Abstract
ETLs are temporal logics employing ω-automata as temporal connectives. This paper presents sound and complete axiom systems for ETL l , ETL f , and ETL r , respectively. Axioms and rules reflecting temporal behaviors of looping, finite and repeating automaton connectives are provided. Moreover, by encoding temporal operators into automaton connectives and instantiating the axioms and rules relating to automaton connectives, one may derive axiom systems for given ETL fragments.
This research is supported by the National Natural Science Foundation of China under Grant No.60233020, 90612009, 60673118; the National High-Tech Research and Development Plan of China under Grant No.2006AA01Z178, 2006AA01Z429; the National Grand Fundamental Research 973 Program of China under Grant No.2005CB321802; Program for New Century Excellent Talents in University under Grant No.NCET-04-0996.
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.
References
Armoni, R., Fix, L., Flaisher, A., Gerth, R., Ginsburg, B., Kanza, T., Landver, A., Mador-Haim, S., Singerman, E., Tiemeyer, A., Vardi, M.Y., Zbar, Y.: The forspec temporal logic: A new temporal property-specification language. In: Katoen, J.-P., Stevens, P. (eds.) ETAPS 2002 and TACAS 2002. LNCS, vol. 2280, pp. 211–296. Springer, Heidelberg (2002)
Armoni, R., Fix, L., Fraer, R., Huddleston, S., Piterman, N., Vardi, M.Y.: Sat-based induction for temporal safety properties. Electr. Notes Theor. Comput. Sci. 119(2), 3–16 (2005)
Banieqbal, B., Barringer, H.: Temporal logic with fixed points. In: Banieqbal, B., Pnueli, A., Barringer, H. (eds.) Temporal Logic in Specification. LNCS, vol. 398, pp. 62–74. Springer, Heidelberg (1989)
French, T., Reynolds, M.: A sound and complete proof system for QPTL. In: Proceedings of 4th Advances in Modal Logic, pp. 127–148. King’s College Publications (2003)
Kaivola, R.: Using Automata to Characterise Fixed Point Temporal Logics. PhD thesis, University of Edinburgh (1997)
Kaivola, R.: Axiomatising extended computation tree logic. Theoretical Computer Science 190(1), 41–60 (1998)
Kupferman, O., Morgenstern, G., Murano, A.: Typeness for ω-regular automata. In: Wang, F. (ed.) ATVA 2004. LNCS, vol. 3299, pp. 324–333. Springer, Heidelberg (2004)
Kesten, Y., Pnueli, A.: A complete proof systems for QPTL. In: Logic in Computer Science, pp. 2–12 (1995)
Kupferman, O., Piterman, N., Vardi, M.Y.: Extended temporal logic revisited. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 519–535. Springer, Heidelberg (2001)
Lange, M., Stirling, C.: Focus games for satisfiability and completeness of temporal logic. In: LICS 2001. Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science, Boston, MA, USA, IEEE Computer Society Press, Los Alamitos (2001)
Piterman, N.: Extending temporal logic with ω-automata. Thesis for the M.Sc Degree, School of the Weizmann Institute of Science (August 2000)
Prasad, S.A., Vardi, M.Y., Wolper, P.: The complementation problem for Büchi automata with applications to temporal logic. Theoretical Computer Science 49, 217–237 (1987)
Vardi, M.Y.: Branching vs. linear time: Final showdown. In: Margaria, T., Yi, W. (eds.) ETAPS 2001 and TACAS 2001. LNCS, vol. 2031, pp. 1–22. Springer, Heidelberg (2001)
Vardi, M.Y., Wolper, P.: Reasoning about infinite computations. Information and Computation 115(1), 1–37 (1994)
Wolper, P.: Temporal logic can be more expressive. Information and Control 56(1-2), 72–99 (1983)
Wolper, P., Vardi, M.Y., Sistla, A.P.: Reasoning about infinite computation paths. In: Proc. 24th IEEE Symposium on Foundations of Computer Science, Tucson, pp. 185–194. IEEE Computer Society Press, Los Alamitos (1983)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liu, W., Wang, J., Dong, W., Chen, H. (2007). Axiomatizing Extended Temporal Logic Fragments Via Instantiation. In: Jones, C.B., Liu, Z., Woodcock, J. (eds) Theoretical Aspects of Computing – ICTAC 2007. ICTAC 2007. Lecture Notes in Computer Science, vol 4711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75292-9_22
Download citation
DOI: https://doi.org/10.1007/978-3-540-75292-9_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75290-5
Online ISBN: 978-3-540-75292-9
eBook Packages: Computer ScienceComputer Science (R0)