We set up a formal framework to describe term deduction systems, such as transition system specifications in the style of Plotkin, and conditional term rewriting
systems. This framework has the power to express many-sortedness, general binding 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 semantics, which states sufficient criteria to ensure that the extension of a transition
system specification with new rules does not affect the behaviour of the original
terms.
Furthermore, we show how general theorems in structured operational semantics 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
field of abstract data types
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