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

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.