Abstract
Conservative extension is an important notion in the theory of formal specification [8]. 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, [3] puts forward the idea of simplifying the task of checking consistency of large theories by decomposing them with the help of an architectural specification [2]. 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).
This work has been supported by the BMBF project SHIP.
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Codescu, M., Mossakowski, T., Maeder, C. (2013). Checking Conservativity with Hets . In: Heckel, R., Milius, S. (eds) Algebra and Coalgebra in Computer Science. CALCO 2013. Lecture Notes in Computer Science, vol 8089. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40206-7_24
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