Technical Report CS0487

Title: Nonmonotonic Default Modal Logics
Authors: M. Tiomkin and M. Kaminski
Abstract: Conclusions by the failure to prove the opposite are frequently used in reasoning about incompletely specified world. This naturally leads to logics for default reasoning, which, in general, are nonmonotinic, i.e. introducing new axioms can invalidate old theorems. Accordingly, a set of axioms of a nonmonotonic theory is called (nonmonotonically) degenerating, if adding new axioms does not invalidate already proved theorems. We study nonmonotonic modal logics based on various sets of defaults and present a necessary and sufficient condition for a set of axioms of modal nomonotonic theory to be degenerating. Also we establish some closure properties of sets of defaults defining nonmonotonic modal logics.
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