Logical Filtering and Smoothing: State Estimation in Partially Observable Domains

Abstract

State estimation is the task of estimating the state of a partially observable dynamical system given a sequence of executed actions and observations. In logical settings, state estimation can be realized via logical filtering, which is exact but can be intractable. We propose logical smoothing, a form of backwards reasoning that works in concert with approximated logical filtering to refine past beliefs in light of new observations. We characterize the notion of logical smoothing together with an algorithm for backwards-forwards state estimation. We also present an approximation of our smoothing algorithm that is space efficient. We prove properties of our algorithms, and experimentally demonstrate their behaviour, contrasting them with state estimation methods for planning. Smoothing and backwards-forwards reasoning are important techniques for reasoning about partially observable dynamical systems, introducing the logical analogue of effective techniques from control theory and dynamic programming.

A survey of knowledge‐based sequential decision‐making under uncertainty

“…One example is the extension of (Chitnis, Kaelbling, and Lozano‐Pérez 2018) that seeks to automatically determine the variables to be modeled in the different representations (Chitnis and Lozano‐Pérez 2020). Another example is the use of logical smoothing to refine past beliefs in light of new observations; the refined beliefs can then be used for diagnostics and to reduce the state space for planning (Mombourquette, Muise, and McIlraith 2017). There is also work on an action language called pBC+, which supports the definition of MDPs and POMDPs over finite and infinite horizons (Wang, Zhang, and Lee 2019).…”