Navigability with Imperfect Information

TL;DR

This paper explores how an autonomous agent can navigate mazes with indistinguishable rooms under imperfect information, introducing restricted navigability and a logical system to characterize its properties.

Contribution

It introduces restricted navigability and a logical framework that captures its properties even without perfect recall, extending previous work on navigability.

Findings

Restricted navigability exhibits a form of transitivity.

A sound and complete logical system for restricted navigability is developed.

The framework applies to agents with imperfect recall in maze navigation.

Abstract

The article studies navigability of an autonomous agent in a maze where some rooms may be indistinguishable. In a previous work the authors have shown that the properties of navigability in such a setting depend on whether an agent has perfect recall. Navigability by an agent with perfect recall is a transitive relation and without is not transitive. This article introduces a notion of restricted navigability and shows that a certain form of transitivity holds for restricted navigability, even for an agent without perfect recall. The main technical result is a sound and complete logical system describing the properties of restricted navigability.