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A Logical Modeling of Severe Ignorance.
S Bonzio1, V Fano2, P Graziani2
1Department of Mathematics and Computer Science, University of Cagliari, Cagliari, Italy.
Journal of Philosophical Logic
|June 26, 2023
Summary
This study introduces a new modal logic to define severe ignorance, distinct from traditional "lack of knowledge" definitions. It models ignorance based on unfamiliarity with meaning, offering a novel content-theoretic perspective.
Area of Science:
- Epistemic Logic
- Modal Logic
- Philosophy of Language
Background:
- Traditional epistemic logic defines ignorance as a mere lack of knowledge.
- This definition struggles to capture ignorance stemming from unfamiliarity with a proposition's meaning (content-theoretic ignorance).
- A need exists for a logical framework that accommodates this nuanced understanding of ignorance.
Purpose of the Study:
- To introduce and investigate a novel modal logic with a primitive operator for ignorance.
- To develop a content-theoretic notion of ignorance, termed 'severe ignorance'.
- To provide a formal system, including semantics, axiomatization, and proofs of completeness and decidability.
Main Methods:
- Construction of a modal logic based on weak Kleene three-valued logic.
- Development of Kripke-style semantics where ignorance is defined by a formula being neither true nor false in accessible worlds.
- Formal axiomatization and proof of completeness and decidability for reflexive three-valued Kripke frames.
Main Results:
- A novel formalization of ignorance, 'severe ignorance', is established.
- This severe ignorance is content-theoretic, arising from unfamiliarity with meaning, unlike traditional epistemic ignorance.
- The proposed logic is axiomatized, and its completeness and decidability are proven for relevant Kripke frames.
Conclusions:
- The developed modal logic successfully models a content-theoretic form of ignorance.
- This approach offers a significant departure from and an advancement over traditional epistemic logic's definition of ignorance.
- The logic provides a formal framework for understanding and analyzing severe ignorance in various contexts.
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