase that cancelsBill’s implicature is “I sell rubber cement, which is what youreally need for your application.” An implicature, once can-celed, implicitly communicates nothing. The added phraseexplains the initial phrase, thus increasing P(a|Mpub) andviolating implicit communication criterion 2.

When it comes to dialog, people have varied and complexmotives for implicating meaning rather than entailing it, in-cluding politeness, sophistication, succinctness, and socialgroup cohesion. A detailed consideration of these objectivesis beyond the scope of this paper.

Grice’s cooperative principle states, “Make your conversa-tional contribution such as is required, at the stage at whichit occurs, by the accepted purpose or direction of the talkexchange in which you are engaged” [15]. Indeed, the coop-erative principle bears more than a passing similarity to thepedestrian bargain of Wolfinger [36], which entreats one tobehave competently and also to trust others to behave com-petently. These principles are both forms of the rationalactor assumption [18].

A vital component of conversational implicature is pro-vided by the four Gricean Maxims, which describe speechthat obeys the cooperative principle. The four maxims are

1. Maxim of Quantity: Make your contribution as infor-mative as is required (but not more so).

2. Maxim of Quality: Make your contribution one that istrue.

3. Maxim of Relation: Be relevant.4. Maxim of Manner: Be perspicuous. Avoid obscurity

or ambiguity; be brief and orderly.

Other maxims have also been proposed, such as “Be po-lite.” Because adherence to the cooperative principle is as-sumed, utterances can be interpreted in light of these max-ims. A speaker can therefore deliberately flout one of themaxims (an improbable action, a) in order to convey thathe is employing implicature. Returning to the previous ex-ample, Ann must apply the following inference steps to con-clude that Bill does not carry paste.

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(a) Contextual premise: it is mutual, public knowledgethat Bill has complete knowledge of the items he sells.

(b) Contextual premise: there is no contextual relationshiplinking sales of paste and rubber cement (inclusive orexclusive).

(c) Assume Bill follows the cooperative principle and max-ims.

(d) By (a), Bill can fully resolve Ann’s question, and by(c), he will.

(e) Only the propositions that Bill does or does not sellpaste can completely resolve the question.

(f) By (b), there is no way to infer from Bill’s answer theproposition that he does sell paste. The cooperativeprinciple forbids obfuscation. Thus, Bill has floutedthe maxim of relevance.

(g) Therefore, we conclude that Bill does not sell paste.

Lines (d)–(g) comprise the narrowing down and resolutionof the search for meaning in Equation (1).

Conversational implicature is absent when all the maximsare satisfied. One indicates the use of implicature by select-ing an action to deliberately flout one of the maxims – inour example, Bill flouts the maxim of Relation.

Sometimes, two maxims conflict and cannot both be sat-isfied with a single utterance, in which case flouting one orthe other maxim is forced. An example of the latter occursin the following exchange:

Mark: Where is the cat?Sue: The cat is in the hamper or under the bed. (a)implicature: Sue does not know where the cat is. (m)

Because Sue does not know where the cat is, providing eitherlocation alone would violate the maxim of Quality. How-ever, providing both locations conflicts with the maxim ofQuantity because the cat is in at most one of the stated loca-tions. Flouting the maxim of Quality would violate implicitcommunication criterion 2 because either location alone isplausible. Thus, Sue chooses to flout the maxim of Quantityin order to trigger Mark to search for an explanation.

5.1.2 Inverse SemanticsThough more direct than conversational implicature, the

simpler speech act of entailment is fundamentally describedby the same mathematics. Knepper et al. [22] present theinverse semantics framework for robots generating naturallanguage help requests. Like most robot speech systems,the framework strives for extremely literal communication.However, it faces a problem of finding pithy, unambiguousmeans of communicating its needs in an automated assem-bly scene cluttered with parts that lack unique names. Sincewords are complex and imperfect containers for meaning, thecareful selection of clear language to achieve entailment fol-lows the same rules of generation as described in Section 3.4.

The core of inverse semantics is a forward semantics mech-anism for understanding natural language, the GeneralizedGrounding Graph (G3) [32]. This structure takes in naturallanguage expressions λ as inputs and returns their meaningsor groundings γ as outputs.

