L\"ob-Safe Logics for Reflective Agents

TL;DR

This paper explores logical frameworks for rational agents capable of reflection, addressing L"ob's Obstacle, and introduces two new L"ob-safe axiom schemes to improve modeling of knowledge and belief.

Contribution

It identifies limitations of existing epistemic and doxastic logics due to L"ob's Theorem and proposes two novel L"ob-safe axiom schemes to overcome this issue.

Findings

Existing logics suffer from L"ob's Obstacle

Two new L"ob-safe axiom schemes are proposed

The new schemes avoid L"ob's Obstacle in agent modeling

Abstract

Epistemic and doxastic logics are modal logics for knowledge and belief, and serve as foundational models for rational agents in game theory, philosophy, and computer science. We examine the consequences of modeling agents capable of a certain sort of reflection. Such agents face a formal difficulty due to L\"ob's Theorem, called L\"ob's Obstacle in the literature. We show how the most popular axiom schemes of epistemic and doxastic logics suffer from L\"ob's Obstacle, and present two axiom schemes that that avoid L\"ob's Obstacle, which we call Reasonable L\"ob-Safe Epistemic Doxastic logic (${LSED}^R$) and Supported L\"ob-Safe Epistemic Doxastic logic (${LSED}^S$).