Automating Access Control Logics in Simple Type Theory with LEO-II

  • Christoph Benzmüller
Part of the IFIP Advances in Information and Communication Technology book series (IFIPAICT, volume 297)


Garg and Abadi recently proved that prominent access control logics can be translated in a sound and complete way into modal logic S4. We have previously outlined how normal multimodal logics, including monomodal logics K and S4, can be embedded in simple type theory and we have demonstrated that the higher-order theorem prover LEO-II can automate reasoning in and about them. In this paper we combine these results and describe a sound (and complete) embedding of different access control logics in simple type theory. Employing this framework we show that the off the shelf theorem prover LEO-II can be applied to automate reasoning in and about prominent access control logics.


Modal Logic Theorem Prover Accessibility Relation Intuitionistic Logic Kripke Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    The TPTP THF library,
  2. 2.
    Abadi, M.: Logic in access control. In: 18th IEEE Symposium on Logic in Computer Science, Ottawa, Canada, Proceedings, 22-25 June 2003. IEEE Computer Society, Los Alamitos (2003)Google Scholar
  3. 3.
    Andrews, P.B.: General models and extensionality. J. of Symbolic Logic 37, 395–397 (1972)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Andrews, P.B.: General models, descriptions, and choice in type theory. J. of Symbolic Logic 37, 385–394 (1972)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Andrews, P.B.: An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof, 2nd edn. Kluwer Academic Publishers, Dordrecht (2002)CrossRefzbMATHGoogle Scholar
  6. 6.
    Andrews, P.B.: Church’s type theory. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (2008),
  7. 7.
    Andrews, P.B., Brown, C.E.: Tps: A hybrid automatic-interactive system for developing proofs. J. Applied Logic 4(4), 367–395 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Benzmüller, C.: Automating access control logics in simple type theory with LEO-II. SEKI Technical Report SR-2008-01, FB Informatik, U. des Saarlandes, Germany (2008)Google Scholar
  9. 9.
    Benzmüller, C., Brown, C.E., Kohlhase, M.: Higher order semantics and extensionality. J. of Symbolic Logic 69, 1027–1088 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Benzmüller, C., Paulson, L.: Festschrift in honour of Peter B. Andrews on his 70th birthday. In: Exploring Properties of Normal Multimodal Logics in Simple Type Theory with LEO-II. IFCoLog, Studies in Logic and the Foundations of Mathematics (2009)Google Scholar
  11. 11.
    Benzmüller, C., Rabe, F., Sutcliffe, G.: The core TPTP language for classical higher-order logic. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS, vol. 5195 (LNAI), pp. 491–506. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Benzmüller, C., Theiss, F., Paulson, L., Fietzke, A.: LEO-II - A cooperative automatic theorem prover for classical higher-order logic (System description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS ( LNAI), vol. 5195, pp. 162–170. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Brown, C.E.: Encoding hybrid logic in higher-order logic. Unpublished slides from an invited talk presented at Loria Nancy, France (April 2005),
  14. 14.
    Carpenter, B.: Type-logical semantics. MIT Press, Cambridge (1998)zbMATHGoogle Scholar
  15. 15.
    Church, A.: A Formulation of the Simple Theory of Types. J. of Symbolic Logic 5, 56–68 (1940)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Gallin, D.: Intensional and Higher-Order Modal Logic. North-Holland Mathematics Studies, vol. 19. North-Holland, Amsterdam (1975)CrossRefzbMATHGoogle Scholar
  17. 17.
    Gamut, L.T.F.: Logic, Language, and Meaning. Intensional Logic and Logical Grammar, vol. II. The University of Chicago Press (1991)Google Scholar
  18. 18.
    Garg, D., Abadi, M.: A modal deconstruction of access control logics. In: Amadio, R. (ed.) FOSSACS 2008. LNCS, vol. 4962, pp. 216–230. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  19. 19.
    Gödel, K.: Eine interpretation des intuitionistischen aussagenkalküls. Ergebnisse eines Mathematischen Kolloquiums 8, 39–40 (1933)zbMATHGoogle Scholar
  20. 20.
    Hardt, M., Smolka, G.: Higher-order syntax and saturation algorithms for hybrid logic. Electr. Notes Theor. Comput. Sci. 174(6), 15–27 (2007)CrossRefzbMATHGoogle Scholar
  21. 21.
    Harrison, J.: HOL Light Tutorial (for version 2.20). Intel JF1-13 (September 2006),
  22. 22.
    Henkin, L.: Completeness in the theory of types. J. of Symbolic Logic 15, 81–91 (1950)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Kaminski, M., Smolka, G.: Terminating tableaux for hybrid logic with the difference modality and converse. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 210–225. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  24. 24.
    Merz, S.: Yet another encoding of TLA in isabelle (1999),
  25. 25.
    Schulz, S.: E – A Brainiac Theorem Prover. Journal of AI Communications 15(2/3), 111–126 (2002)zbMATHGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2009

Authors and Affiliations

  • Christoph Benzmüller
    • 1
  1. 1.International University in GermanyBruchsalGermany

Personalised recommendations