The inverse semantics framework inverts G3 to performgeneration by searching over the space of possible Englishsentences, sorted from shortest to longest, and inputtingeach to G3. Inverse semantics compares the output of G3

with the target grounding needed by the help request. Thesearch halts with the first sentence that attains over a thresh-

old confidence match between the two groundings. The ex-pression given for generation,

argmaxλ

P(γ|λ, φ,M), (4)

strongly resembles our own framework’s Equation (2). Here,φ is a correspondence variable used to indicate the semanticlikelihood of a match between λ and γ. Like our model,M symbolizes the context model in which the meaning isinterpreted.

5.2 Communicative MotionBesides natural language usage, the robotics community

has studied other types of actions. An especially expressiveaction class for implicit communication is motion.

5.2.1 LegibilityLet us consider again the joint assembly activity in which

Steve and Cathy cooperate to build furniture. Many formsof communicative action arise. One class of actions studiedrecently by Dragan, Lee, and Srinivasa [10] involves reachingmotions. Among parts cluttering a table, Steve has to pickup a particular one. The shape of his reaching trajectorymay or may not inform Cathy about Steve’s intent. A directreaching motion is predictable (high probability P(a|Mpub))and therefore not communicative. A curved trajectory, incontrast, helps Cathy to identify the target of Steve’s reachbefore he gets there.

In general, assume that an actor Q is aiming at reach-ing a goal GQ from a set of goals G in front of an observerR. The agents share a model P(G|ξ) that probabilisticallyattributes a goal G ∈ G to an observed trajectory ξ. Theactor can leverage this knowledge to design his trajectory ina way that indicates his intended goal to the observer. Fol-lowing the insights of Csibra and Gergely [8] regarding thetendency of humans to interpret observed actions as goal-directed (teleological reasoning), Dragan, Lee, and Srinivasa[10] introduced the Legibility score to quantify the intent-expressiveness of a trajectory ξ with respect to a goal GQ:

Legibility(ξ) =

∫ T0

P(GQ|ξ0→t)f(t)dt∫ T0f(t)dt

(5)

where T is the duration of the trajectory and f(t) is a func-tion that weights partial trajectories ξ0→t higher in the be-ginning and lower later. It should be noted that f(t) is aproxy for the role of the observer in reducing her receptiv-ity (see Section 4.3) as Q’s intended goal GQ becomes morecertain to her. The model P(G|ξ) scores goals higher if theycan be achieved efficiently (with a low energy trajectory ξ)and scores goals lower if they require higher energy.

The legibility score is essentially a weighted sum of theprobabilities that the observers assign to the actor’s intendedgoal GQ throughout the whole trajectory ξ. Trajectoriesof higher legibility tend to be more curved towards the in-tended goal GQ, biasing the observers towards predictingthe actor’s actual goal, while biasing them against predict-ing other goals. Note that a more curved trajectory is lessprobable out of context due to the extra energy it expends.As a result, it might be perceived as surprising. This sur-prise would trigger a search for an explanation, which, inthe perceived context, would lead to the conclusion that theactor Q is aiming at reaching the goal GQ.

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P(a)

P(a|Mpub)

a0a1a2a3

m

Figure 3: The red, navigating agent (human orrobot) selects an action a. Out of context (top),the red agent (human or robot) is not avoiding anobstacle, and so the probability of expending need-less extra energy is low. In the case of an oncomingblue agent (m), the likelihood of the oblivious actionP(a0|Mpub) is low due to social norms, despite beinglow energy. Conversely, the normally-improbableact of spending extra energy becomes probable inthis context. An observer who sees only the redagent’s motion can infer m from observing a3.

5.2.2 Dynamic LegibilityConsider now the case of a dynamic environment, where

the agents are not explicitly collaborating but since the de-cisions they make are coupled, it is beneficial for everyone tomutually agree on a joint strategy. Assuming again no ex-plicit communication, the only way agents are able to agreeon a strategy is to encode their understanding and prefer-ences into their actions.

Social navigation constitutes a representative example ofthis class of scenarios. Although humans might not oftenrealize that navigation in crowded environments is a col-laborative activity, according to sociology studies [36], it isestablished on implicit cooperation. Pedestrians follow andreinforce the pedestrian bargain, a social convention com-prising two foundational rules: (1)“pedestrians must behavelike competent pedestrians” and (2) “pedestrians must trustthat co-present others behave like competent pedestrians”.Since the pedestrian bargain serves as a cooperative princi-ple for social navigation, we may formulate a set of maximsfor motion that echo the Gricean Maxims of conversationalimplicature,

1. Maxim of Efficiency: Be parsimonious.2. Maxim of Motion: Do not collide with objects or ob-

struct another agent’s motion.3. Maxim of Manner: Be perspicuous and orderly.

