Building Representations of Common Ground with Intelligent Agents: Papers from the 2011 AAAI Fall Symposium (FS-11-02) Modeling Expert Effects and Common Ground Using Questions Under Discussion Alex Djalali, David Clausen, Sven Lauer, Karl Schultz†, and Christopher Potts Stanford University †University of Massachusetts Amherst Stanford CA 94305 Amherst MA 10003 [djalali, clausend, sven.lauer, cgpotts]@stanford.edu, [email protected] Abstract first resolve whether B would like to go to Europe before in- quiring about specific European countries. If, and only if, A We present a graph-theoretic model of discourse based on the and B arrive jointly at a positive resolution of the Europe Questions Under Discussion (QUD) framework. Questions question should they press on to inquire about Germany, and assertions are treated as edges connecting discourse states in a rooted graph, modeling the introduction and resolution Hungary, and so forth. of various QUDs as paths through this graph. The amount Of course, most discourse does not march from general to of common ground presupposed by interlocutors at any given specific in this transparent way. Speakers often begin with point in a discourse corresponds to graphical depth. We intro- very specific questions; A might in fact begin the vacation duce a new task-oriented dialogue corpus and show that ex- discussion by asking which of Germany or Hungary they perts, presuming a richer common ground, initiate discourse should visit. In such cases, the speaker presupposes that the at a deeper level than novices. The QUD-graph model thus more general issues have already been settled, or else acts as enables us to quantify the experthood of a speaker relative though the addressee will accommodate resolutions of those to a fixed domain and to characterize the ways in which rich more general issues that make sense given the specific ques- common ground facilitates more efficient communication. tion posed. Where it works, this can be an efficient strategy of inquiry, allowing the participants to resolve many issues 1 Introduction at once. Where it fails, it leads to confusion and a rapid retreat back to more general issues. The presuppositions of a speaker’s utterance are often a rich We present a formal model of these accommodation pro- source of insights into her understanding of the context — cesses. Questions and assertions are treated as edges in what she assumes to be mutual knowledge of the discourse a rooted graph, connecting potential discourse states. The participants, what she regards as the current goals, what edges thus model the introduction and resolution of various kinds of information she regards as relevant to those goals, QUDs. The information that a speaker presupposes with an and so forth. These inferences are an important part of ro- utterance U can be characterized via the position of U in bust utterance understanding and thus vital for research in the QUD graph, and the amount of information presupposed linguistic pragmatics and artificial intelligence (Thomason with U is given by its depth in the QUD-graph. 1990; Stone, Thomason, and DeVault 2007). To evaluate this proposal, we introduce a new task- In this paper, we present a method for deriving (some of) oriented dialogue corpus that represents not only the partici- these inferences based on a speaker’s utterances and a par- pants’ utterances, but also their goals and actions, thereby al- tial understanding of the context. We begin from the notion lowing us to precisely model the context of utterance at any that discourse is collaborative inquiry into the state of the stage of play. In particular, if a player poses or addresses world (Stalnaker 1974; 1998; 2002). This inquiry is guided a task-oriented question Q, then we can identify where Q by a partially ordered set of abstract questions under dis- sits in the QUD-graph determined by the nature of the task, cussion (QUDs), which determine what is relevant, help to which provides an estimate of the amount and kind of infor- define the domain of discourse, and influence the common mation contributed by Q. We show that expert players tend ground (Groenendijk and Stokhof 1984; Groenendijk 1999; to initiate discourse at greater depth in the QUD graph than Ginzburg 1996; Roberts 1996; Cooper and Larsson 2001; do novices. This behavior is explicable in terms of the as- Roberts 2004; Buring¨ 1999; Buring¨ 2003; Stone 2002; sumption that experts are more likely to presume rich com- van Rooy 2003). mon ground than novices, which allows them to bypass gen- In very well organized (idealized) inquiry, the participants eral questions in favor of more