Affiliations: Department of Computer Science, University of Kentucky, Lexington, KY 40506, E-mail: marek@cs.uky.edu | Mathematical Sciences Institute, Cornell University, Ithaca, NY 14853, E-mail: anil@math.cornell.edu | Department of Mathematics, University of California, La Jolla, CA 92093. E-mail: remmel@kleene.ucsd.edu
Note: [] Research partially supported by NSF grant IRI-9619233, and ARO contract DAAH04-96-1-0398.
Note: [] Research supported by US ARO contract DAAL03-91-C-0027.
Note: [] Research partially supported by NSF grant DMS-9306427.
Abstract: Normal default logic, the fragment of default logic obtained by restricting defaults to rules of the form α:Mβ/β, is the most important and widely studied part of default logic. In [20], we proved a basis theorem for extensions of recursive propositional logic normal default theories and hence for finite predicate logic normal default theories. That is, we proved that every recursive propositional normal default theory possesses an extension which is r.e. in 0′. Here we show that this bound is tight. Specifically, we show that for every r.e. set A and every set B r.e. in A there is a recursive normal default theory 〈D, W〉 with a unique extension which is Turing-equivalent to A ⌖ B. A similar result holds for finite predicate logic normal default theories.
