A Conservative Look at Term Deduction Systems with Variable Binding

We set up a formal framework to describe term deduction systems such as tran sition system speci cations in the style of Plotkin and conditional term rewriting systems This framework has the power to express many sortedness general bind ing mechanisms and substitutions among other notions such as negative premises and unary predicates on terms The framework is used to present a conservativity format in operational se mantics which states su cient criteria to ensure that the extension of a transition system speci cation with new rules does not a ect the behaviour of the original terms Furthermore we show how general theorems in structured operational seman tics can be transformed into results in conditional term rewriting We apply this approach to the conservativity theorem which yields a result that is useful in the eld of abstract data types