We take the internalization of the concept of Pivotal Rules Consequence ( \(\textsf{PRC}\) ) into Public Announcement Logic ( \(\textsf{PAL}\) ) in [2] and rework it into Action Model Logic ( \(\textsf{AML}\) ) [5]. \(\textsf{PRC}\) is introduced in [9] as a way of building a “bridge” from monotonic to nonmonotonic consequence using so called pivotal rules. Particularly interesting is how \(\textsf{PRC}\) leads gradually to consequence in Default Logic ( \(\textsf{DL}\) ) [11]. In [2], drawing inspiration from the dynamic take on consequence proposed in [3, 4], it is shown how \(\textsf{PRC}\) can be captured into \(\textsf{PAL}\)  [10] by encoding pivotal rules as announcements. Here we rework the ideas in [2] into \(\textsf{AML}\) by casting pivotal rules into action models. We consider action models provide a more accurate way of modeling the semantics of pivotal rules as standalone elements of \(\textsf{PRC}\) ; therefore providing a better account of the dynamic effect of pivotal rules. More interesting, we consider the internalization of pivotal rules as action models to open the door to a way for thinking about agent-dependent pivotal rules, i.e., pivotal rules associated to individual agents. This would allow, for instance, to model exceptions to general rules but from the viewpoint of a particular agent rather than the global nature of exceptions to rules found in Default Logics.

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Pivotal Rules Consequence in Action Model Logic

  • Valentin Cassano,
  • Sabine Frittella

摘要

We take the internalization of the concept of Pivotal Rules Consequence ( \(\textsf{PRC}\) ) into Public Announcement Logic ( \(\textsf{PAL}\) ) in [2] and rework it into Action Model Logic ( \(\textsf{AML}\) ) [5]. \(\textsf{PRC}\) is introduced in [9] as a way of building a “bridge” from monotonic to nonmonotonic consequence using so called pivotal rules. Particularly interesting is how \(\textsf{PRC}\) leads gradually to consequence in Default Logic ( \(\textsf{DL}\) ) [11]. In [2], drawing inspiration from the dynamic take on consequence proposed in [3, 4], it is shown how \(\textsf{PRC}\) can be captured into \(\textsf{PAL}\)  [10] by encoding pivotal rules as announcements. Here we rework the ideas in [2] into \(\textsf{AML}\) by casting pivotal rules into action models. We consider action models provide a more accurate way of modeling the semantics of pivotal rules as standalone elements of \(\textsf{PRC}\) ; therefore providing a better account of the dynamic effect of pivotal rules. More interesting, we consider the internalization of pivotal rules as action models to open the door to a way for thinking about agent-dependent pivotal rules, i.e., pivotal rules associated to individual agents. This would allow, for instance, to model exceptions to general rules but from the viewpoint of a particular agent rather than the global nature of exceptions to rules found in Default Logics.