TL;DR
This paper develops new axiomatizations for Rumsfeld ignorance by distinguishing its accessibility relation from ignorance, avoiding previous definability issues and analyzing logical properties.
Contribution
It introduces a framework with separate accessibility relations for ignorance and Rumsfeld ignorance, enabling meaningful axiomatizations and analysis.
Findings
Axiomatizations over various bi-frame classes are provided.
The framework clarifies the logical properties of Rumsfeld ignorance.
Previous results are re-evaluated within the new framework.
Abstract
In a recent paper, Kit Fine presents some striking results concerning the logical properties of (first-order) ignorance, second-order ignorance and Rumsfeld ignorance. However, Rumsfeld ignorance is definable in terms of ignorance, which makes some existing results and the axiomatization problem trivial. A main reason is that the accessibility relations for the implicit knowledge operator contained in the packaged operators of ignorance and Rumsfeld ignorance are the same. In this work, we assume the two accessibility relations to be different so that one of them is an arbitrary subset of the other. This will avoid the definability issue and retain most of the previous validities. The main results are axiomatizations over various proper bi-frame classes. Finally we apply our framework to analyze Fine's results.
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