Abstract
We approach the concept of Pivotal Rule Consequence (PRC) proposed in [14, 15] from a semantical perspective, resorting to model updates in Public Announcement Logic (PAL
) [17]. In doing this, we take inspiration from the notion of dynamic consequence from [3, 6]. Our perspective gains in interest since 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 PRC in 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 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.
) [17]. In doing this, we take inspiration from the notion of dynamic consequence from [3, 6]. Our perspective gains in interest since 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 PRC in 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 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.
| Original language | English |
|---|---|
| Title of host publication | International Workshop on Logic, Language, Information, and Computation |
| Publisher | Springer International Publishing |
| DOIs | |
| State | Published - 9 Sep 2022 |
| Externally published | Yes |