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Formalising the intentional stance 1: attributing goals and beliefs to stochastic processes

Simon McGregor, timorl, Nathaniel Virgo

TL;DR

The paper formalises Dennett's intentional stance by introducing teleo-environments—transducers coupled to goal-driven environments—that yield normative-epistemic descriptions of agents. It shows that a policy is optimal for a teleo-environment if it maximises the probability of achieving success at least once, and that updated attributions under evolution follow a value-laden filtering rule, not plain Bayes updating. A key result is that every system admits a normative-epistemic interpretation, while unique specification occurs only for deterministic behaviours, with bounded rationality introducing further constraints. The framework connects to decision theory, the free energy principle, IRL, and computational mechanics, offering a rigorous lens for analyzing agency across bounded cognition and providing foundations for future extensions to more complex, interacting systems.

Abstract

This article presents a formalism inspired by Dennett's notion of the intentional stance. Whereas Dennett's treatment of these concepts is informal, we aim to provide a more formal analogue. We introduce a framework based on stochastic processes with inputs and outputs, in which we can talk precisely about *interpreting* systems as having *normative-epistemic states*, which combine belief-like and desire-like features. Our framework is based on optimality but nevertheless allows us to model some forms of bounded cognition. One might expect that the systems that can be described in normative-epistemic terms would be some special subset of all systems, but we show that this is not the case: every system admits a (possibly trivial) normative-epistemic interpretation, and those that can be *uniquely specified* by a normative-epistemic description are exactly the deterministic ones. Finally, we show that there is a suitable notion of Bayesian updating for normative-epistemic states, which we call *value-laden filtering*, since it involves both normative and epistemic elements. For unbounded cognition it is always permissible to attribute beliefs that update in this way. This is not always the case for bounded cognition, but we give a sufficient condition under which it is. This paper gives an overview of our framework aimed at cognitive scientists, with a formal mathematical treatment given in a companion paper.

Formalising the intentional stance 1: attributing goals and beliefs to stochastic processes

TL;DR

The paper formalises Dennett's intentional stance by introducing teleo-environments—transducers coupled to goal-driven environments—that yield normative-epistemic descriptions of agents. It shows that a policy is optimal for a teleo-environment if it maximises the probability of achieving success at least once, and that updated attributions under evolution follow a value-laden filtering rule, not plain Bayes updating. A key result is that every system admits a normative-epistemic interpretation, while unique specification occurs only for deterministic behaviours, with bounded rationality introducing further constraints. The framework connects to decision theory, the free energy principle, IRL, and computational mechanics, offering a rigorous lens for analyzing agency across bounded cognition and providing foundations for future extensions to more complex, interacting systems.

Abstract

This article presents a formalism inspired by Dennett's notion of the intentional stance. Whereas Dennett's treatment of these concepts is informal, we aim to provide a more formal analogue. We introduce a framework based on stochastic processes with inputs and outputs, in which we can talk precisely about *interpreting* systems as having *normative-epistemic states*, which combine belief-like and desire-like features. Our framework is based on optimality but nevertheless allows us to model some forms of bounded cognition. One might expect that the systems that can be described in normative-epistemic terms would be some special subset of all systems, but we show that this is not the case: every system admits a (possibly trivial) normative-epistemic interpretation, and those that can be *uniquely specified* by a normative-epistemic description are exactly the deterministic ones. Finally, we show that there is a suitable notion of Bayesian updating for normative-epistemic states, which we call *value-laden filtering*, since it involves both normative and epistemic elements. For unbounded cognition it is always permissible to attribute beliefs that update in this way. This is not always the case for bounded cognition, but we give a sufficient condition under which it is. This paper gives an overview of our framework aimed at cognitive scientists, with a formal mathematical treatment given in a companion paper.
Paper Structure (14 sections, 2 theorems, 1 figure)

This paper contains 14 sections, 2 theorems, 1 figure.

Table of Contents

  1. Introduction
  2. The 'As-If' Approach And Dennett's Intentional Stance
  3. The Teleo-Environment Framework
  4. Transducers
  5. Teleo-environments
  6. Filtering and the Bellman property
  7. Specification
  8. Bounded rationality
  9. Relation To Other Frameworks
  10. Representation Theorems For Expected Utility Theory
  11. The free energy principle
  12. Inverse Reinforcement Learning
  13. Computational Mechanics
  14. Limitations and future work

Key Result

Theorem 1

If a policy $\pi$ is optimal for an environment $\varepsilon$, then given a possible sequence of actions $\mathbf{a}$ and sensor values $\mathbf{s}$ the policy $\pi'$, is optimal for the environment $\varepsilon'$. Here, $\pi'$ is $\pi$ evolved by $\mathbf{a}$ and $\mathbf{s}$, and $\varepsilon'$ is

Figures (1)

  • Figure 1: Two ways in which a theorist might describe the behaviour of a physical system. $(a)$ in a mechanistic description the theorist posits an internal state to the system such that its dynamics can explain the observable behaviour; in the case of a robot this could include hypothesised workings of internal control systems in addition to the literal mechanical gears depicted here. We formalise mechanistic descriptions in terms of stochastic Moore machines in the companion paper. $(b)$ in a normative-epistemic description the theorist posits an environment that the system believes itself to be in (according to the theorist's interpretation) and a goal that it seeks to achieve --- in this case the apple --- such that the system's behaviour can be explained by acting optimally in order to reach the goal. Normative-epistemic descriptions are the focus of our paper and are formalised in terms of teleo-environments. We emphasise that these are two different kinds of explanation for the same behaviour of the same system, and not two different types of system or two competing hypotheses.

Theorems & Definitions (3)

  • Definition : 3.0.1 in the companion paper
  • Theorem : Corollary 5.0.3 in the companion paper
  • Theorem : 6.2.3 and 6.3.2 in the companion paper