A theory of hierarchical consequence and conditionals

We introduce -ranked preferential structures and combine them with an accessibility relation. -ranked preferential structures are intermediate between simple preferential structures and ranked structures. The additional accessibility relation allows us to consider only parts of the overall -ranked structure. This framework allows us to formalize contrary to duty obligations, and other pictures where we have a hierarchy of situations, and maybe not all are accessible to all possible worlds. Representation results are proved.
Keywords Deontic logic  Contrary-to-duties  Preferential structures  Ranked structures  Nonmonotonic logic  Representation results
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DOI 10.1007/s10849-009-9096-7
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Dov M. Gabbay & Karl Schlechta (2009). Roadmap for Preferential Logics. Journal of Applied Non-Classical Logics 19 (1):43-95.

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