TeMP: A Temporal Monodic Prover

  • Ullrich Hustadt
  • Boris Konev
  • Alexandre Riazanov
  • Andrei Voronkov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3097)


First-Order Temporal Logic, FOTL, is an extension of classical first-order logic by temporal operators for a discrete linear model of time (isomorphic to ℕ, that is, the most commonly used model of time). Formulae of this logic are interpreted over structures that associate with each element n of ℕ, representing a moment in time, a first-order structure (Dn,In) with its own non-empty domain Dn. In this paper we make the expanding domain assumption, that is, DnDm if n<m. The set of valid formulae of this logic is not recursively enumerable. However, the set of valid monodic formulae is known to be finitely axiomatisable [13].


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  1. 1.
    Artale, A., Franconi, E., Wolter, F., Zakharyaschev, M.: A temporal description logic for reasoning over conceptual schemas and queries. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424, pp. 98–110. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Bachmair, L., Ganzinger, H.: Resolution theorem proving. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 19–99. Elsevier, Amsterdam (2001)CrossRefGoogle Scholar
  3. 3.
    Fisher, M., Dixon, C., Peim, M.: Clausal temporal resolution. ACM Transactions on Computational Logic 2(1), 12–56 (2001)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Fisher, M., Lisitsa, A.: Temporal verification of monodic abstract state machines. Technical Report ULCS-03-011, Department of Computer Science, University of Liverpool (2003)Google Scholar
  5. 5.
    Gabelaia, D., Kontchakov, R., Kurucz, A., Wolter, F., Zakharyaschev, M.: On the computational complexity of spatio-temporal logics. In: Proc. FLAIRS 2003, pp. 460–464. AAAI Press, Menlo Park (2003)Google Scholar
  6. 6.
    Hustadt, U., Konev, B.: TRP++ 2.0: A temporal resolution prover. In: Baader, F. (ed.) CADE 2003. LNCS(LNAI), vol. 2741, pp. 274–278. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Hustadt, U., Schmidt, R.A.: Scientific benchmarking with temporal logic decision procedures. In: Proc. KR 2002, pp. 533–544. Morgan Kaufmann, San Francisco (2002)Google Scholar
  8. 8.
    Janssen, G.: Logics for Digital Circuit Verification: Theory, Algorithms, and Applications. PhD thesis, Eindhoven University of Technology, The Netherlands (1999)Google Scholar
  9. 9.
    Konev, B., Degtyarev, A., Dixon, C., Fisher, M., Hustadt, U.: Mechanising first-order temporal resolution. Technical Report ULCS-03-023, University of Liverpool, Department of Computer Science (2003), http://www.csc.liv.ac.uk/research/
  10. 10.
    Kontchakov, R., Lutz, C., Wolter, F., Zakharyaschev, M.: Temporalising tableaux. Studia Logica 76(1), 91–134 (2004)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Riazanov, A., Voronkov, A.: The design and implementation of Vampire. AI Communications 15(2-3), 91–110 (2002)MATHGoogle Scholar
  12. 12.
    Schwendimann, S.: Aspects of Computational Logic. PhD thesis, Universität Bern, Switzerland (1998)Google Scholar
  13. 13.
    Wolter, F., Zakharyaschev, M.: Axiomatizing the monodic fragment of first-order temporal logic. Annals of Pure and Applied logic 118, 133–145 (2002)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Ullrich Hustadt
    • 1
  • Boris Konev
    • 1
  • Alexandre Riazanov
    • 2
  • Andrei Voronkov
    • 2
  1. 1.Department of Computer ScienceUniversity of LiverpoolUK
  2. 2.Department of Computer ScienceUniversity of ManchesterUK

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