A conservative theory of gradable modality

In the tradition of modal semantics stemming from the work of Kratzer (1981, 1991), several attempts have been made to analyze adjectives like important, which are both modal and gradable. I show that existing theories of such gradable modal adjectives (GMAs) in this framework do not allow for comparisons across distinct sets or prioritizations of premises, as the basis for comparison in these theories is too closely wedded to the particular choice and ranking of priorities. To fix this, I include modal degrees in the ontology, with sets of premises being relativized to those degrees. What results is a theory that allows comparison across sets of priorities, while still retaining the premise-based world ordering and quantification that lies at the heart of Kratzer\u27s approach. This theory is then extended to account for existentially-quantifying GMAs like permissible, as well as entailment relations between modal auxiliaries and GMAs