Advertisement

Logic-Based Formalisms

  • Carlo A. Furia
  • Dino Mandrioli
  • Angelo Morzenti
  • Matteo Rossi
Chapter
Part of the Monographs in Theoretical Computer Science. An EATCS Series book series (EATCS)

Abstract

In this chapter, we discuss logic-based formalism as descriptive notations that allow users to provide and analyze system models in terms of their properties. We discuss and compare various types of temporal logic with respect to their expressive power, their relation to transition systems, and the features of the assumed underlying time domain. We also present other logic-based formalisms that entertain an explicit notion of time without using the modal operators typical of temporal logics, and we introduce probabilistic logic-based models that assign probabilities to events and can therefore express requirements on the probability of certain system evolutions to occur. The chapter concludes with a brief review of the tools supporting the analysis techniques associated with the formalism.

Keywords

Temporal Logic Linear Temporal Logic Computation Tree Logic Linear Temporal Logic Formula Duration Calculus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Abadi, M., Lamport, L.: An old-fashioned recipe for real time. ACM Trans. Program. Lang. Syst. 16(5), 1543–1571 (1994)Google Scholar
  2. 2.
    Alur, R., Henzinger, T.A.: Real-time logics: complexity and expressiveness. Inf. Comput. 104(1), 35–77 (1993)Google Scholar
  3. 3.
    Alur, R., Henzinger, T.A.: A really temporal logic. J. ACM 41(1), 181–204 (1994)Google Scholar
  4. 4.
    Alur, R., Feder, T., Henzinger, T.A.: The benefits of relaxing punctuality. J. ACM 43(1), 116–146 (1996)Google Scholar
  5. 5.
    Archer, M., Heitmeyer, C.L.: Human-style theorem proving using PVS. In: Gunter, E.L., Felty, A.P. (eds.) Theorem Proving in Higher Order Logics, Proceedings of the 10th International Conference, TPHOLs’97, Murray Hill, 19–22 August 1997. Lecture Notes in Computer Science, vol. 1275, pp. 33–48. Springer, Berlin/Heidelberg (1997)Google Scholar
  6. 6.
    Archer, M., Heitmeyer, C.L., Riccobene, E.: Proving invariants of I/O automata with TAME. Autom. Softw. Eng. 9(3), 201–232 (2002)Google Scholar
  7. 7.
    Aziz, A., Sanwal, K., Singhal, V., Brayton, R.K.: Model-checking continous-time Markov chains. ACM Trans. Comput. Log. 1(1), 162–170 (2000)Google Scholar
  8. 8.
    Baier, C., Haverkort, B., Hermanns, H., Katoen, J.P.: Model-checking algorithms for continuous-time Markov chains. IEEE Trans. Softw. Eng. 29(6), 524–541 (2003)Google Scholar
  9. 9.
    Bauer, A., Leucker, M., Schallhart, C.: Runtime verification for LTL and TLTL. ACM Trans. Softw. Eng. Methodol. 20(4), 14 (2011)Google Scholar
  10. 10.
    Biere, A., Heljanko, K., Junttila, T.A., Latvala, T., Schuppan, V.: Linear encodings of bounded LTL model checking. Log. Methods Comput. Sci. 2(5) (2006)Google Scholar
  11. 11.
    Bouyer, P., Chevalier, F., Markey, N.: On the expressiveness of TPTL and MTL. In: Ramanujam, R., Sen, S. (eds.) Proceedings of the 25th International Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS’05). Lecture Notes in Computer Science, vol. 3821, pp. 432–443. Springer, Berlin/New York/Heidelberg (2005)Google Scholar
  12. 12.
    Bresolin, D., Della Monica, D., Goranko, V., Montanari, A., Sciavicco, G.: The dark side of interval temporal logic: sharpening the undecidability border. In: Combi, C., Leucker, M., Wolter, F. (eds.) Eighteenth International Symposium on Temporal Representation and Reasoning, TIME 2011, Lübeck, 12–14 September 2011, pp. 131–138. IEEE Computer Society (2011)Google Scholar
  13. 13.
    Burns, A., Hayes, I.J.: A timeband framework for modelling real-time systems. Real-Time Syst. 45(1–2), 106–142 (2010)Google Scholar
  14. 14.
    Chaochen, Z., Hansen, M.R.: Duration Calculus: A Formal Approach to Real-Time Systems. Springer, Berlin/New York (2004)Google Scholar
  15. 15.
