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).
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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)
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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
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DOI: https://doi.org/10.1007/11532231_15
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