Ordering combination for modal comparison

The well-known ordering semantics for modality has recently been challenged by a number of puzzles which may cast doubt on the viability of this approach. We investigate the properties of the ordering relations used in ordering semantics with a focus on how to derive appropriate orderings based on intuitively correct premises. We use these tools to propose solutions to two of the puzzles and discuss how they relate to other puzzles that have been raised in the literature, and to modal semantics more generally.