Skip to main content

Completeness of a logical system for structured specifications

  • Contributed Papers
  • Conference paper
  • First Online:
Recent Trends in Algebraic Development Techniques (WADT 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1376))

Included in the following conference series:

Abstract

The main aim of this paper is to present a completeness proof of a formal system for reasoning about logical consequences of structured specifications. The system is based on the proof rules for structural specifications build in an arbitrary institution as presented in [ST 88]. The proof of its completeness is inspired by the proof due to M. V. Cengarle (see [Cen 94]) for specifications in first-order logic and the logical system for reasoning about them presented also in [Wir 91].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. L. Bell, M. Machover. A course in mathematical logic. North-Holland, 1986.

    Google Scholar 

  2. J. A. Bergstra, J. Heering, P. Klint. Module algebra. Journal of the ACM, 37(2):335–372, April 1990.

    Article  Google Scholar 

  3. M. V. Cengarle. Formal Specifications with High-Order Parameterization. Ph.D. thesis, Institut für Informatik, Ludwig-Maximilians-Universität Müenchen, 1994.

    Google Scholar 

  4. R. Diaconescu, J. Goguen, P. Stefaneas. Logical Support for Modularization. In: G. Huet, G. Plotkin, editors Logical Environments, Proceedings of a Workshop held in Edinburgh, Scotland, May 1991, Cambridge University Press, pages 83–130, 1993.

    Google Scholar 

  5. J. Farrés Casals. Verification in ASL and Related Specification Languages. Ph.D. thesis, report CST-92-92, Dept. of Computer Science, University of Edinburgh, 1992.

    Google Scholar 

  6. J. A. Goguen, R. M. Burstall. Institutions: abstract model theory for specifications and programming. Report ECS-LFCS-90-106, University of Edinburgh, 1990.

    Google Scholar 

  7. J. A. Goguen, J.Meseguer. Completeness of many-sorted equational logic. Houston Journal of Mathematics, volume. 11(3), pages 307–334, 1985.

    Google Scholar 

  8. P. D. Mosses. CoFI: The Common Framework Initiative for Algebraic Specification and Development. Theory and Practice of Software Development, volume 1214 of LNCS, pages 115–137, Springer-Verlag, 1997.

    Google Scholar 

  9. D. Sannella, R. Burstall. Structured Theories in LCF. Proc. 8th Colloq. on Trees in Algebra and Programming, L'Aquila, LNCS 159, pp. 377–391, Springer 1983.

    Google Scholar 

  10. D. Sannella, S. Sokolowski, A. Tarlecki. Towards formal development of programs from algebraic specification: parameterization revised. Acta Informatica, volume 29, pages 689–736, 1992.

    Google Scholar 

  11. D. Sannella, A. Tarlecki. Specifications in an Arbitrary Institution Information and Computation, volume 76, pages 165–210, 1988.

    Article  Google Scholar 

  12. D. Sannella, A. Tarlecki. Essential concepts of algebraic specification and program development. To appear in: Formal Aspects of Computing.

    Google Scholar 

  13. A. Tarlecki. Bits and pieces of the theory of institutions. Proc. Workshop on Category Theory and Computer Programming, Guildford. Springer LNCS 240, pages 334–363, 1986.

    Google Scholar 

  14. A. Tarlecki. Moving between logical systems. Recent Trends in Data Type Specifications. Selected Papers. 11th Workshop on Specification of Abstract Data Types ADT'95, Olso, September 1995, eds. M. Haveraaen, O. J. Dahl, O. Owe, Springer LNCS 1130, pages 478–502, 1996.

    Google Scholar 

  15. M. Wirsing. Structured Specifications: Syntax, Semantics and Proof Calculus. In F. L. Bauer, W. Brauer, and H. Schwichtenberg, editors, Logic and Algebra of Specification, volume 94 of NATO ASI Series F: Computer and Systems Sciences, pages 411–442. Springer Verlag, 1991.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Francesco Parisi Presicce

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Borzyszkowski, T. (1998). Completeness of a logical system for structured specifications. In: Presicce, F.P. (eds) Recent Trends in Algebraic Development Techniques. WADT 1997. Lecture Notes in Computer Science, vol 1376. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-64299-4_29

Download citation

  • DOI: https://doi.org/10.1007/3-540-64299-4_29

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64299-2

  • Online ISBN: 978-3-540-69719-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics