Logics of Ignorance and Being Wrong

This article investigates the connections between the logics of being wrong, introduced in Steinsvold (2011, Notre Dame J. Form. Log., 52, 245-253), and factive ignorance, presented in Kubyshkina and Petrolo (2021, Synthese, 198, 5917-5928). The first part of the paper provides a sound and complete axiomatization of the logic of factive ignorance that corrects errors in Kubyshkina and Petrolo (2021, Synthese, 198, 5917-5928) and resolves questions about the expressivity of the language. In the second half, it is shown that the relationship between the two logics suggests an alternative axiomatization for the logic of factive ignorance, the adequacy of which is easily proved via straightforward translations.

Automated summary

This article investigates the connections between the logics of being wrong and factive ignorance, providing a sound and complete axiomatization of the latter. It also suggests an alternative axiomatization for the logic of factive ignorance, which is easily proved via straightforward translations.