Simultaneous Replacement in Normal Programs

The simultaneous replacement transformation operation is here defined and studied w.r.t. normal programs. We give applicability conditions able to ensure the correctness of the operation w.r.t. the set of logical consequences of the completed database. We consider separately the cases in which the underlying language is infinite and finite; in this latter case we also distinguish according to the kind of domain closure axioms adopted. As corollaries we obtain results for Fitting's and Kunen's semantics. We also show how simultaneous replacement can mimic other transformation operations such as thinning, fattening and folding, thus producing applicability conditions for them too

More on Unfold/Fold Transformations of Normal Programs: Preservation of Fitting's Semantics

The unfold/fold transformation system defined by Tamaki and Sato was meant for definite programs. It transforms a program into an equivalent one in the sense of both the least Herbrand model semantics and the Computed Answer Substitution semantics. Seki extended the method to normal programs and specialized it in order to preserve also the finite failure set. The resulting system is correct wrt nearly all the declarative semantics for normal programs. An exception is Fitting's model semantics. In this paper we consider a slight variation of Seki's method and we study its correctness wrt Fitting's semantics. We define an applicability condition for the fold operation and we show that it ensures the preservation of the considered semantics through the transformation

Simultaneous Replacement in Normal Programs

The simultaneous replacement transformation operation, is here defined and studied wrt normal programs. We give applicability conditions able to ensure the correctness of the operation wrt the set of logical consequences of the completed database. We consider separately the cases in which the underlying language is infinite and finite; in this latter case we also distinguish according to the kind of domain closure axioms adopted. As corollaries we obtain results for Fitting's and Kunen's semantics. We also show how simultaneous replacement can mimic other transformation operations such as thinning, fattening and folding, thus producing applicability conditions for them too