Reasoning about Discrete and Continuous Noisy Sensors and Effectors in Dynamical Systems

TL;DR

This paper extends a logical framework for reasoning about belief updates in noisy sensor and effector environments to include both discrete and continuous domains, enhancing its applicability to complex robotic systems.

Contribution

It introduces a unified logical approach that handles both discrete distributions and continuous densities for belief updates in noisy dynamical systems.

Findings

Unified logical formalism for discrete and continuous belief updates

Enhanced applicability to robotic sensing and acting scenarios

Theoretical foundation for complex noisy domain reasoning

Abstract

Among the many approaches for reasoning about degrees of belief in the presence of noisy sensing and acting, the logical account proposed by Bacchus, Halpern, and Levesque is perhaps the most expressive. While their formalism is quite general, it is restricted to fluents whose values are drawn from discrete finite domains, as opposed to the continuous domains seen in many robotic applications. In this work, we show how this limitation in that approach can be lifted. By dealing seamlessly with both discrete distributions and continuous densities within a rich theory of action, we provide a very general logical specification of how belief should change after acting and sensing in complex noisy domains.