Checking Conservativity with Hets
Conservative extension is an important notion in the theory of formal specification . If we can implement a specification SP, we can implement any conservative extension of SP as well. Hence, a specification can be shown consistent by starting with a consistent specification and extending it using a number of conservative extension steps. This is important, because during a formal development, it is desirable to guarantee consistency of specifications as soon as possible. Checks for conservative extensions also arise in calculi for proofs in structured specifications [12,9]. Furthermore, consistency is a special case of conservativity: it is just conservativity over the empty specification. Moreover, using consistency, also non-consequence can be checked: an axiom does not follow from a specification if the specification augmented by the negation of the axiom is consistent. Finally,  puts forward the idea of simplifying the task of checking consistency of large theories by decomposing them with the help of an architectural specification . In order to show that an architectural specification is consistent, it is necessary to show that a number of extensions are conservative (more precisely, the specifications of its generic units need to be conservative extensions of their argument specifications, and those of the non-generic units need to be consistent).
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