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.

在逻辑背景下，无知传统上被定义为反复出现在认知逻辑中。特别是，无知本质上被解释为“缺乏知识”。正如我们所指出的，这种公认的观点存在一些问题，特别是我们将强调它如何不允许表达一种内容论的无知，即由于不熟悉其含义而对φ的无知。与这种趋势相反，在本文中，我们引入并研究了一种具有原始认知算子I的模态逻辑，即对无知进行建模。我们的模态逻辑本质上是基于 Segerberg 引入的弱 Kleene 三值逻辑的模态逻辑构建的（Theoria, 33 (1):53–71, 1997）。这种非经典命题基础允许用以下非常直观的解释来定义克里普克式语义：如果在代理可访问的每个世界中φ既不是真也不是假，则代理将忽略公式φ 。作为这种选择的结果，我们获得了一种内容论的无知概念，它与传统方法本质上不同。我们称之为严重无知。我们公理化，证明自反（三值）克里普克框架逻辑的完整性和可判定性，我们找到了最适合我们新颖提议的候选者，最后，将我们的方法与最传统的方法进行比较。