Armstrong's Axioms and Navigation Strategies
This work addresses the problem of navigability under imperfect information for researchers in logic and database theory, providing foundational insights but is incremental as it builds on existing axioms.
The paper investigates navigability with imperfect information, showing that Armstrong's axioms from database theory capture navigability with perfect recall, and introduces two weaker principles for the case without perfect recall, with main results being soundness and completeness theorems for these logical systems.
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.