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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arkoudas, K.: Athena, http://www.cag.csail.mit.edu/~kostas/dpls/athena
Arkoudas, K.: Denotational Proof Languages. PhD dissertation, MIT (2000)
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)
Arvizo, T.: A virtual machine for a type-ω denotational proof language. Masters thesis, MIT (June 2002)
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)
Claessen, K., Sorensson, N.: New techniques that improve Mace-style finite model building. In: Model Computation—principles, algorithms, applications, Miami, Florida, USA (1973)
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)
Gordon, M.J.C., Melham, T.F.: Introduction to HOL, a theorem proving environment for higher-order logic. Cambridge University Press, Cambridge (1993)
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)
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)
Hurd, J.: Integrating Gandalf and HOL. In: Theorem proving in higher-order logics, pp. 311–321 (1999)
Jackson, D.: Railway Safety (2002), http://alloy.mit.edu/case-studies.html
Jackson, D.: Alloy: a lightweight object modelling notation. Software Engineering and Methodology 11(2), 256–290 (2002)
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)
Josephson, J.R., Josephson, S.G. (eds.): Abductive Inference: Computation, Philosophy, Technology. Cambridge University Press, Cambridge (1994)
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)
Kaufmann, M., Manolios, P., Moore, J.S. (eds.): Computer-Aided Reasoning: ACL2 Case Studies. Kluwer Academic Press, Dordrecht (2000)
Khurshid, S., Jackson, D.: Exploring the design of an intentional naming scheme with an automatic constraint analyzer. In: 15th IEEE ASE (2000)
Lamport, L.: How to write a proof. Research Report 94, Systems Research Center, DEC (February 1993)
Manna, Z., Waldinger, R.: The logical basis for computer programming. Addison Wesley, Reading (1985)
Manzano, M.: Extensions of first-order logic. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge (1996)
McCune, W.: A Davis-Putnam program and its application to finite first-order model search. Technical Report ANL/MCS-TM-194, ANL (1994)
Owre, S., Shankar, N., Rushby, J.M.: The PVS specification language (draft). Research report, Computer Science Laboratory, SRI International, Menlo Park, California (February 1993)
Paulson, L.: Isabelle, A Generic Theorem Prover. LNCS. Springer, Heidelberg (1994)
Pelletier, F.J.: A Brief History of Natural Deduction. History and Philosophy of Logic 20, 1–31 (1999)
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)
Spivey, J.M.: The Z Notation: A Reference Manual. Prentice-Hall, Inc., Englewood Cliffs (1992)
Suttner, C., Sutcliffe, G.: Technical Report on the TPTP Problem Library, http://www.cs.miami.edu/~tptp/TPTP/TR/TPTPTR.shtml
Tammet, T.: Gandalf, http://www.cs.chalmers.se/~tammet/gandalf/
Voronkov, A.: The anatomy of Vampire: implementing bottom-up procedures with code trees. Journal of Automated Reasoning 15(2) (1995)
Weidenbach, C.: Combining superposition, sorts, and splitting. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. 2, North-Holland, Amsterdam (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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