A Logical Modeling of Severe Ignorance

Journal of Philosophical Logic 52 (4):1053-1080 (2023)
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In the logical context, ignorance is traditionally defined recurring to epistemic logic. In particular, ignorance is essentially interpreted as “lack of knowledge”. This received view has - as we point out - some problems, in particular we will highlight how it does not allow to express a type of content-theoretic ignorance, i.e. an ignorance of φ that stems from an unfamiliarity with its meaning. Contrarily to this trend, in this paper, we introduce and investigate a modal logic having a primitive epistemic operator I, modeling ignorance. Our modal logic is essentially constructed on the modal logics based on weak Kleene three-valued logic introduced by Segerberg (Theoria, 33(1):53–71, 1997). Such non-classical propositional basis allows to define a Kripke-style semantics with the following, very intuitive, interpretation: a formula φ is ignored by an agent if φ is neither true nor false in every world accessible to the agent. As a consequence of this choice, we obtain a type of content-theoretic notion of ignorance, which is essentially different from the traditional approach. We dub it severe ignorance. We axiomatize, prove completeness and decidability for the logic of reflexive (three-valued) Kripke frames, which we find the most suitable candidate for our novel proposal and, finally, compare our approach with the most traditional one.



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Author Profiles

Stefano Bonzio
University of Turin
Pierluigi Graziani
Università degli Studi di Urbino
Vincenzo Fano
Università degli Studi di Urbino

Citations of this work

Axiomatizing Rumsfeld Ignorance.Jie Fan - 2023 - Journal of Philosophical Logic 53 (1):79-97.

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Knowledge and belief.Jaakko Hintikka - 1962 - Ithaca, N.Y.,: Cornell University Press.
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The Logic of Nonsense.Sören Halldén - 1949 - Uppsala, Sweden: Upsala Universitets Arsskrift.

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