Fair Derivations in Monodic Temporal Reasoning

  • Michel Ludwig
  • Ullrich Hustadt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5663)


Ordered fine-grained resolution with selection is a sound and complete resolution-based calculus for monodic first-order temporal logic. The inference rules of the calculus are based on standard resolution between different types of temporal clauses on one hand and inference rules with semi-decidable applicability conditions that handle eventualities on the other hand. In this paper we illustrate how the combination of these two different types of inference rules can lead to unfair derivations in practice. We also present an inference procedure that allows us to construct fair derivations and prove its refutational completeness. We conclude with some experimental results obtained with the implementation of the new procedure in the theorem prover TSPASS.


Temporal Logic Inference Rule Inference Procedure Loop Formula Step Resolution 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bachmair, L., Ganzinger, H.: Resolution theorem proving. In: Robinson, J.A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. 1, pp. 19–99. Elsevier, Amsterdam (2001)CrossRefGoogle Scholar
  2. 2.
    Behdenna, A., Dixon, C., Fisher, M.: Deductive verification of simple foraging robotic behaviours (under review)Google Scholar
  3. 3.
    Degtyarev, A., Fisher, M., Konev, B.: Monodic temporal resolution. In: Baader, F. (ed.) CADE 2003. LNCS (LNAI), vol. 2741, pp. 397–411. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Degtyarev, A., Fisher, M., Konev, B.: Monodic temporal resolution. ACM Transactions On Computational Logic 7(1), 108–150 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Emerson, E.A.: Temporal and modal logic. In: Handbook of Theoretical Computer Science. Formal Models and Semantics, vol. B, pp. 995–1072 (1990)Google Scholar
  6. 6.
    Fisher, M., Dixon, C., Peim, M.: Clausal temporal resolution. ACM Transactions on Computational Logic 2(1), 12–56 (2001)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Gago, M.C.F., Fisher, M., Dixon, C.: Algorithms for guiding clausal temporal resolution. In: Jarke, M., Koehler, J., Lakemeyer, G. (eds.) KI 2002. LNCS, vol. 2479, pp. 235–252. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    Hodkinson, I., Wolter, F., Zakharyaschev, M.: Decidable fragments of first-order temporal logics. Annals of Pure and Applied Logic 106, 85–134 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Hustadt, U., Konev, B., Riazanov, A., Voronkov, A.: TeMP: A temporal monodic prover. In: Basin, D., Rusinowitch, M. (eds.) IJCAR 2004. LNCS (LNAI), vol. 3097, pp. 326–330. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    Hustadt, U., Konev, B., Schmidt, R.A.: Deciding monodic fragments by temporal resolution. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 204–218. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Konev, B., Degtyarev, A., Dixon, C., Fisher, M., Hustadt, U.: Towards the implementation of first-order temporal resolution: the expanding domain case. In: Proc. TIME-ICTL 2003, pp. 72–82. IEEE Computer Society, Los Alamitos (2003)Google Scholar
  12. 12.
    Konev, B., Degtyarev, A., Dixon, C., Fisher, M., Hustadt, U.: Mechanising first-order temporal resolution. Information and Computation 199(1-2), 55–86 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Ludwig, M., Hustadt, U.: Implementing a fair monodic temporal logic prover. AI Communications (to appear)Google Scholar
  14. 14.
    Weidenbach, C., Schmidt, R., Hillenbrand, T., Rusev, R., Topic, D.: System description: SPASS version 3.0. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 514–520. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  15. 15.
    Wolter, F., Zakharyaschev, M.: Axiomatizing the monodic fragment of first-order temporal logic. Annals of Pure and Applied logic 118, 133–145 (2002)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Michel Ludwig
    • 1
  • Ullrich Hustadt
    • 1
  1. 1.Department of Computer ScienceUniversity of LiverpoolUnited Kingdom

Personalised recommendations