Abstract
In this paper we study the decidability of various fragments of monodic first-order temporal logic by temporal resolution. We focus on two resolution calculi, namely, monodic temporal resolution and fine-grained temporal resolution. For the first, we state a very general decidability result, which is independent of the particular decision procedure used to decide the first-order part of the logic. For the second, we introduce refinements using orderings and selection functions. This allows us to transfer existing results on decidability by resolution for first-order fragments to monodic first-order temporal logic and obtain new decision procedures. The latter is of immediate practical value, due to the availability of TeMP, an implementation of fine-grained temporal resolution.
Supported by EPSRC (grant GR/L87491) and the Nuffield foundation (grant NAL/00841/G30).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bachmair, L., Ganzinger, H.: Resolution theorem proving. In: Robinson, Voronkov (eds.) [22], ch. 2, pp. 19–99.
Börger, E., Grädel, E., Gurevich, Y.: The Classical Decision Problem. Springer, Heidelberg (1997)
de Nivelle, H.: Splitting through new proposition symbols. In: Nieuwenhuis, R., Voronkov, A. (eds.) LPAR 2001. LNCS (LNAI), vol. 2250, pp. 172–185. Springer, Heidelberg (2001)
Degtyarev, A., Fisher, M., Konev, B.: Monodic temporal resolution. ACM Transactions on Computational Logic (To appear)
Degtyarev, A.B., Fisher, M., Konev, B.: Monodic temporal resolution. In: Baader, F. (ed.) CADE 2003. LNCS (LNAI), vol. 2741, pp. 397–411. Springer, Heidelberg (2003)
Emerson, E.A.: Temporal and modal logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, ch. 16, pp. 997–1072. Elsevier, Amsterdam (1990)
Fermüller, C., Leitsch, A., Hustadt, U., Tammet, T.: Resolution decision procedures. In: Robinson, Voronkov (eds.) [21], ch. 25, pp. 1791–1850.
Fisher, M., Dixon, C., Peim, M.: Clausal temporal resolution. ACM Transactions on Computational Logic 2(1), 12–56 (2001)
Ganzinger, H., de Nivelle, H.: A superposition decision procedure for the guarded fragment with equality. In: Proc. LICS’99, pp. 295–304. IEEE Computer Society Press, Los Alamitos (1999)
Hodkinson, I.: Monodic packed fragment with equality is decidable. Studia Logica 72(2), 185–197 (2002)
Hodkinson, I., Wolter, F., Zakharyaschev, M.: Decidable fragments of first-order temporal logics. Annals of Pure and Applied Logic 106, 85–134 (2000)
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)
Hustadt, U., Schmidt, R.A.: Maslov’s class K revisited. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol. 1632, pp. 172–186. Springer, Heidelberg (1999)
Konev, B., Degtyarev, A., Dixon, C., Fisher, M., Hustadt, U.: Mechanising first-order temporal resolution. In: Information and Computation (2003) (To appear) Also available as Technical Report ULCS-03-023, Dep. Comp. Sci., Univ. Liverpool
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 Press, Los Alamitos (2003)
Konev, B., Degtyarev, A., Fisher, M.: Handling equality in monodic temporal resolution. In: Y. Vardi, M., Voronkov, A. (eds.) LPAR 2003. LNCS, vol. 2850, pp. 214–228. Springer, Heidelberg (2003)
Kontchakov, R., Lutz, C., Wolter, F., Zakharyaschev, M.: Temporalising tableaux. Studia Logica 76(1), 91–134 (2004)
Maslov, S.J.: The inverse method for establishing deducibility for logical calculi. In: Orevkov, V.P. (ed.) The Calculi of Symbolic Logic I: Proceedings of the Steklov Institute of Mathematics, vol. 98(1968), pp. 25–96. American Math. Soc, Providence (1971)
Nieuwenhuis, R., Rubio, A.: Paramodulation-based theorem proving. In: Robinson, Voronkov (eds.) [22], ch. 7, pp. 371–443.
Nonnengart, A., Weidenbach, C.: Computing small clause normal forms. In: Robinson, Voronkov (eds.) [22], ch. 6, pp. 335–370.
Riazanov, A., Voronkov, A.: Splitting without backtracking. In: Proc. IJCAI 2001, pp. 611–617. Morgan Kaufmann, San Francisco (2001)
Robinson, A., Voronkov, A.(ed.): Handbook of Automated Reasoning. Elsevier, Amsterdam (2001)
Wolter, F., Zakharyaschev, M.: Axiomatizing the monodic fragment of first-order temporal logic. Annals of Pure and Applied logic 118, 133–145 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hustadt, U., Konev, B., Schmidt, R.A. (2005). Deciding Monodic Fragments by Temporal Resolution. In: Nieuwenhuis, R. (eds) Automated Deduction – CADE-20. CADE 2005. Lecture Notes in Computer Science(), vol 3632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11532231_15
Download citation
DOI: https://doi.org/10.1007/11532231_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28005-7
Online ISBN: 978-3-540-31864-4
eBook Packages: Computer ScienceComputer Science (R0)