Relevance in a Logic of Only Knowing About and its Axiomatization

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In previous work we defined the concept of x is all an agent knows about y by augmenting Levesque’s logic of only-knowing with appropriate modal operators. In this paper we demonstrate how various notions of relevance can be captured within such a logic of only-knowing-about. For example, we are able to formalize what it means for a sentence to be relevant to a subject matter (set of atomic propositions) or for one atomic proposition to be relevant to another relative to some background theory. Moreover, we provide a proof theory for the logic of only-knowing-about. While we have not been able to prove completeness for the whole logic, completeness is established for the class of sentences which is used to define our various notions of relevance.