arXiv subjects

timorl

Publications and source records attributed to timorl.

2 recordsLinked to original sources

arXiv2025

Formalising the intentional stance 2: a coinductive approach

Given a stochastic process with inputs and outputs, how might its behaviour be related to pursuit of a goal? We model this using 'transducers', objects that capture only the external behaviour of a system and not its internal state. A companion paper summarises our results for cognitive scientists; the current paper gives formal definitions and proofs. To formalise the concept of a system that behaves as if it were pursuing a goal, we consider what happens when a transducer (a 'policy') is coupled to another transducer that comes equipped with a success condition (a 'teleo-environment'). An optimal policy is identified with a transducer that behaves as if it were perfectly rational in the pursuit of a goal; our framework also allows us to model constrained rationality. Optimal policies obey a version of Bellman's principle: a policy that's optimal in one time step will again be optimal in the next time step, but with respect to a different teleo-environment (obtained from the original one by a modified version of Bayesian filtering). This property sometimes also applies to the bounded-rational case; we give a sufficient condition. A policy is deterministic if and only if there exists a teleo-environment for which it is uniquely optimal among the set of all policies; we relate this to classical representation theorems from decision theory. This result need not hold in the bounded-rational case; we give an example related to the absent-minded driver problem. The formalism is defined using coinduction, following the style proposed by Czajka.

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arXiv2024

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.

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