Ignorance as an excuse, formally

TL;DR

The paper formalizes ignorance as a moral excuse by introducing LEI, a complete and sound logic of excusable ignorance with a primitive modality $I$ embedded in a Kripke framework that allows incomplete worlds and Kleene-style three-valued truth. It then extends this static framework with a dynamic public-announcement mechanism, LEI$^{up}$, designed to preserve prior truths while accommodating new content, including non-true announcements when consistent with current knowledge. Through canonical models and extended-model semantics, the authors prove soundness and completeness for LEI and LEI$^{up}$ and illustrate how excusable ignorance can evolve into non-excusable ignorance under announcements, aligning with Peels' ethical scenarios. The work provides a rigorous tool for analyzing moral responsibility under ignorance, with a dynamic mechanism that could be applied to broader epistemic and doxastic logics.

Abstract

There is a lively debate in the current literature on epistemology on which type of ignorance may provide a moral excuse. A good candidate is the one in which an agent has never thought about or considered as true a proposition $p$. From a logical perspective, it is usual to model situations involving ignorance by means of epistemic logic. However, no formal analysis has been provided for ignorance as an excuse. We fill this gap by proposing an original logical setting for modelling this type of ignorance. In particular, we introduce a complete and sound logic in which excusable ignorance is expressed as a primitive modality. This logic is characterized by Kripke semantics with possibly incomplete worlds. Moreover, to consider the conditions of a possible change of an agent's ignorance, we will extend the setting to public announcement logic equipped with a novel update procedure.

Figures (9)

• Figure 1: Various forms of ignorance
• Figure 2: Model $\mathcal{M}_{1}$
• Figure 3: Model $\mathcal{M}_{1}|_{p}$
• Figure 4: Model $\mathcal{M}_{1}|'_{p}$
• Figure 5: Model $\mathcal{M}_{2}$

Theorems & Definitions (60)

• Definition 1
• Definition 2: Frames, Models, and Satisfaction
• Definition 3: System Lt2
• Proposition 1
• Definition 4: System LEI
• Proposition 2
• Proposition 3
• Proposition 4
• Proposition 5
• Lemma 1: Soundness