Bayesian updates from coalgebraic determinisation
This work addresses the limitation of traditional POMDP determinization methods, which discard intermediate observations and thus fail to support full-history Bayesian updating. By integrating unifilarisation into a coalgebraic determinization framework, the authors introduce a support structure over a monoid that represents system states as prior distributions and defines transitions via Bayesian filtering. They establish, for the first time, that unifilarisation is a special case of coalgebraic determinization, thereby naturally embedding Bayesian updating within a categorical semantics. This approach extends to stochastic Mealy machines equipped with support structures, yielding a semantics finer than conventional Moore models. The resulting framework generates, for each input word, a family of output distributions satisfying causal constraints, making it well-suited for modeling reinforcement learning and sequential decision-making problems.