Skip to main content
SpringerLink
Log in

Specification, Abduction, and Proof

  • Conference paper
Automated Technology for Verification and Analysis (ATVA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3299))

Abstract

Researchers in formal methods have emphasized the need to make specification analysis as automatic as possible and to provide an array of tools in a uniform setting. Athena is a new interactive proof system that supports specification, structured natural deduction proofs, and trusted tactics. It places heavy emphasis on automation, seamlessly incorporating off-the-shelf state-of-the-art tools for model generation and automated theorem proving. We use a case study of railroad safety to illustrate several aspects of Athena. A formal specification of a railroad system is given in Athena’s multi-sorted first-order logic. Automatic model generation is used abductively to develop from scratch a policy for controlling the movement of trains on the tracks. The safety of the policy is proved automatically. Finally, a structured high-level proof of the policy’s correctness is presented in Athena’s natural deduction calculus.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Arkoudas, K.: Athena, http://www.cag.csail.mit.edu/~kostas/dpls/athena

  2. Arkoudas, K.: Denotational Proof Languages. PhD dissertation, MIT (2000)

    Google Scholar 

  3. Arkoudas, K., Khurshid, S., Marinov, D., Rinard, M.: Integrating model checking and theorem proving for relational reasoning. In: Proceedings of the 7th International Seminar on Relational Methods in Computer Science (RelMiCS 7), Malente, Germany (May 2003)

    Google Scholar 

  4. Arvizo, T.: A virtual machine for a type-ω denotational proof language. Masters thesis, MIT (June 2002)

    Google Scholar 

  5. Ball, T., Rajamani, S.: Automatically validating temporal safety properties of interfaces. In: Dwyer, M.B. (ed.) SPIN 2001. LNCS, vol. 2057, p. 103. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  6. Claessen, K., Sorensson, N.: New techniques that improve Mace-style finite model building. In: Model Computation—principles, algorithms, applications, Miami, Florida, USA (1973)

    Google Scholar 

  7. Cyrluk, D., Rajan, S., Shankar, N., Srivas, M.K.: Effective theorem proving for hardware verification. In: Kumar, R., Kropf, T. (eds.) TPCD 1994. LNCS, vol. 901, pp. 203–222. Springer, Heidelberg (1995)

    Google Scholar 

  8. Gordon, M.J.C., Melham, T.F.: Introduction to HOL, a theorem proving environment for higher-order logic. Cambridge University Press, Cambridge (1993)

    MATH  Google Scholar 

  9. Halpern, J.Y., Harper, R., Immerman, N., Kolaitis, P.G., Vardi, M.Y., Vianu, V.: On the unusual effectiveness of logic in computer science. The Bulletin of Symbolic Logic 7(2), 213–236 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  10. Heitmeyer, C.L.: On the need for practical formal methods. In: Proceedings of the 5th International Symposium on Formal Techniques in Real-Time and Fault- Tolerant Systems, pp. 18–26. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  11. Hurd, J.: Integrating Gandalf and HOL. In: Theorem proving in higher-order logics, pp. 311–321 (1999)

    Google Scholar 

  12. Jackson, D.: Railway Safety (2002), http://alloy.mit.edu/case-studies.html

  13. Jackson, D.: Alloy: a lightweight object modelling notation. Software Engineering and Methodology 11(2), 256–290 (2002)

    Article  Google Scholar 

  14. Jackson, D., Sullivan, K.: COM revisited: Tool-assisted modeling of an architectural framework. In: Proc. 8th ACM SIGSOFT Symposium on the Foundations of Software Engineering (FSE), San Diego, CA (2000)

    Google Scholar 

  15. Josephson, J.R., Josephson, S.G. (eds.): Abductive Inference: Computation, Philosophy, Technology. Cambridge University Press, Cambridge (1994)

    MATH  Google Scholar 

  16. Kakas, C., Denecker, M.: Abduction in logic programming. In: Kakas, A.C., Sadri, F. (eds.) Computational Logic: Logic Programming and Beyond. LNCS (LNAI), vol. 2407, pp. 402–436. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  17. Kaufmann, M., Manolios, P., Moore, J.S. (eds.): Computer-Aided Reasoning: ACL2 Case Studies. Kluwer Academic Press, Dordrecht (2000)

    Google Scholar 

  18. Khurshid, S., Jackson, D.: Exploring the design of an intentional naming scheme with an automatic constraint analyzer. In: 15th IEEE ASE (2000)

    Google Scholar 

  19. Lamport, L.: How to write a proof. Research Report 94, Systems Research Center, DEC (February 1993)

    Google Scholar 

  20. Manna, Z., Waldinger, R.: The logical basis for computer programming. Addison Wesley, Reading (1985)

    MATH  Google Scholar 

  21. Manzano, M.: Extensions of first-order logic. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge (1996)

    Google Scholar 

  22. McCune, W.: A Davis-Putnam program and its application to finite first-order model search. Technical Report ANL/MCS-TM-194, ANL (1994)

    Google Scholar 

  23. Owre, S., Shankar, N., Rushby, J.M.: The PVS specification language (draft). Research report, Computer Science Laboratory, SRI International, Menlo Park, California (February 1993)

    Google Scholar 

  24. Paulson, L.: Isabelle, A Generic Theorem Prover. LNCS. Springer, Heidelberg (1994)

    MATH  Google Scholar 

  25. Pelletier, F.J.: A Brief History of Natural Deduction. History and Philosophy of Logic 20, 1–31 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  26. Schumann, J.: Automated theorem proving in high-quality software design. In: Hölldobler, S. (ed.) Intellectics and Computational Logic. Applied Logic Series, vol. 19, Kluwer, Dordrecht (2000)

    Google Scholar 

  27. Spivey, J.M.: The Z Notation: A Reference Manual. Prentice-Hall, Inc., Englewood Cliffs (1992)

    Google Scholar 

  28. Suttner, C., Sutcliffe, G.: Technical Report on the TPTP Problem Library, http://www.cs.miami.edu/~tptp/TPTP/TR/TPTPTR.shtml

  29. Tammet, T.: Gandalf, http://www.cs.chalmers.se/~tammet/gandalf/

  30. Voronkov, A.: The anatomy of Vampire: implementing bottom-up procedures with code trees. Journal of Automated Reasoning 15(2) (1995)

    Google Scholar 

  31. Weidenbach, C.: Combining superposition, sorts, and splitting. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. 2, North-Holland, Amsterdam (2001)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. MIT Computer Science and AI Lab,  

    Konstantine Arkoudas

Authors
  1. Konstantine Arkoudas
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Grad. Inst. of Electronic Engineering, National Taiwan University, Taiwan, ROC

    Farn Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Arkoudas, K. (2004). Specification, Abduction, and Proof. In: Wang, F. (eds) Automated Technology for Verification and Analysis. ATVA 2004. Lecture Notes in Computer Science, vol 3299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30476-0_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-30476-0_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23610-8

  • Online ISBN: 978-3-540-30476-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation