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On Using Conditional Definitions in Formal Theories

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ZB 2002:Formal Specification and Development in Z and B (ZB 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2272))

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Abstract

In this paper, our intention is to explore the notion of definition in formal theories and, in particular, that of conditional definitions. We are also interested in analyzingthe consequences of the latter on the structure of corresponding proof systems. Finally, we shall investigate the various ways such proof systems can be simplified.

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References

  1. J.R. Abrial. The B-Book:Assigning Programs to Meanings. Cambridge University Press (1996).

    Google Scholar 

  2. H. Barringer, J.H. Cheng, C.B. Jones. A Logic Covering Undefinedness in Program Proofs. Acta Informatica 21: 251–269 (1984).

    Article  MATH  MathSciNet  Google Scholar 

  3. P. Behm, L. Burdy, J.M. Meynadier. Well defined B. Second B International Conference. (Bert editor) LNCS 1393 Springer (1998).

    Google Scholar 

  4. L. Burdy Traitement des expressions dépourvues de sens de la théorie des ensembles. Thèse de Doctorat (2000).

    Google Scholar 

  5. J.H. Cheng, C.B. Jones On the Usability of Logics which Handle Partial Functions. Proceedings of Third Refinement Workshop. (1990).

    Google Scholar 

  6. D. Gries. Foundations for Calculational Logic in Mathematical Methods in Program Development (M. Broy and B. Schieder Editors). Springer (1996).

    Google Scholar 

  7. C.B. Jones Partial Functions and Logics: a warning. Information Processing Letter 54 (1995).

    Google Scholar 

  8. B. Stoddart, S. Dunne, A. Galloway. Undefined Expressions and Logic in Z and B. Formal Methods in System Design, 15 (1999).

    Google Scholar 

  9. P. Suppes. Introduction to Logic. Wadsworth International Group (1957).

    Google Scholar 

  10. W.M. Farmer and J.D. Guttman. A Set Theory with Support for Partial Functions in Partiality and Modality. (E. Thijsse, F. Lepage, and H. Wansing Editors). Special issue of Logica Studia (2000).

    Google Scholar 

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© 2002 Springer-Verlag Berlin Heidelberg

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Abrial, JR., Mussat, L. (2002). On Using Conditional Definitions in Formal Theories. In: Bert, D., Bowen, J.P., Henson, M.C., Robinson, K. (eds) ZB 2002:Formal Specification and Development in Z and B. ZB 2002. Lecture Notes in Computer Science, vol 2272. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45648-1_13

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  • DOI: https://doi.org/10.1007/3-540-45648-1_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43166-4

  • Online ISBN: 978-3-540-45648-3

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