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.