Abstract
We study proof systems for reasoning about logical consequences and refinement of structured specifications, based on similar systems proposed earlier in the literature (Inform. and Comput. 76 (1988) 165; in: F.L. Bauer, W. Brauer, H. Schwichtenberg (Eds.), Logic and Algebra of Specification, NATO ASI Series F: Computer and Systems Sciences, vol. 94, Springer, Berlin, 1991, p. 411). Following Goguen and Burstall, the notion of an underlying logical system over which we build specifications is formalized as an institution and extended to a more general notion, called ( D, T) -institution. We show that under simple assumptions (essentially: amalgamation and interpolation) the proposed proof systems are sound and complete. The completeness proofs are inspired by proofs due to Cengarle (Ph.D. Thesis, Institut für Informatik, Ludwig-Maximilians-Universität Müenchen, 1994) for specifications in first-order logic and the logical systems for reasoning about them. We then propose a methodology for reusing proof systems built over institutions rich enough to satisfy the properties required for the completeness results for specifications built over poorer institutions where these properties need not hold.
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