Minimal Revision and Classical Kripke Models

Abstract

Dynamic modal logics are modal logics that have statements of the form [π]ψ. The truth value of such statements, when evaluated in a pointed model 〈$\cal F$, V, ω〉, is determined by the truth value that ψ takes in the pointed models 〈$\cal F\prime$, V′, ω′〉 that stand in a relation $\xrightarrow{\pi}$ to 〈$\cal F$, V, ω〉.

This paper introduces new dynamic operators that minimally revise finite classical Kripke models to make almost any satisfiable modal formula φ true. To this end, we define the minimal revision relations $\xrightarrow{\dagger \phi}$ and $\xrightarrow{\ddagger \phi}$, where $\xrightarrow{\dagger \phi}$ revises only the valuation function and $\xrightarrow{\ddagger \phi}$ also changes the frame.

We show that our language enables us to count the number of accessible worlds and to characterize irreflexive frames. We also demonstrate that any consistent formula can be made true, conditional only on modest seriality and finiteness presumptions.