specific ones. begin from the most general questions and then move sys- tematically to the most specific ones. For example, if A is 2 The QUD model trying to find out where B would like to vacation, A should We now develop a graph-theoretic model of discourse, Copyright c 2011, Association for the Advancement of Artificial which we refer to as the QUD graph model. This model Intelligence (www.aaai.org). All rights reserved. is based on those of Roberts (1996), Ginzburg (1996) Groe- 10 nendijk (1999), and Buring¨ (2003), though we have made defined in terms of D and W (def. 1) and QUD is a partition various simplifications and modifications. The intuitive idea on W . is that any discourse can be viewed as a sequence of ques- Equipped with these ancillary notions, we define a QUD tions and their answers, all of which address sub-issues of graph as a graph whose vertices are discourse states and the current topic of conversation, until all such issues are ex- whose edges represent assertions and questions: haustively resolved. At any point in the discourse, there is a current QUD, which interlocutors attempt to resolve, ei- Definition 4 (QUD Graph). A QUD graph is a directed G = V, A, Q V ther directly or by tackling a series of sub-questions, whose graph , where a set of discourse states (ver- A Q answers, taken together, fully resolve that QUD. The over- tices); is a set of edges corresponding to answers; and arching topic of conversation can be viewed as a (typically is a set of edges corresponding to questions. Then for any m n quite general) question, e.g., What is the state of the world?, two states and , and all moves in a discourse are in the service of resolving 1. mQn iff CGm = CGn and QUD m CGm QUD n its sub-questions. 2. mAn iff CGm ⊃ CGn and QUD m is the closest unre- To make this precise, we assume a possible-worlds frame- solved QUD in the path from m to the root node. work. Our most basic discourse notion is the common mQn ground, which includes vast quantities of basic world knowl- Question-edges relate two states ( ) iff the first con- edge as well as information about the public commitments tains a sub-question of the second. Answer-edges relate two mAn of the discourse participants, the salience of various objects, states ( ) iff the QUD of the first is (at least partially) an- a record of previous utterance events, and so forth. swered by the common ground of the second and the QUD of the second is constrained to be the closest unresolved Definition 1 (Common ground). Let W be a set of possible question in the graph. worlds and D a set of discourse participants. The common As we discussed above, speakers will typically not obey ground for D is the subset of W in which all and only the the strict structure of such a QUD graph in terms of their public commitments of all the individuals in D are true. actual utterances. However, their utterances will indicate A question is a partition on W . Intuitively, each cell of the where in the graph they currently take themselves to be in partition is a complete resolution of the issue (Groenendijk the discourse, and they will expect the other discourse par- and Stokhof 1984). For example, if p is the proposition that ticipants to reason in terms of the graph, by quietly resolving it is raining, then R = {p, W −p} is the question of whether super-questions in a way that delivers sensible results for the it is raining. The question of what the weather is like corre- sub-questions they pose, and by properly relating assertions sponds to the set of propositions C = {p,q,r,...}, where to the corresponding QUDs. Thus, the length of the short- p is the proposition that it raining (and nothing else), q is est path between two explicit moves can serve as a measure the proposition that it is snowing (and nothing else), r is the of how far the interlocutors have progressed in a given dis- proposition that it is hailing (and nothing else), and so on for course with respect to resolving a QUD, and, indirectly, how all the mutually exclusive weather propositions. much knowledge they take to be in the CG. We say that Q1 is a sub-question of Q2 relative to com- mon ground CG iff every complete answer to Q1 in CG ex- 3 Experiment cludes (at least) some possible answers to Q2 (Groenendijk We now present our evaluation of the QUD-graph model. and Stokhof 1984; 1997; van Rooy 2003): We first introduce the Cards corpus and describe the ad- Definition 2 (Contextual sub-question). Q1 is a sub- ditional annotations that were used to construct the Cards question of Q2 relative to CG, written Q1 CG Q2,iff graph, a QUD-graph informed by the structure of the task.