Simultaneous Replacement in Normal Programs

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