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Despite the fact that beliefs are mental states that cannot be directly observed, humans talk about each others' beliefs on a regular basis, often using rich compositional language to describe what others think and know. What explains this capacity to interpret the hidden epistemic content of other minds? In this paper, we take a step towards an answer by grounding the semantics of belief statements in a Bayesian theory-of-mind: By modeling how humans jointly infer coherent sets of goals, beliefs, and plans that explain an agent's actions, then evaluating statements about the agent's beliefs against these inferences via epistemic logic, our framework provides a functional role semantics for belief, explaining the gradedness and compositionality of human belief attributions, as well as their intimate connection with goals and plans. We evaluate this framework by studying how humans attribute goals and evaluate belief sentences while watching an agent solve a doors-and-keys gridworld puzzle that requires instrumental reasoning about hidden objects. In contrast to pure logical deduction, non-mentalizing baselines, and mentalizing that ignores the role of instrumental plans, our model provides a much better fit to human goal and belief attributions, demonstrating the importance of theory-of-mind for modeling how humans understand language about beliefs.

Bayesian inference has been used in the past to model visual perception (Kerstenm 2004), accounting for the Helmholtz principle of perception as “unconscious inference” that is constrained by bottom-up sensory evidence (likelihood) while subject to top-down expectation, priming, or other contextual influences (prior bias); here "unconsciousness" merely relates to the "directness" of perception in the sense of Gibson. Here, we adopt the same Bayesian framework to model emotion process in accordance with Schachter-Singer’s Two-Factor theory, which argues that emotion is the outcome of cognitive labeling or attribution of a diffuse pattern of autonomic arousal (Schachter & Singer, 1962). In analogous to visual perception, we conceptualize the emotion process, in which emotional labels are constructed, as an instance of Bayesian inference, either consciously or unconsciously combining the contextual information with a person’s physiological arousal patterns. Drift-diffusion models were constructed to simulate emotional processes, where the decision boundaries correspond to the emotional state experienced by the participants, and boundary-crossing constitutes “labeling” in Schachter-Singer’s sense. Our model is tested against experimental data from the Schachter & Singer's study (1962) on context-modulated emotional state labeling and the Ross et al. study (1969) on fear reduction through mis-attribution. Two model scenarios are investigated, in which arousal pattern as one factor is pitted against contextual interaction with an confederate (in Schachter-Singer case) or explicitly instructed mis-attribution (in Ross et al. case) as another factor, mapping onto the Bayesian prior (initial position of the drift) and the likelihood function (evidence accumulation or drift rate). We find that the first scenario (arousal as the prior and context as the likelihood) has a better fit with Schachter & Singer (1962) whereas the second scenario (context as the prior and arousal as the likelihood) has a better fit with Ross et al. (1969).