Non-monotonic Reasoning via Dynamic Consequence
Logic, Language, Information, and Computation(2022)
摘要
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.
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关键词
dynamic,reasoning,non-monotonic
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