My work with Victor Marek: a mathematician looks at answer set programming
Annals of Mathematics and Artificial Intelligence
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Normal default logic, the fragment of default logic obtained by restricting defaults to rules of the form a:Mb/b (here a and b are sentences of underlying language) is the most important and widely studied part of default logic. In an earlier paper 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 (here + is the operation of disjoint union of sets) . A similar result holds for finite predicate logic normal default theories.}