    Chaochen, Z., Xiaoshan, L.: A mean value calculus of durations, pp. 431–451. Prentice Hall, Hertfordshire (1994)Google Scholar
  16. 16.
    Chaochen, Z., Hoare, C.A.R., Ravn, A.P.: A calculus of duration. Inf. Process. Lett. 40(5), 269–276 (1991)Google Scholar
  17. 17.
    Chaudhuri, K., Doligez, D., Lamport, L., Merz, S.: The TLA +  proof system: building a hete-rogeneous verification platform. In: Cavalcanti, A., Déharbe, D., Gaudel, M.C., Woodcock, J. (eds.) ICTAC. Lecture Notes in Computer Science, vol. 6255, p. 44. Springer, Berlin (2010)Google Scholar
  18. 18.
    Ciapessoni, E., Mirandola, P., Coen-Porisini, A., Mandrioli, D., Morzenti, A.: From formal models to formally based methods: an industrial experience. ACM Trans. Softw. Eng. Methodol. 8(1), 79–113 (1999)Google Scholar
  19. 19.
    Clarke, E.M., Draghicescu, I.A.: Expressibility results for linear-time and branching-time logics. In: de Bakker, J.W., de Roever, W.P., Rozenberg, G. (eds.) REX Workshop. Lecture Notes in Computer Science, vol. 354, pp. 428–437. Springer, Berlin/New York (1988)Google Scholar
  20. 20.
    Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching-time temporal logic. In: Logic of Programs, Workshop, pp. 52–71. Springer, London (1982)Google Scholar
  21. 21.
    Clarke, E.M., Biere, A., Raimi, R., Zhu, Y.: Bounded model checking using satisfiability solving. Form. Methods Syst. Des. 19(1), 7–34 (2001)Google Scholar
  22. 22.
    Corsetti, E., Crivelli, E., Mandrioli, D., Morzenti, A., Montanari, A., San Pietro, P., Ratto, E.: Dealing with different time scales in formal specifications. In: Proceedings of the 6th International Workshop on Software Specification and Design, pp. 92–101. IEEE Computer Society, Los Alamitos (1991)Google Scholar
  23. 23.
    Donatelli, S., Haddad, S., Sproston, J.: Model checking timed and stochastic properties with CSL{ TA}. IEEE Trans. Softw. Eng. 35(2), 224–240 (2009)Google Scholar
  24. 24.
    Emerson, E.A.: Temporal and modal logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol. B, pp. 996–1072. Elsevier, Amsterdam/New York (1990)Google Scholar
  25. 25.
    Fainekos, G.E., Pappas, G.J.: Robustness of temporal logic specifications for continuous-time signals. Theor. Comput. Sci. 410(42), 4262–4291 (2009)Google Scholar
  26. 26.
    Franceschet, M., Montanari, A.: Temporalized logics and automata for time granularity. TPLP 4(5–6), 621–658 (2004)Google Scholar
  27. 27.
    Furia, C.A., Rossi, M.: Integrating discrete- and continuous-time metric temporal logics through sampling. In: Asarin, E., Bouyer, P. (eds.) Proceedings of the 4th International Conference on Formal Modelling and Analysis of Timed Systems (FORMATS’06). Lecture Notes in Computer Science, vol. 4202, pp. 215–229. Springer, Berlin/New York (2006)Google Scholar
  28. 28.
    Furia, C.A., Rossi, M.: On the expressiveness of MTL variants over dense time. In: Raskin, J.F., Thiagarajan, P.S. (eds.) Proceedings of the 5th International Conference on Formal Modelling and Analysis of Timed Systems (FORMATS’07). Lecture Notes in Computer Science, vol. 4763, pp. 163–178. Springer, Berlin/New York (2007)Google Scholar
  29. 29.
    Furia, C.A., Rossi, M.: MTL with bounded variability: decidability and complexity. In: Cassez, F., Jard, C. (eds.) Proceedings of the 6th International Conference on Formal Modelling and Analysis of Timed Systems (FORMATS’08). Lecture Notes in Computer Science, vol. 5215, pp. 109–123. Springer, Berlin (2008)Google Scholar
  30. 30.
    Furia, C.A., Rossi, M.: A theory of sampling for continuous-time metric temporal logic. ACM Trans. Comput. Log. 12(1), 1–40 (2010). Article 8Google Scholar
  31. 31.
