Non-monotonic Reasoning via Dynamic Consequence

C. Areces, V. Cassano, and R. Fervari. Non-monotonic Reasoning via Dynamic Consequence. In A. Ciabattoni, E. Pimentel, and R. de Queiroz, editors, Logic, Language, Information, and Computation - 28th International Workshop, WoLLIC 2022, Ia\csi, Romania, September 20-23, 2022, Proceedings, Lecture Notes in Computer Science, pp. 395–410, Springer, 2022.

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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.

BibTeX

@InCollection{ArecesCF22,
  author =       "C. Areces and V. Cassano and R. Fervari",
  booktitle =    "Logic, Language, Information, and Computation - 28th
                 International Workshop, WoLLIC 2022, Ia{\c{s}}i,
                 Romania, September 20-23, 2022, Proceedings",
  title =        "Non-monotonic Reasoning via Dynamic Consequence",
  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.",
  year =         "2022",
  editor =       "A. Ciabattoni and E. Pimentel and R. de Queiroz",
  pages =        "395--410",
  publisher =    "Springer",
  series =       "Lecture Notes in Computer Science",
  volume =       "13468",
  biburl =       "https://dblp.org/rec/conf/wollic/ArecesCF22.bib",
  doi =          "10.1007/978-3-031-15298-6\_25",
  timestamp =    "Mon, 19 Sep 2022 18:41:40 +0200",
  URL =          "https://doi.org/10.1007/978-3-031-15298-6\_25",
  ISBN =         "978-3-031-15297-9",
}