These maxims readily come into conflict where multiple agentsare present. Much as in the case of implicature, the actorwill choose to deliberately flout one of the maxims – typicallythe maxim of Efficiency – in order to obey the cooperativeprinciple. It is only by considering the collision-avoidancecontext that an observer is able to appreciate that by tak-ing an exaggerated trajectory such as a3 in Figure 3, theglobal welfare is improved, as measured by increased energyefficiency and decreased uncertainty.

Enforcing the pedestrian bargain leads to a consensus overa mutually beneficial joint strategy that allows everyone tocomfortably reach their destinations. The agents contin-uously monitor the progress toward consensus and adjusttheir decision-making accordingly. Once consensus appears

to have been reached, receptivity drops to zero as pedestri-ans initiate civil inattention [12, 21]. Following this modeswitch, agents look away from one another as a signal thatthey have stopped actively avoiding each other and will in-stead follow their previous planned collision-free path.

Mavrogiannis and Knepper [28, 29] present a recent nav-igation framework that reproduces the implicit communi-cation of social navigation. They model consensus S as atopological joint strategy using braids [3], and they developa game-theoretic decision making policy corresponding toa utility function that compromises between efficiency andimplicit communication. This utility function is defined as:

u(a) = λE(a)− (1− λ)H(a) (6)

where λ is a weighting factor, E represents the efficiencyof an action a and H is the entropy of the agents’ beliefregarding the emerging strategy S:

H(a) = −∑S∈S

P(S|Z+,M) log P(S|Z+,M) (7)

with Z+ comprising Z (the state history of all agents so far),augmented with the action in consideration a and M beingthe context.

Picking actions that maximize the utility leads to a quickdecrease in the uncertainty regarding the global joint strat-egy (i.e., how each agent will avoid each other), while ensur-ing progress towards the agent’s destination. The selectionof actions with a strong communicative component, espe-cially in the beginning, was shown to reduce the likelihoodof livelocks or deadlocks.

6. OTHER EXAMPLESTeams exchange implicit information in cooperative games

when the rules forbid free exchange of information. For ex-ample, the bidding conventions of contract bridge allow part-ners to exchange information about the respective strengthsof their hands and arrive at an appropriate contract.

Finally, among married couples, this type of implicit com-munication eases over time across all modalities (speech, ges-ture, gaze, etc.) because spouses develop extremely sensitivemodels of P(a|Mpub), due to familiarity. Remarkably sophis-ticated notions can be conveyed between spouses by carefulaction selection in almost any context. We have considerablework remaining before robots can achieve a similar level ofunderstanding of people.

6.1 TactImplicit communication is also the primary tool of tactful

communication, as it alleviates the risk of awkwardness dueto misunderstandings about what facts the observer alreadyknows. Reflecting on the implicit communication criteriagiven in Section 3.3, an attempted implicit communicationof a fact that the observer already knows does not even seemlike implicit communication – it would come across as a pre-dictable, functional action. In this case, criterion 3 is clearlyviolated because m ∈Mpub, and criterion 2 is probably alsoviolated because a would seem likely.

To offer a concrete example of how speakers leverage im-plicit communication to achieve tact, consider a married cou-ple discussing dinner plans:

Jack: Remember, my friend Irving is coming fordinner.implicatures: Irving is vegetarian; Irving needs

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to be served a vegetarian meal.Kate: Let’s make my mother’s lasagna recipe.implicatures: Kate knows that Irving is vegetar-ian; Kate’s mother’s lasagna recipe is vegetarian;the recipe satisfies Irving’s need for a vegetarianmeal.

Observe that this exchange can be read at two levels. If bothparties are oblivious to the implicature because the sentencesare judged predictable, then it is a simple, matter-of-factdialog.

The statements can also be read as implicature. In bothcases, the implicated statements are things that the listenershould have already known. Only in the context of the cou-ple’s normal conversation can we judge how unusual it is forJack to remind Kate about a guest (a fact she may be un-likely to forget), or for Kate to make her mother’s lasagnarecipe.

Only if these events are atypical can they truly be re-garded as implicit communication. However, they also servea tactful reminder function, in case Kate forgot about theguest or Jack forgot that Kate’s mother’s lasagna is vege-tarian. A failing memory may therefore cause an action tobe judged as unusual, in which case the reminder acts as animplicature. Thus, a related virtue of implicit communica-tion is that it allows the observer to maintain the pretenseof having already known a fact that they forgot.

