Ranked ordering sources and embedded modality

I present an ordering semantics for modality in which possible worlds are ordered by ordering sources augmented with a partial order structure. This extension of Kratzer's (1991) ordering semantics allows propositions to contribute to the ideal defined by an ordering source with differing degrees of priority and allows this priority relation to vary with the world of evaluation. Although the * operator of Katz et al. (2012) also allows ordering sources to be combined with different degrees of priority, I show that it does not account for a variant of Goble's (1996) Medicine Problem in which a modal is embedded under an attitude verb. I also extend the investigation by Katz et al. (2012) into the combinatorial structure of complex ordering sources by proposing a generalization of their * operator for partially ordered ordering sources