How do people understand and evaluate claims about others' beliefs, even though these beliefs cannot be directly observed? In this paper, we introduce a cognitive model of epistemic language interpretation, grounded in Bayesian inferences about other agents' goals, beliefs, and intentions: a language-augmented Bayesian theory-of-mind (LaBToM). By translating natural language into an epistemic ``language-of-thought'', then evaluating these translations against the inferences produced by inverting a probabilistic generative model of rational action and perception, LaBToM captures graded plausibility judgments about epistemic claims. We validate our model in an experiment where participants watch an agent navigate a maze to find keys hidden in boxes needed to reach their goal, then rate sentences about the agent's beliefs. In contrast with multimodal LLMs (GPT-4o, Gemini Pro) and ablated models, our model correlates highly with human judgments for a wide range of expressions, including modal language, uncertainty expressions, knowledge claims, likelihood comparisons, and attributions of false belief.

A general game player automatically learns to play arbitrary new games solely by being told their rules. For this purpose games are specified in the game description language GDL, a variant of Datalog with function symbols and a few known keywords. In its latest version GDL allows to describe nondeterministic games with any number of players who may have imperfect, asymmetric information. We analyse the epistemic structure and expressiveness of this language in terms of epistemic modal logic and present two main results: The operational semantics of GDL entails that the situation at any stage of a game can be characterised by a multi-agent epistemic (i.e., S5-) model; (2) GDL is sufficiently expressive to model any situation that can be described by a (finite) multi-agent epistemic model.