7. PRACTICAL IMPLEMENTATIONInference, both generation and understanding, is imple-

mented as a search over actions and facts, respectively. Tech-niques are needed to streamline both search problems, dueto the intractability of the literal brute force search impliedby argmax in (1)–(2). Existing implementations of instancesof implicit communication employ AI search-pruning tech-niques [22, 34] or restrict the action space Af in order tonarrow the set of options under consideration [10, 29]. Inpractical terms, the set of feasible actions Af is typicallyhard-coded for a domain, raising the possibility that it mis-matches with some human’s expectation. Two people maysimilarly encounter a mismatch in expectation about Af .Interestingly, the machinery described in this paper couldbe used by a robot to infer that an observed human actionis intended to accomplish a (surprising) functional goal byleveraging the context, leading to extension of Af .

Another challenge is to build Mpub, the common groundmodel among agents. A complete model is often both unnec-essary (since many facts in the agents’ shared knowledge areirrelevant for the joint activity at hand) and infeasible (sincethe task of modeling the full common ground presents a highcognitive burden). As a result, Mpub need only consist of thefacts that are pertinent to the success of the joint activity.For example, in the social navigation of Mavrogiannis andKnepper [29], Mpub might contain an updated belief regard-ing the destinations and intentions of observed agents. Mpub

is therefore instantiated as the mutual understanding thatthe agents involved intend to participate in the joint activityalong with shared knowledge about the kinds of actions thatagents will likely take to contribute to the activity [4].

For humans, Mpub does not necessarily include all task-relevant facts at the start of the activity. It is frequentlyless costly to repair a misunderstanding that results fromnot sharing a piece of information than to expend the effortrequired to ground that piece of information through theprinciple of least collaborative effort [7, 30]. Mpub is then

updated interactively throughout the course of the joint ac-tivity, either when new information about the intents of theagents becomes publicly available or when the agents issuea repair that helps align their own mental models of the sit-uation (and in doing so adds to the common ground) [26].Machine-interpretable ontologies using tools like RDF andOWL address the general problem of managing and search-ing Mpub, as exemplified by the KnowRob project of Tenorthand Beetz [33].

Finally, the distribution P (a|M) is generally best mod-eled through machine learning. The particular context inwhich one takes an action affects the probabilities of observ-ing various possible actions, often in complex ways. Forexample, Knepper et al. [22] employ Tellex’s generalizedgrounding graph (G3) [32]. Based on a conditional randomfield, G3 employs a set of correspondence variables to valuatethe correspondence probability of a given language phraseand grounding concept. These learned relationships captureconcepts including objects, actions, and spatial relations.

8. DISCUSSIONConversational implicature and legibility, though originat-

ing in different domains, are connected by techniques of en-coding and decoding meaning using teleological inference [8].These methods rely heavily on common ground to provideclues about when a message is encoded on an action andwhat information the message contains. The inference pro-cess can be quite complex in real-life situations. Particularlyin the case of implicature, many rules must be brought tobear in order to correctly interpret what is being implicated.Several authors [14, 34] show promising early results in mod-eling a simple form of implicature and performing inferenceby model inversion.

8.1 A Call to ActionIn the coming years, modeling of implied meaning, in-

cluding through implicature and legible motion, will becomean increasing focus within robotics – not least because hu-mans already use these forms of implicit communication onrobots today. Humans are also already interpreting robots’actions through the lens of implicit communication. Sincefew robots are cognizant of the implicit meaning of their ac-tions, today’s robots send random signals to humans. Byand large, humans are unable to interpret robot actions inthe purely functional manner that they are intended. Thus,the robotics research community must find techniques to ef-ficiently generate and understand implicit communication.

This direction will drive the need for improved modelingof common ground. A major hurdle to performing theseinferences on robots in real-world situations is salience; to-day, the robot must perform a fairly undirected, brute-forcesearch in order to discover which elements of the context areapplicable. Humans, in contrast, seem to learn filters andpartially pre-compute functions to expedite real-time infer-ence in ambiguous situations. These processes are not yetunderstood in humans, but they will need to be deployed onrobots in order to promote responsive behavior and avoidmajor misunderstandings.

AcknowledgmentsThis material is based upon research supported by the Officeof Naval Research under Award Number N00014-16-1-2080and by the National Science Foundation under Grant No.1526035. We are grateful for this support.

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