Armstrong's Axioms and Navigation Strategies

TL;DR

This paper explores how navigability under imperfect information can be characterized logically, extending Armstrong's axioms from database theory to account for scenarios lacking perfect recall.

Contribution

It establishes soundness and completeness theorems for logical systems describing navigability with and without perfect recall, introducing weaker principles when perfect recall is absent.

Findings

Armstrong's axioms characterize navigability with perfect recall.

Without perfect recall, Armstrong's transitivity is invalid but can be replaced.

Logical systems are sound and complete for both scenarios.

Abstract

The paper investigates navigability with imperfect information. It shows that the properties of navigability with perfect recall are exactly those captured by Armstrong's axioms from the database theory. If the assumption of perfect recall is omitted, then Armstrong's transitivity axiom is not valid, but it can be replaced by two new weaker principles. The main technical results are soundness and completeness theorems for the logical systems describing properties of navigability with and without perfect recall.