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A decision procedure for propositional projection temporal logic with infinite models

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Abstract

This paper investigates the satisfiability of Propositional Projection Temporal Logic (PPTL) with infinite models. A decision procedure for PPTL formulas is given. To this end, Normal Form (NF) and Labeled Normal Form Graph (LNFG) for PPTL formulas are defined, and algorithms for transforming a formula to its normal form and constructing the LNFG for the given formula are presented. Further, the finiteness of LNFGs is proved in details. Moreover, the decision procedure is extended to check the satisfiability of the formulas of Propositional Interval Temporal Logic. In addition, examples are also given to illustrate how the decision procedure works.

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References

  1. Moszkowski, B.C.: Reasoning about digital circuits. PhD Thesis, Stanford University. TRSTAN-CS-83-970 (1983)

  2. Rosner, R., Pnueli, A.: A choppy logic. In: First annual IEEE symposium on logic in computer science, LICS, pp. 306–314 (1986)

  3. Moszkowski, B.C.: A complete axiomatization of interval temporal logic with infinite time. In: 15th Annual IEEE symposium on logic in computer science (LICS’00), LICS, p. 241, (2000)

  4. Chaochen Z., Hoare C.A.R. and Ravn A.P. (1991). A calculus of duration. Inf. Process. Lett. 40(5): 269–275

    Article  MATH  MathSciNet  Google Scholar 

  5. Bowman H. and Thompson S. (2003). A decision procedure and complete axiomatization of interval temporal logic with projection. J. Logic Comput. 13(2): 195–239

    Article  MATH  MathSciNet  Google Scholar 

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

  7. Wang, H., Xu, Q.: Temporal logics over infinite intervals. Technical Report 158, UNU/IIST, Macau (1999)

  8. Halpern, J., Manna, Z., Moszkowski, B.: A hardware semantics based on temporal intervals. In: Proceedings of the 10th international conlloquium on automata, Languages and Programming, vol. 154. Springer, LNCS, Barcelona (1983)

  9. Kono, S.: A combination of clausal and non-clausal temporal logic programs. In: Lecture notes in artificial intelligence, vol. 897, pp. 40–57. Springer, Heidelberg (1995)

  10. Bowman, H., Thompson, S.: A Tableau method for interval temporal logic with projection. In: de Swart, H. (ed.) TABLEAUX98, LNAI 1397, Springer, Berlin (1998)

  11. Duan, Z.: An extended interval temporal logic and a framing technique for temporal logic programming. PhD thesis, University of Newcastle Upon Tyne (1996)

  12. Duan Z. (2006). Temporal Logic and Temporal Logic Programming Language. Science press, Beijing

    Google Scholar 

  13. Duan, Z., Koutny, M., Holt, C.: Projection in temporal logic programming. In: Pfenning, F. (ed.) Proceedings of logic programming and automatic reasoning, Lecture Notes in Artificial Intelligence, vol. 822, pp. 333–344. Springer, Heidelberg (1994)

  14. Duan Z. and Koutny M. (2004). A framed temporal logic programming language. J. Comput. Sci. Technol. 19: 333–344

    MathSciNet  Google Scholar 

  15. Duan, Z., Yang, X., Kounty, M.: Semantics of framed temporal logic programs. In: Proceedings of ICLP 2005, vol. 3668, pp. 256–270. LNCS, Barcelona (2005)

  16. Moszkowski, B.C.: Compositional reasoning about projected and infinite time. In: Proceeding of the first IEEE international conference on engineering of complex computer systems (ICECCS’95), pp. 238–245. IEEE Computer Society Press (1995)

  17. Manna Z. and Pnueli A. (1992). The Temporal Logic of Reactive and Concurrent Systems. Springer, Heidelberg

    Google Scholar 

  18. 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, People’s Republic of China, http://www.paper.edu.cn/en/paper.php?serial_number=200611-427 (2005)

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

    MATH  MathSciNet  Google Scholar 

  20. Winskel, G.: The Formal Semantics of Programming Languages. Foundations of Computing. MIT, Cambridge

  21. Holzmann G.J. (1997). The Model Checker Spin. IEEE Trans. Softw. Eng. 23(5): 279–295

    Article  MathSciNet  Google Scholar 

  22. McMillan, K.L.: Symbolic Model Checking. Kluwer (1993)

  23. Harel D., Kozen D. and Parikh R. (1982). Process logic: expressiveness, decidability, completeness. J. Comput. Syst. Sci. 25(2): 144–170

    Article  MATH  MathSciNet  Google Scholar 

  24. Chandra A., Halpern J., Meyer A. and Parikh R. (1985). Equations between regular terms and an application to process logic. SIAM J. Comput. 14(4): 935–942

    Article  MATH  MathSciNet  Google Scholar 

  25. Moszkowski B. (1986). Executing Temporal Logic Programs. Cambridge University Press, Cambridge

    Google Scholar 

  26. Duan Z. (2005). Modelling and Analysis of Hybrid Systems. Science Press, Beijing

    Google Scholar 

  27. Duan Z., Holcombe M. and Bell A. (2000). A logic for biosystems. Biosystems 55(1-3): 93–105

    Article  Google Scholar 

  28. Paech, B.: Gentzen-systems for propositional temporal logics. In: Borger, E., Kleine Buning, H., Richter, M.M. (eds.) Proceedings of the 2nd workshop on computer science logic, Duisburg (FRG), vol. 385, pp. 240–253. Springer, Heidelberg (1988)

  29. Pnueli, A.: The temporal logic of programs. In: Proceedings of 18th IEEE symposium on foundations of computer science, pp. 46–57 (1977)

  30. Tian, C., Duan, Z.: Model Checking Propositional Projection Temporal Logic Based on SPIN, ICFEM 2007, LNCS4789, pp. 246-265, Springer, Heidelberg (2007)

  31. Kröger, F.: Temporal Logic of Programs. EATCS Monographs on Theoretical Computer Science, vol. 8. Springer, Heidelberg (1987)

  32. Wolper P.L. (1983). Temporal logic can be more expressive. Inf. Control 56: 72–99

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Computing Theory and Technology, Xidian University, Xi’an, 710071, People’s Republic of China

    Zhenhua Duan, Cong Tian & Li Zhang

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  1. Zhenhua Duan
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  2. Cong Tian
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  3. Li Zhang
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Corresponding author

Correspondence to Zhenhua Duan.

Additional information

This research is supported by the NSFC Grant No. 60373103 and 60433010, and Defence Pre-Research Project of China, No. 51315050105.

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Duan, Z., Tian, C. & Zhang, L. A decision procedure for propositional projection temporal logic with infinite models. Acta Informatica 45, 43–78 (2008). https://doi.org/10.1007/s00236-007-0062-z

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