A Theory of Hierarchical Consequence and Conditionals |
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| Authors: | Dov M. Gabbay Karl Schlechta |
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| Affiliation: | 1.Department of Computer Science,King’s College London,London,UK;2.Department of Computer Science,Bar-Ilan University,Ramat-Gan,Israel;3.Laboratoire d’Informatique Fondamentale de Marseille, UMR 6166,CNRS and Université de Provence,Marseille Cedex 13,France |
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| Abstract: | We introduce A{mathcal{A}} -ranked preferential structures and combine them with an accessibility relation. A{mathcal{A}} -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 A{mathcal{A}} -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. |
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