    Furia, C.A., Spoletini, P.: On relaxing metric information in linear temporal logic. In: Combi, C., Leucker, M., Wolter, F. (eds.) Proceedings of the 18th International Symposium on Temporal Representation and Reasoning (TIME’11), pp. 72–79. IEEE Computer Society, Los Alamitos (2011)Google Scholar
  32. 32.
    Gabbay, D.M.: The declarative past and imperative future. In: Banieqbal, B., Barringer, H., Pnueli, A. (eds.) Proceeding of Temporal Logic in Specification (TLS’87). Lecture Notes in Computer Science, vol. 398, pp. 409–448. Springer, Altrincham (1987)Google Scholar
  33. 33.
    Gabbay, D.M., Pnueli, A., Shelah, S., Stavi, J.: On the temporal basis of fairness. In: Conference Record of the 7th Annual ACM Symposium on Principles of Programming Languages (POPL’80), pp. 163–173. ACM, New York (1980)Google Scholar
  34. 34.
    Gabbay, D.M., Hodkinson, I., Reynolds, M.: Temporal logic (vol. 1): Mathematical foundations and computational aspects. Oxford Logic Guides, vol. 28. Oxford University Press, New York (1994)Google Scholar
  35. 35.
    Gargantini, A., Morzenti, A.: Automated deductive requirements analysis of critical systems. ACM Trans. Softw. Eng. Methodol. 10(3), 255–307 (2001)Google Scholar
  36. 36.
    Gargantini, A., Morzenti, A.: Automated verification of continuous time systems by discrete temporal induction. In: Proceedings of the 13th International Symposium on Temporal Representation and Reasoning (TIME’06). IEEE Computer Society Press, Los Alamitos (2006)Google Scholar
  37. 37.
    Ghezzi, C., Mandrioli, D., Morzenti, A.: TRIO: a logic language for executable specifications of real-time systems. J. Syst. Softw. 12(2), 107–123 (1990)Google Scholar
  38. 38.
    Goranko, V., Montanari, A., Sciavicco, G.: A road map of interval temporal logics and duration calculi. J. Appl. Non-Class. Log. 14(1–2), 9–54 (2004)Google Scholar
  39. 39.
    Goranko, V., Montanari, A., Sala, P., Sciavicco, G.: A general tableau method for propositional interval temporal logics: Theory and implementation. J. Appl. Log. 4(3), 305–330 (2006)Google Scholar
  40. 40.
    Hansen, M.R., Chaochen, Z.: Duration calculus: logical foundations. Form. Asp. Comput. 9(3), 283–330 (1997)Google Scholar
  41. 41.
    Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Form. Asp. Comput. 6(5), 512–535 (1994)Google Scholar
  42. 42.
    Havlicek, J., Little, S., Maler, O., Nickovic, D.: Property-based monitoring of analog and mixed-signal systems. In: Chatterjee, K., Henzinger, T.A. (eds.) Formal Modeling and Analysis of Timed Systems—8th International Conference, FORMATS 2010, Klosterneuburg, 8–10 September 2010. Proceedings. Lecture Notes in Computer Science, vol. 6246, pp. 23–24. Springer, Berlin/Heidelberg (2010)Google Scholar
  43. 43.
    Hennessy, M., Milner, R.: Algebraic laws for nondeterminism and concurrency. J. ACM 32(1), 137–161 (1985)Google Scholar
  44. 44.
    Hirshfeld, Y., Rabinovich, A.M.: Logics for real time: decidability and complexity. Fundam. Informormaticae 62(1), 1–28 (2004)Google Scholar
  45. 45.
    Hirshfeld, Y., Rabinovich, A.M.: Decidable metric logics. Inf. Comput. 206(12), 1425–1442 (2008)Google Scholar
  46. 46.
    Jahanian, F., Mok, A.K.: Safety analysis of timing properties in real-time systems. IEEE Trans. Softw. Eng. 12(9), 890–904 (1986)Google Scholar
  47. 47.
    Jahanian, F., Mok, A.K.: Modechart: a specification language for real-time systems. IEEE Trans. Softw. Eng. 20(12), 933–947 (1994)Google Scholar
  48. 48.
    Kamp, J.A.W.: Tense logic and the theory of linear order. Ph.D. thesis, University of California at Los Angeles (1968)Google Scholar
  49. 49.
    Koymans, R.: Specifying real-time properties with metric temporal logic. Real-Time Syst. 2(4), 255–299 (1990)Google Scholar
  50. 50.
