Formalising the intentional stance 2: a coinductive approach
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910786640674816 |
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| author | McGregor, Simon timorl Virgo, Nathaniel |
| author_facet | McGregor, Simon timorl Virgo, Nathaniel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09173 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Formalising the intentional stance 2: a coinductive approach McGregor, Simon timorl Virgo, Nathaniel Optimization and Control Systems and Control Probability 91E99, 93-10, 93E03 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. |
| title | Formalising the intentional stance 2: a coinductive approach |
| topic | Optimization and Control Systems and Control Probability 91E99, 93-10, 93E03 |
| url | https://arxiv.org/abs/2501.09173 |