Revisable Justified Belief: Preliminary Report

TL;DR

This paper introduces a new logical framework, JCDL, that models revisable justified beliefs by integrating reasons into belief revision, extending the existing CDL theory with justification structures.

Contribution

The paper develops JCDL, a logic that incorporates reasons into belief revision, establishing a correspondence with CDL and enabling formal reasoning about revisable justified beliefs.

Findings

JCDL theorems are equivalent to CDL theorems

JCDL provides a formal structure for revisable justified beliefs

The theory bridges belief revision and justification logic

Abstract

The theory $\mathsf{CDL}$ of Conditional Doxastic Logic is the single-agent version of Board's multi-agent theory $\mathsf{BRSIC}$ of conditional belief. $\mathsf{CDL}$ may be viewed as a version of AGM belief revision theory in which Boolean combinations of revisions are expressible in the language. We introduce a theory $\mathsf{JCDL}$ of Justified Conditional Doxastic Logic that replaces conditional belief formulas $B^\psi\varphi$ by expressions $t{\,:^{\psi}}\varphi$ made up of a term $t$ whose syntactic structure suggests a derivation of the belief $\varphi$ after revision by $\psi$. This allows us to think of terms $t$ as reasons justifying a belief in various formulas after a revision takes place. We show that $\mathsf{JCDL}$-theorems are the exact analogs of $\mathsf{CDL}$-theorems, and that this result holds the other way around as well. This allows us to think of $\mathsf{JCDL}$ as a theory of revisable justified belief.