Capturing mental state reasoning with influence diagrams

Capturing mental state reasoning with influence diagrams Alan Jern and Charles Kemp {ajern,ckemp}@cmu.edu Department of Psychology Carnegie Mellon University Abstract People have a keen ability to reason about others’ mental states, which is central for communication and cooperation. A core question for cognitive science is what mental represen- tations support this ability. We offer one proposal based on the framework of influence diagrams, an extension of Bayes nets that is suited for representing intentional goal-directed agents. We evaluate this framework in two experiments that require participants to make inferences about what another per- son knows or values. In both experiments, participants’ judg- ments were better predicted by our influence diagrams account than by several alternative accounts. Keywords: theory of mind; social cognition; influence dia- grams; Bayes nets People rarely articulate everything they are thinking. Thus, one of the major inductive problems we face is how to infer other people’s thoughts from their observable behavior. As a concrete example, suppose your friend asks you to join him in visiting the art museum today, a Monday, which is a day on which you happen to know the museum is closed. You might infer then that your friend does not know the museum is closed on Mondays, or that he does not know that today is Monday, or perhaps neither. You suggest going to the natu- ral history museum instead, which is open but is both more expensive and farther away than the art museum. Your friend declines. Now you might infer that he did not want to spend more money, or that he did not want to travel so far, or per- haps both; it’s also possible that your friend simply doesn’t like the natural history museum. People generally find these types of inferences about others natural and exhibit relatively rich intuitive theories of mental states and behavior (D’Andrade, 1987). Mental state reason- ing, also called theory of mind, poses some standard ques- tions for cognitive science: Namely, what mental representa- tions support mental state reasoning and what computations are carried out over these representations (Perner, 1991). We propose that these representations are similar to influence dia- grams (IDs), an extension of Bayes nets that includes a notion of goal-directed action (Howard & Matheson, 2005). The ID framework provides a graphical language for rep- resenting decision problems and an associated formal seman- tics that supports quantitative predictions. The framework re- tains all of the strengths of Bayes nets, including the ability to make a distinction between the existence of relationships among variables and the strength of those relationships, to concisely specify a distribution over many variables, and to predict the outcomes of interventions (Sloman, 2005). IDs, however, build on Bayes nets by providing a formal way of making predictions and inferences about intentional behavior. Computer scientists have previously used IDs to model the behavior of intentional agents, particularly in games (Gal & Pfeffer, 2008; Koller & Milch, 2003), but this research has focused primarily on relatively complex scenarios involving multiple agents, rather than the simple scenarios that have been the subject of most theory of mind research—like the example at the beginning of this paper. And although there are several existing computational models of mental state rea- soning (Baker, Saxe, & Tenenbaum, 2009; Oztop, Wolpert, & Kawato, 2005; Schultz, 1988; Wahl & Spada, 2000), the ID framework has received little attention in the psychological literature. We argue that IDs serve as a useful model of the mental representations that support human reasoning. The rest of the paper is organized as follows. First, we describe the ID framework and discuss some of its strengths for reasoning about other people’s mental states and behavior. Then, we apply the framework to a specific task that involves inferring what someone else knows or values and evaluate its ability to predict human performance on the task. Influence diagrams We will introduce the ID framework using the following sim- ple scenario. Alice is playing a game in which a two-color die is rolled. Alice chooses a color and receives a reward if her choice matches the color of the die. Thus, there are three variables: the color of the rolled die, Alice’s chosen color, and the value of the reward. Two variations of this scenario can be represented by the IDs in Figure 1a and 1b, where the three variables are denoted R, D, and U, respectively. IDs differ from standard Bayes nets in that they allow for the representation of three semantically distinct types of vari- ables, each of which is shown in the example IDs. First are chance variables, depicted by ovals, which represent proba- bilistic events like the outcome of the die roll R. Just as in causal Bayes nets, incoming edges to chance nodes represent causal dependencies between events; therefore, we will refer to these edges as causal edges. Second are decision variables, depicted by rectangles, which represent intentional decisions, like Alice’s choice D. Incoming edges to decision nodes rep- resent information available when making the decision; we will refer to these edges as knowledge edges. For example, the IDs in Figure 1a and 1b differ in the presence of a knowl- edge edge from R to D. The ID in 1a represents a situation where Alice knows nothing about the roll before making her choice and the ID in 1b represents a situation where Alice gets to see the rolled color before making her choice. Lastly are utility variables, depicted by diamonds, which represent a decision maker’s utility, like Alice’s reward U. Incoming