Ignorance with(out) Grasping

TL;DR

This paper introduces a hyperintensional approach to modeling different forms of ignorance using topic-sensitive semantics, providing new logical systems that better reflect intuitive distinctions in what agents know or ignore.

Contribution

It develops a formal, sound, and complete framework for representing various ignorance types through topic-sensitive semantics, improving upon standard Kripke semantics.

Findings

Formalizes ignorance as a hyperintensional notion

Provides sound and complete systems for three ignorance forms

Addresses the logical omniscience problem with content-aware models

Abstract

In this work, we argue that ignorance can be inherently understood as a hyperintensional notion. When faced with two logically or necessarily equivalent propositions, an agent may be ignorant of one while not of the other. To capture formally this intuition, we employ a topic-sensitive semantics, enabling the modeling of an agent's attitude toward the content of a proposition. Within this framework, we reevaluate three existing logical systems, usually characterized by standard Kripke semantics, to account for three forms of ignorance: ignorance whether, ignorance as unknown truth, and disbelieving ignorance. For each form, we present a sound and complete system. To highlight the advantage of this approach, we apply it to address the problem of logical omniscience rephrased in terms of ignorance. The resulting framework considers an agent's capacity to grasp the content of a proposition, bridging the gap between standard relational settings for ignorance representation and natural intuitions about the role of content in forming one's ignorance.