An observational subset of first-order logic cannot specify the behaviour of a counter (extended abstract)
An “observational” specification language for abstract data types is one that allows only observable aspects of a type to be specified. An observational sublanguage of first-order logic must not contain equations between values of hidden sorts. It is shown that in such a sublanguage the behaviour of a simple counter data type cannot be finitely specified. This implies that more than first-order logic is needed for a useful observational specification language, and that more than first-order logic or a stronger proof rule than previously proposed is needed to work with nonstandard “behavioural” semantics of specifications.
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