This paper studies the transformation of "predicate introduction": replacing a complex formula in an existing logic program by a newly defined predicate. From a knowledge representation perspective, such transformations can be used to eliminate redundancy or to simplify a theory. From a more practical point of view, they can also be used to transform a theory into a normal form imposed by certain inference programs or theorems, e.g., through the elimination of universal quantifiers. In this paper, we study when predicate introduction is equivalence preserving under the stable and well-founded semantics. We do this in the algebraic framework of "approximation theory"; this is a fixpoint theory for non-monotone operators that generalizes all main semantics of various non-monotone logics, including Logic Programming, Default Logic and Autoepistemic Logic. We prove an abstract, algebraic equivalence result and then instantiate this abstract theorem to Logic Programming under the stable and well-founded semantics.
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