Skip to main content
SpringerLink
Log in

Decidability of Propositional Projection Temporal Logic with Infinite Models

  • Conference paper
Theory and Applications of Models of Computation (TAMC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4484))

Abstract

This paper investigates the satisfiability of Propositional Projection Temporal Logic (PPTL) with infinite models. A decision procedure for PPTL formulas is formalized. To this end, Normal Form (NF) and Normal Form Graph (NFG) for PPTL formulas are defined and an algorithm constructing NFG for PPTL formulas is presented. Further, examples are also given to illustrate how the decision algorithm works.

This research is supported by the NSFC Grant No. 60373103 and 60433010.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Kripke, S.A.: Semantical analysis of modal logic I: normal propositional calculi. Z. Math. Logik Grund. Math. 9, 67–96 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  2. Rosner, R., Pnueli, A.: A choppy logic. In: First Annual IEEE Symposium on Logic In Computer Science, LICS, pp. 306–314 (1986)

    Google Scholar 

  3. Moszkowski, B.C.: Reasoning about digital circuits. Ph.D Thesis, Department of Computer Science, Stanford University. TRSTAN-CS-83-970 (1983)

    Google Scholar 

  4. Moszkowski, B.: A Complete Axiomatization of Interval Temporal Logic with Infinite Time. In: 15th Annual IEEE Symposium on Logic in Computer Science (LICS’00), p. 241 (2000)

    Google Scholar 

  5. Zhou, C., Hoare, C.A.R., Ravn, A.P.: A calculus of duration. Information Processing Letters 40(5), 269–275 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  6. Duan, Z.: Temporal Logic and Temporal Logic Programming. Science Press of China, Beijing (2006)

    Google Scholar 

  7. Duan, Z., Koutny, M.: A Framed Temporal Logic Programming Language. Journal of Computer Science and Technology 19(3), 341–351 (2004)

    Article  MathSciNet  Google Scholar 

  8. Duan, Z., Yang, X., Koutny, M.: Semantics of Framed Temporal Logic Programs. In: Gabbrielli, M., Gupta, G. (eds.) ICLP 2005. LNCS, vol. 3668, pp. 256–270. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  9. Duan, Z., Zhang, L.: A Decision Procedure for Propositional Projection Temporal Logic. Technical Report No.1, Institute of computing Theory and Technology, Xidian University, Xi’an, P.R. China (2005), http://www.paper.edu.cn/process/download.jsp?file=200611-427

  10. Duan, Z., Tian, C.: Decison Prodedure for Propositional Projection Temporal Logic with Infinite Models. Technical Report No.1, Institute of computing Theory and Technology, Xidian University, Xi’an, P.R. China (2006), http://www.paper.edu.cn/process/download.jsp?file=200611-444

  11. Duan, Z., Koutny, M., Holt, C.: Projection in temporal logic programming. In: Pfenning, F. (ed.) LPAR 1994. LNCS, vol. 822, pp. 333–344. Springer, Heidelberg (1994)

    Google Scholar 

  12. Kono, S.: A combination of clausal and non-clausal temporal logic programs. In: Fisher, M., Owens, R. (eds.) IJCAI-WS 1993. LNCS, vol. 897, pp. 40–57. Springer, Heidelberg (1995)

    Google Scholar 

  13. Bowman, H., Thompson, S.: A decision procedure and complete axiomatization of interval temporal logic with projection. Journal of logic and Computation 13(2), 195–239 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  14. Dutertre, B.: Complete proof systems for first order interval temporal logic. In: Proceedings of LICS’95, pp. 36–43 (1995)

    Google Scholar 

  15. Manna, Z., Pnueli, A.: The temporal logic of reactive and concurrent systems. Springer, Heidelberg (1992)

    Google Scholar 

  16. Holzmann, G.J.: The Model Checker Spin. IEEE Trans. on Software Engineering 23(5), 279–295 (1997)

    Article  MathSciNet  Google Scholar 

  17. McMillan, K.L.: Symbolic Model Checking. Kluwer Academic Publishers, Dordrecht (1993)

    MATH  Google Scholar 

  18. Wang, H., Xu, Q.: Completeness of Temporal Logics over Infinite Models. Discrete Applied Mathematics 136, 87–103 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  19. Yang, X., Duan, Z.: Operational Semantics of Framed Temporal Logic Programs. In: van Leeuwen, J., et al. (eds.) SOFSEM 2007. LNCS, vol. 4362, pp. 566–578. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computing Theory and Technology, Xidian University, Xi’an, 710071, P.R. China

    Zhenhua Duan & Cong Tian

Authors
  1. Zhenhua Duan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cong Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jin-Yi Cai S. Barry Cooper Hong Zhu

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Duan, Z., Tian, C. (2007). Decidability of Propositional Projection Temporal Logic with Infinite Models. In: Cai, JY., Cooper, S.B., Zhu, H. (eds) Theory and Applications of Models of Computation. TAMC 2007. Lecture Notes in Computer Science, vol 4484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72504-6_47

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-72504-6_47

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72503-9

  • Online ISBN: 978-3-540-72504-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation