Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

Finite Quantified Linear Temporal Logic and Its Satisfiability Checking

  • Conference paper
  • First Online:
Artificial Intelligence Logic and Applications (AILA 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1657))

Included in the following conference series:

  • 364 Accesses

Abstract

In this paper, we present Finite Quantified Linear Temporal Logic (FQLTL), a new formal specification language which extends Linear Temporal Logic (LTL) with quantifiers over finite domains. Explicitly, FQLTL leverages quantifiers and predicates to constrain the domains in the system and utilizes temporal operators from LTL to specify properties with time sequences. Compared to LTL, FQLTL is more suitable and accessible to describe the specification with both restricted domains and temporal properties, which can be applied to the scenarios such as railway transition systems. In addition, this paper proposes a methodology to check FQLTL satisfiability, releasing the corresponding checker for potential users to further use. Towards experiments, we show that by applying the logic to the railway transit system, most of the safety specifications can be formalized and several inconsistent specifications are reported through our implemented satisfiability checker.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 64.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 84.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Bae, K., Lee, J.: Bounded model checking of signal temporal logic properties using syntactic separation. In: Proceedings of the ACM on Programming Languages 3(POPL), pp. 1–30 (2019)

    Google Scholar 

  2. Bjørner, D., Havelund, K.: 40 years of formal methods. In: Jones, C., Pihlajasaari, P., Sun, J. (eds.) FM 2014. LNCS, vol. 8442, pp. 42–61. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-06410-9_4

    Chapter  Google Scholar 

  3. Clarke, E.M.: The birth of model checking. In: 25 Years of Model Checking-History, Achievements, Perspectives (2008)

    Google Scholar 

  4. Feng, J., et al.: FREPA: an automated and formal approach to requirement modeling and analysis in aircraft control domain. In: ESEC/FSE 2020: 28th ACM Joint European Software Engineering Conference and Symposium on the Foundations of Software Engineering, pp. 1376–1386 (2020)

    Google Scholar 

  5. Song, F., Wu, Z.: Extending temporal logics with data variable quantifications. In: 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2014)

    Google Scholar 

  6. Giacomo, G.D., Vardi, M.Y.: Linear temporal logic and linear dynamic logic on finite traces. AAAI Press (2013)

    Google Scholar 

  7. Giacomo, G.D., Vardi, M.Y.: Synthesis for LTL and LDL on finite traces. AAAI Press (2015)

    Google Scholar 

  8. Hird, G.R.: Formal methods in software engineering. In: 9th IEEE/AIAA/NASA Conference on Digital Avionics Systems (2002)

    Google Scholar 

  9. Holzmann, G.J.: The model checker - spin. IEEE Trans. Softw. Eng. 23, 279–295 (1997)

    Article  Google Scholar 

  10. Hustadt, U., Konev, B.: TRP++2.0: a temporal resolution prover. In: International Conference on Automated Deduction-cade (2002)

    Google Scholar 

  11. Kuperberg, D., Brunel, J., Chemouil, D.: On finite domains in first-order linear temporal logic. In: Artho, C., Legay, A., Peled, D. (eds.) ATVA 2016. LNCS, vol. 9938, pp. 211–226. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46520-3_14

    Chapter  Google Scholar 

  12. Li, J., Zhu, S., Pu, G., Vardi, M.Y.: SAT-based explicit LTL reasoning. In: Piterman, N. (ed.) HVC 2015. LNCS, vol. 9434, pp. 209–224. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-26287-1_13

    Chapter  Google Scholar 

  13. Li, J., Yao, Y., Pu, G., Zhang, L., He, J.: Aalta: an LTL satisfiability checker over infinite/finite traces. In: The 22nd ACM SIGSOFT International Symposium, pp. 731–734 (2014)

    Google Scholar 

  14. Li, J., Zhang, L., Pu, G., Vardi, M.Y., He, J.: LTL satisfiability checking revisited. In: 2013 20th International Symposium on Temporal Representation and Reasoning (TIME), pp. 91–98 (2013)

