|Title:||No More than Necessary: beyond the 'four rules', and a bug report|
|Comment:||Renotated, with terminology update, May 2, 2007. A few typos removed, Feb. 29, 2008|
|Abstract:||After proposing four 'rules of inference' to be used in the program OTSoft for simplifying collections of ranking arguments, Hayes 1997 implicitly raises the question of whether these rules suffice. In this note, the simplification goal is spelled out within the analytical framework of Prince 2002a and Brasoveanu & Prince 2005, in prep. and the question is settled (negatively). A broader generalization subsuming two of Hayesâ€™s rules is offered, however, and shown to provide a complete solution to the simplification problem as formulated. A tighter characterization of the role of disjunctive ranking relations then follows.
Having rules of inference in hand is not the same as having a procedure that uses them effectively. As of this writing, the only known algorithm that produces a fully simplified set of ranking conditions guaranteed to be both individually necessary and jointly sufficient is Fusional Reduction (FRed), presented in Brasoveanu & Prince (op. cit.), which relies on different inferential assumptions.
Consequences for the use of OTSoft are noted. The typological calculations and the stratified hierarchies produced in response to a ranking request are unchallenged. Those subparts of the program which deal with the necessity of ranking conditions (and concomitantly, necessary/non-necessary presence of constraints) must however be used with circumspection and should be supplemented with other methods. Some bugs in this part of the program are reported.