Bayesian Theory of Mind (BToM) @cite{baker-jara-ettinger-saxe-tenenbaum-2017} #

@cite{clark-1996} @cite{houlihan-kleiman-weiner-hewitt-tenenbaum-saxe-2023} @cite{kratzer-2006} @cite{ying-zhi-xuan-wong-mansinghka-tenenbaum-2025}

Domain-general cognitive architecture for action explanation: how observers explain agents' behavior by jointly inferring mental states, shared states, and environmental constraints.

BToM is not specific to language — it applies equally to physical action understanding, game-theoretic reasoning, emotion attribution, and communication. Linguistic specialization (RSA) is established via the RSA-BToM bridge.

Latent Variable Ontology #

Latent variables in the generative model fall into three ontological categories:

Mental: Individual mental states private to the agent — Belief, Desire, Percept. These are properties of a single mind.
Shared: Intersubjective states maintained between agents — common ground, mutual belief, established precedents. Not reducible to either agent's individual mental state.
Medium: Non-mental environmental constraints on action — the structure of the communication channel, conventions, physical affordances.

The Generative Model #

An agent's action is generated by the causal chain:

World → Percept → Belief
                    ↓
              Belief × Desire × Shared × Medium → Plan → Action
                                                          ↓
                                    Shared × Action × World → Shared'

The observer sees an action and jointly infers the latent variables across all three categories via Bayesian inversion:

P(p, b, d, s, m, w | a) ∝ P(a | b, d, s, m) · P(b | p) · P(p | w) · P(d | w) · P(s) · P(m) · P(w)

Note that P(d | w) is world-conditioned: in many domains, the prior distribution over desires depends on the world state. In RSA, this corresponds to latentPrior(w, l) — the distribution over speaker latent states may depend on the true world (e.g., observation probability in @cite{goodman-stuhlmuller-2013}).

Causal Structure #

The perception chain W → P → B is one specific causal architecture — it decomposes world-to-belief inference into observation then updating. Other architectures are possible (direct world-to-belief, joint perception-belief formation, belief from memory + percept). The current structure follows @cite{baker-jara-ettinger-saxe-tenenbaum-2017} and is sufficient for RSA grounding, where the chain collapses to identity (perfect perception and knowledge).

Limitations #

This is a first-order model: the observer inverts a single agent's generative model. It does not represent recursive mentalizing ("I think that you think that I think..."). Extending to recursive BToM would require nesting: the agent's planModel would itself contain a BToM inference step over the observer's mental states. This is conceptually straightforward but computationally expensive and not needed for single-utterance RSA models.

Extensibility #

The model is designed for domain-specific extension without modification:

Discourse dynamics: sharedUpdate chains BToM inference steps via shared-state evolution (discourse referent introduction, QUD push/pop, presupposition accommodation, Clarkian conceptual pacts).
Emotion attribution: Post-inference appraisals (goal congruence, prediction error, counterfactual reasoning) can be computed from the inferred marginals without extending the generative model itself.