Revisable Justified Belief: Preliminary Report
This work addresses a foundational issue in logic and belief revision theory, but it appears incremental as it extends existing theories without demonstrating broad practical impact.
The paper tackles the problem of formalizing revisable justified belief by introducing a theory of Justified Conditional Doxastic Logic (JCDL) that replaces conditional belief formulas with term-based expressions, showing that JCDL-theorems are exact analogs of those in Conditional Doxastic Logic (CDL).
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 $B^ψ\varphi$ by expressions $t{\,:^ψ}\varphi$ made up of a term $t$ whose syntactic structure suggests a derivation of the belief $\varphi$ after revision by $ψ$. 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.