A Hierarchical Characterization of Ignorance in Epistemic Logic [Special Issue]

Aldini, Alessandro; Graziani, Pierluigi; Tagliaferri, Mirko

We study different forms of ignorance and their correlations in a bi-modal logical language expressing the two modalities of knowledge and belief. In particular, we are mainly interested in clarifying which definitions of ignorance and which circumstances trigger higher-order forms of ignorance, inducing ignorance about ignorance and so on. To this aim, three ground conditions concerning knowledge and belief are presented, which may be seen as a cause of ignorance and can help us to identify the conditions enabling the emergence of higher-order forms of ignorance.

In 1962 Jakko Hintikka published a very influential book for discussions about knowledge (and its lack). The title of this seminal book is Knowledge and beliefs: An introduction to the logic of the two notions (Hintikka 1962). In this work, Hintikka provides a propositional axiomatization of the modal operators K (for knowledge) and B (for belief), as well as insights on the meaning of various forms of knowledge and lack of knowledge, like, e.g., not knowing whether f (Hintikka 1962: 3), which is represented by Hintikka as ~Kf Ù ~K~f (Hintikka 1962: 12). This form of lack of knowledge, which we refer as ignorance whether and will denote in the following with I(f), has indeed been widely investigated in several logical frameworks focused on ignorance, see, e.g., Fan et al. 2015, Steinsvold 2008, and…

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