Skip to main content

A Proof System with Bounded Non-determinism in Database Transformations

  • Conference paper
Book cover Semantics in Data and Knowledge Bases (SDKB 2010)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 6834))

Included in the following conference series:

Abstract

Database Abstract State Machines (DB-ASMs) provide a universal computation model for database transformations that encompass queries and updates. In this paper we present a proof system for DB-ASMs. It is shown that the proof system for DB-ASMs is sound. As DB-ASMs are restricted by allowing quantifiers over only the database part of a state which is a finite structure, we can formalise non-determinism of DB-ASMs by utilising a modal operator [] for an update set or multiset generated by a DB-ASM rule. In doing so, we lay down a solid foundation for the completeness proof of the proof system proposed for DB-ASMs in this paper.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Börger, E., Stärk, R.F.: Abstract State Machines: A Method for High-Level System Design and Analysis. Springer, Heidelberg (2003)

    Book  MATH  Google Scholar 

  2. Grädel, E., Gurevich, Y.: Metafinite model theory. Information and Computation 140(1), 26–81 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. Groenboom, R., de Renardel Lavalette, G.: Reasoning about dynamic features in specification languages - a modal view on creation and modification. In: Proceedings of the International Workshop on Semantics of Specification Languages (SoSL), pp. 340–355. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  4. Groenboom, R., de Renardel Lavalette, G.: A formalization of evolving algebras. In: Proceedings of Accolade 1995 (1995); Dutch Research School in Logic

    Google Scholar 

  5. Gurevich, Y.: Sequential abstract state machines capture sequential algorithms. ACM Transactions on Computational Logic 1(1), 77–111 (2000)

    Article  MathSciNet  Google Scholar 

  6. Hughes, G., Cresswell, M.: A new introduction to modal logic. Burns & Oates (1996)

    Google Scholar 

  7. de Renardel Lavalette, G.: A logic of modification and creation. In: Logical Perspectives on Language and Information. CSLI publications, Stanford (2001)

    Google Scholar 

  8. Schewe, K.-D., Wang, Q.: A customised ASM thesis for database transformations. Acta Cybernetica 19(4), 765–805 (2010)

    MathSciNet  MATH  Google Scholar 

  9. Schönegge, A.: Extending Dynamic Logic for Reasoning about Evolving Algebras. Technical Report 49/95, Universität Karlsruhe, Fakultät für Informatik (1995)

    Google Scholar 

  10. Stärk, R., Nanchen, S.: A logic for abstract state machine. Journal of Universal Computer Science 7(11) (2001)

    Google Scholar 

  11. Van den Bussche, J.: Formal Aspects of Object Identity in Database Manipulation. PhD thesis, University of Antwerp (1993)

    Google Scholar 

  12. Van den Bussche, J., Van Gucht, D.: Semi-determinism (extended abstract). In: Proceedings of the Eleventh ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pp. 191–201. ACM Press, New York (1992)

    Chapter  Google Scholar 

  13. Wang, Q.: Logical Foundations of Database Transformations for Complex-Value Databases. Logos Verlag, Berlin (2010)

    Google Scholar 

  14. Wang, Q., Schewe, K.-D.: Axiomatization of database transformations. In: Proceedings of the 14th International ASM Workshop (2007)

    Google Scholar 

  15. Wang, Q., Schewe, K.-D.: Towards a Logic for Abstract MetaFinite State Machines. In: Hartmann, S., Kern-Isberner, G. (eds.) FoIKS 2008. LNCS, vol. 4932, pp. 365–380. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wang, Q. (2011). A Proof System with Bounded Non-determinism in Database Transformations. In: Schewe, KD., Thalheim, B. (eds) Semantics in Data and Knowledge Bases. SDKB 2010. Lecture Notes in Computer Science, vol 6834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23441-5_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-23441-5_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23440-8

  • Online ISBN: 978-3-642-23441-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics