Time and Relational Theory, 2nd Edition

Appendix B

Is Ordinality Necessary?

This appendix considers the possibility of dropping the so called discreteness assumption (the assumption, that is, that the timeline consists of a finite number of discrete time points); in other words, it investigates the idea of defining intervals over a point type that’s ordered but not ordinal, and using such intervals in practical applications. Allen’s operators are reexamined in this light and are found still to be applicable, though their definitions need to be refined somewhat. However, UNPACK doesn’t apply, and there are serious problems in even representing such intervals (none of the usual styles—closed:closed, etc.—turns out to be completely satisfactory). The conclusion is that there’s nothing ...