Non-monotonic Reasoning via Dynamic Consequence

Abstract

We approach the concept of Pivotal Rule Consequence ($\textsf{PRC}$) proposed in [14, 15] from a semantical perspective, resorting to model updates in Public Announcement Logic ($\textsf{PAL}$) [17]. In doing this, we take inspiration from the notion of dynamic consequence from [3, 6]. Our perspective gains in interest since $\textsf{PRC}$ serves as a “bridge” from Classical Logic to Default Logic –one of the most well-known non-monotonic formalisms. We show how the internalization of $\textsf{PRC}$ in $\textsf{PAL}$ leads to clear semantics of the former, and to completeness and transfer results. Moreover, we address the case of credulous consequence in Default Logic as a particular case of $\textsf{PRC}$. Interestingly, we cast credulous consequence as a model checking problem. We argue that our results open the way to use well-known semantic tools from modal logic to study properties of different non-monotonic logics.