, Volume 19, Issue 1, pp 3-32
Date: 14 Jun 2009

A Theory of Hierarchical Consequence and Conditionals

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We introduce \({\mathcal{A}}\) -ranked preferential structures and combine them with an accessibility relation. \({\mathcal{A}}\) -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 \({\mathcal{A}}\) -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.