Nonmonotonic default modal logics
Michael Tiomkin, Michael Kaminski · Journal of the ACM · 1991
Conclusions by failure to prove the opposite are frequently used in reasoning about an incompletely specdied world.This naturally leads to logics for default reasoning that, in general, are nonmonotonic; that is, introducing new facts can invalidate previously made conclusions.Accordingly, a nonmonotonic theory is called (nonmonotonically) degenerate, if adding new axioms does not invalidate already-proved theorems.Nonmonotonic logics are studied on the basis of various sets of defaults and a necessary and sufficient condition is presented for a nonmonotonic modal theory to be degenerate.In particular, this condition provides several alternative descriptions of degenerate theories.Also some closure properties of sets of defaults defining a nonmonotonic modal logic are established.