This paper provides new examples of vagueness phenomena with comparatives. I show that comparatives of the form ‘x is ADJ-er than y’ can be vague due to a fuzziness in how much of some property makes for a difference in ADJ-ness. The sorites examples I provide cannot be assimilated to cases of indiscriminability or fuzziness in relevant dimensions, standards, or measurement procedures. A revised degree-based semantics with semiorders, a well studied threshold structure, is developed. The treatment of equatives captures (...) the truth of the claim that adjacent items in the sorites series are not relevantly distinguishable in ADJ-ness; and it avoids validating transitivities that would yield paradoxical conclusions. (shrink)

Darwiche and Pearl’s seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. Most suggestions have resulted in a form of ‘reductionism’ that identifies belief states with orderings of worlds. However, this position has recently been criticised as being unacceptably strong. Other proposals, such as the popular principle (P), aka ‘Independence’, characteristic of ‘admissible’ operators, remain commendably more modest. In this (...) paper, we supplement the DP postulates and (P) with a number of novel conditions. While the DP postulates constrain the relation between a prior and a posterior conditional belief set, our new principles notably govern the relation between two posterior conditional belief sets obtained from a common prior by different revisions. We show that operators from the resulting family, which subsumes both lexicographic and restrained revision, can be represented as relating belief states associated with a ‘proper ordinal interval’ (POI) assignment, a structure more fine-grained than a simple ordering of worlds. We close the paper by noting that these operators satisfy iterated versions of many AGM era postulates, including Superexpansion, that are not sound for admissible operators in general. (shrink)