Understanding Epistemic Language with a Language-augmented Bayesian Theory of Mind

TL;DR

LaBToM presents a two-module framework that grounds interpretation of epistemic language in a Bayesian theory-of-mind and an epistemic language of thought (ELoT). Natural-language statements are translated into ELoT via grammar-constrained decoding and then evaluated against probabilistic inferences $\mathbf{Pr}(A, \phi)$ about agents' beliefs and goals, computed by a Bayesian ToM (BToM). The approach is validated on Doors, Keys, & Gems puzzles, showing strong correspondence with human judgments ($r$ roughly $0.76$–$0.81$) and surpassing multimodal LLM baselines, with ELoT translations and online inference enabling nuanced handling of modal, uncertain, and knowledge claims. The results highlight the importance of language-aligned epistemic representations and coherent theory-of-mind reasoning for grounded interpretation of epistemic language, with implications for both cognitive modeling and AI systems that reason about others' minds.

Abstract

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'' with grammar-constrained LLM decoding, then evaluating these translations against the inferences produced by inverting a generative model of rational action and perception, LaBToM captures graded plausibility judgments of 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.

Figures (5)

• Figure 1: Overview of our model, a Language-augmented Bayesian Theory of Mind (LaBToM). Here, our model evaluates the plausibility of epistemic language about a player character trying to find keys in boxes so as to reach one of four goals (gems with different shapes/colors, $\textsf{g}_1$-- $\textsf{g}_4$) which may be locked behind doors. (Top) We translate natural language statements about the player's initial ($\sigma_1$) and current beliefs ($\sigma_2$) into an unambiguous epistemic language of thought (ELoT) via grammar-constrained LLM parsing. ELoT statements (i.e. epistemic formulas $\varphi$) are interpreted with a probability-based semantics (lowered formulas $\varphi'$). (Bottom) We use our Bayesian theory-of-mind (BToM) module to produce inferences (bar charts) about the environment state (top left), the player's goal (bottom left), and the player's belief state (right) at each step $t$, given observations across time. Each possible belief state $\textsf{b}_i$ is itself a distribution over environment states $\textsf{s}_j$, where state $\textsf{s}_j$ corresponds to a blue key being in box $j$. (Middle) We evaluate the posterior probability$^*$ of each ELoT statement $\varphi$ from the BToM inferences at each step $t$ ($^*$under a 50-50 prior over statement truth). Statement $\sigma_1$ ("The player thought that the blue key must be in box 3.") increases in probability from $t$$=$$6$ to $t$$=$$9$, then stays high, since it becomes clear from the player looking in box 3 at $t$$=$$9$ that they initially thought a key must be in box 3. Statement $\sigma_2$ ("The player believes that a blue key is more likely to be in box 1 than box 2.") decreases in probability as the player walks away from box 1 at $t$$=$$6$ through $t$$=$$9$. However, when the player finds box 3 empty, then moves past box 2 up to box 1 at $t$$=$$15$, it becomes much more probable that the player currently thinks a key is more likely to be in box 1 rather than box 2.
• Figure 2: Human correlation plots for LaBToM and GPT-4o. Black dots are from statements not accurately translated to ELoT. LaBToM provides a much stronger qualitative fit with human ratings compared to the best GPT-4o baseline, which fails to use the full scale.
• Figure 3: Step-by-step ratings by humans and models across three scenarios. Judgement points are annotated on each map, and show the player's location before opening the nearest box. Keys picked up along the way are shown in light colors. Our model largely matches human responses qualitatively and quantitatively, unlike GPT-4o.
• Figure A1: Interfaces used for collecting (top) and evaluating (bottom) epistemic language.
• Figure C2: Scenario illustrating differences in human and model ratings of knowledge claims.