    Google Scholar 

  15. Li, J., Zhu, S., Pu, G., Zhang, L., Vardi, M.Y.: SAT-based explicit LTL reasoning and its application to satisfiability checking. Form. Methods Syst. Des. 54(2), 164–190 (2019). https://doi.org/10.1007/s10703-018-00326-5

    Article  Google Scholar 

  16. Michaud, T., Colange, M.: Reactive synthesis from LTL specification with spot. In: Proceedings of the 7th Workshop on Synthesis (2018)

    Google Scholar 

  17. Piribauer, J., Baier, C.B.N.: Quantified linear temporal logic over probabilistic systems with an application to vacuity checking. In: International Conference on Concurrency Theory (2021)

    Google Scholar 

  18. Pnueli, A.: The temporal logic in programs. In: Proceedings of the 18th Annual IEEE Symposium on Foundations of Computer Science, pp. 46–57 (1977)

    Google Scholar 

  19. Pnueli, A.: The temporal logic of programs. In: 18th Annual Symposium on Foundations of Computer Science (sfcs 1977), pp. 46–57 (1977). https://doi.org/10.1109/SFCS.1977.32

  20. Putnam, H.: Three-valued logic. The Logico-Algebraic Approach to Quantum Mechanics (1975)

    Google Scholar 

  21. Rozier, K.Y., Vardi, M.Y.: LTL satisfiability checking. In: Bošnački, D., Edelkamp, S. (eds.) SPIN 2007. LNCS, vol. 4595, pp. 149–167. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73370-6_11

    Chapter  Google Scholar 

  22. Schwendimann, S.: A new one-pass Tableau calculus for PLTL. In: de Swart, H. (ed.) TABLEAUX 1998. LNCS (LNAI), vol. 1397, pp. 277–291. Springer, Heidelberg (1998). https://doi.org/10.1007/3-540-69778-0_28

    Chapter  Google Scholar 

  23. Suda, M., Weidenbach, C.: A PLTL-prover based on labelled superposition with partial model guidance. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS (LNAI), vol. 7364, pp. 537–543. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31365-3_42

    Chapter  Google Scholar 

  24. Vardi, M.Y.: Branching vs. linear time: final showdown. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 1–22. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45319-9_1

    Chapter  Google Scholar 

  25. Vardi, M.Y.: From church and prior to PSL. In: Grumberg, O., Veith, H. (eds.) 25 Years of Model Checking. LNCS, vol. 5000, pp. 150–171. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-69850-0_10

    Chapter  Google Scholar 

  26. Vardi, M.Y.: An automata-theoretic approach to linear temporal logic. In: Moller, F., Birtwistle, G. (eds.) Logics for Concurrency. LNCS, vol. 1043, pp. 238–266. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-60915-6_6

    Chapter  Google Scholar 

  27. Zhu, S., Giacomo, G.D., Pu, G., Vardi, M.: LTLf synthesis with fairness and stability assumptions. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 34, No. 03, pp. 3088–3095 (2019)

    Google Scholar 

  28. Zhu, W.: Big data on linear temporal logic formulas. In: 2021 IEEE 4th Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC), vol. 4, pp. 544–547 (2021)

    Google Scholar 

Download references

Acknowledgment

We thank anonymous reviewers for their helpful comments. This work is supported by Chinese National Key Research and Development Program (Grant No. 2020AAA0107800), Shanghai Trusted Industry Internet Software Collaborative Innovation Center, Shanghai Pujiang Talent Plan (Grant No. 19511103602) and National Natural Science Foundation of China (Grant No. 62002118 and U21B2015).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jianwen Li .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Chen, Y., Zhang, X., Li, J. (2022). Finite Quantified Linear Temporal Logic and Its Satisfiability Checking. In: Chen, Y., Zhang, S. (eds) Artificial Intelligence Logic and Applications. AILA 2022. Communications in Computer and Information Science, vol 1657. Springer, Singapore. https://doi.org/10.1007/978-981-19-7510-3_1

Download citation

  • DOI: https://doi.org/10.1007/978-981-19-7510-3_1

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-19-7509-7

  • Online ISBN: 978-981-19-7510-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics