Reasoning about reasoning by nested conditioning: Modeling theory of mind with probabilistic programs

Abstract

A wide range of human reasoning patterns can be explained as conditioning in probabilistic models; however, conditioning has traditionally been viewed as an operation applied to such models, not represented in such models. We describe how probabilistic programs can explicitly represent conditioning as part of a model. This enables us to describe reasoning about others' reasoning using nested conditioning. Much of human reasoning is about the beliefs, desires, and intentions of other people; we use probabilistic programs to formalize these inferences in a way that captures the flexibility and inherent uncertainty of reasoning about other agents. We express examples from game theory, artificial intelligence, and linguistics as recursive probabilistic programs and illustrate how this representation language makes it easy to explore new directions in each of these fields. We discuss the algorithmic challenges posed by these kinds of models and describe how Dynamic Programming techniques can help address these challenges.

Imitation: Neither instinct nor gadget, but a cultural starting point?

“…Despite the claims of "theory theories" (e.g., Davies & Stone 1995), the field has made little progress beyond "common sense platitudes" (e.g., Lewis 1970) when articulating rules or principles governing the relations among mental states or between mental states and behaviour. Approaches that formalise aspects of mindreading as Bayesian inverse inferences (e.g., Jara-Ettinger et al 2016) are promising for scenarios that artificially limit the set of possible mental states that could be ascribed, but are unlikely to be extensible to more realistic scenarios (Stuhlmüller & Goodman 2014). There are good grounds for thinking "theory theories" have made limited progress because the rules or principles governing relations among mental states are uncodifiable (e.g., Davidson 1990).…”

How is mindreading really like reading?

“…Despite the claims of “theory theories” (e.g., Davies & Stone 1995), the field has made little progress beyond “common sense platitudes” (e.g., Lewis 1970) when articulating rules or principles governing the relations among mental states or between mental states and behaviour. Approaches that formalise aspects of mindreading as Bayesian inverse inferences (e.g., Jara-Ettinger et al 2016) are promising for scenarios that artificially limit the set of possible mental states that could be ascribed, but are unlikely to be extensible to more realistic scenarios (Stuhlmüller & Goodman 2014). There are good grounds for thinking “theory theories” have made limited progress because the rules or principles governing relations among mental states are uncodifiable (e.g., Davidson 1990).…”

On the Consistency of Approximate Multi-agent Probability Theory

“…On the other hand, if she uses a ''soft'' maximization rule in the style of Stuhlmüller and Goodman [18], sec. 3.1], she would merely be more predisposed to choose the oversampled bar.…”

“…In a recent article, Goodman and Stuhlmüller [18] have proposed a different approach to this problem. The system they propose is implemented in the stochastic programming language Church [10] and models probability distributions over probability distributions in terms of sampling schemes that sample other sampling schemes.…”