Ignorance as an excuse, formally

TL;DR

This paper introduces a new logical framework to formally analyze ignorance as a moral excuse, focusing on ignorance due to lack of consideration, using epistemic logic with incomplete worlds and public announcement updates.

Contribution

It develops a complete and sound logic with a primitive modality for excusable ignorance and extends it with a novel update procedure for modeling changes in ignorance.

Findings

Introduces a new logical system for modeling ignorance as an excuse.

Provides Kripke semantics with possibly incomplete worlds.

Extends the logic with a novel update mechanism for public announcements.

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.