    Koymans, R.: (Real) time: a philosophical perspective. In: de Bakker, J.W., Huizing, C., de Roever, W.P., Rozenberg, G. (eds.) Proceedings of the REX Workshop: “Real-Time: Theory in Practice”. Lecture Notes in Computer Science, vol. 600, pp. 353–370. Springer, Berlin/New York (1992)Google Scholar
  51. 51.
    Kozen, D.: Results on the propositional mu-calculus. Theor. Comput. Sci. 27, 333–354 (1983)Google Scholar
  52. 52.
    Kripke, S.A.: Semantical analysis of modal logic I. Z. Math. Log. Grundl. Math. 9, 67–96 (1963)Google Scholar
  53. 53.
    Lamport, L.: The temporal logic of actions. ACM Trans. Program. Lang. Syst. 16(3), 872–923 (1994)Google Scholar
  54. 54.
    Laroussinie, F., Markey, N., Schnoebelen, P.: Temporal logic with forgettable past. In: Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science (LICS’02), pp. 383–392. IEEE Computer Society Press, Los Alamitos (2002)Google Scholar
  55. 55.
    Lichtenstein, O., Pnueli, A., Zuck, L.D.: The glory of the past. In: Proceedings of 3rd Workshop on Logic of Programs, Brooklyn. Lecture Notes in Computer Science, vol. 193, pp. 196–218. Springer (1985)Google Scholar
  56. 56.
    Lutz, C., Walther, D., Wolter, F.: Quantitative temporal logics over the reals: PSPACE and below. Inf. Comput. 205(1), 99–123 (2007)Google Scholar
  57. 57.
    Maler, O., Nickovic, D.: Monitoring temporal properties of continuous signals. In: Lakhnech, Y., Yovine, S. (eds.) Formal Techniques, Modelling and Analysis of Timed and Fault-Tolerant Systems, Proceedings of the Joint International Conferences on Formal Modelling and Analysis of Timed Systems, FORMATS 2004 and Formal Techniques in Real-Time and Fault-Tolerant Systems, FTRTFT 2004, Grenoble, 22–24 September 2004. Lecture Notes in Computer Science, vol. 3253, pp. 152–166. Springer, Berlin/New York (2004)Google Scholar
  58. 58.
    Maler, O., Nickovic, D., Pnueli, A.: From MITL to timed automata. In: Asarin, E., Bouyer, P. (eds.) Formal Modeling and Analysis of Timed Systems, Proceedings of the 4th International Conference, FORMATS 2006, Paris, 25–27 September 2006. Lecture Notes in Computer Science, vol. 4202, pp. 274–289. Springer, Berlin/New York (2006)Google Scholar
  59. 59.
    Morzenti, A., Pietro, P.S.: Object-oriented logical specification of time-critical systems. ACM Trans. Softw. Eng. Methodol. 3(1), 56–98 (1994)Google Scholar
  60. 60.
    Morzenti, A., Mandrioli, D., Ghezzi, C.: A model parametric real-time logic. ACM Trans. Program. Lang. Syst. 14(4), 521–573 (1992)Google Scholar
  61. 61.
    Moszkowski, B.: Executing Temporal Logic Programs. Cambridge University Press, New York/Cambridge (1986)Google Scholar
  62. 62.
    Ouaknine, J., Worrell, J.: On the decidability and complexity of metric temporal logic over finite words. Log. Methods Comput. Sci. 3(1), 8 (2007)Google Scholar
  63. 63.
    Ouaknine, J., Rabinovich, A., Worrell, J.: Time-bounded verification. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009—Concurrency Theory, Proceedings of the 20th International Conference, CONCUR 2009, Bologna, 1–4 September 2009. Lecture Notes in Computer Science, vol. 5710, pp. 496–510. Springer, Berlin/New York/Heidelberg (2009)Google Scholar
  64. 64.
    Pandya, P.K.: Interval duration logic: expressiveness and decidability. Electron. Notes Theor. Comput. Sci. 65(6), 254–272 (2002)Google Scholar
  65. 65.
    Pnueli, A.: The temporal logic of programs. In: Proceedings of the 18th IEEE Symposium on Foundations of Computer Science (FOCS’77), pp. 46–67. IEEE Computer Society, New York (1977)Google Scholar
  66. 66.
    Pnueli, A.: Linear and branching structures in the semantics and logics of reactive systems. In: Brauer, W. (ed.) Proceedings of the 12th Colloquium on Automata, Languages and Programming (ICALP’85). Lecture Notes in Computer Science, vol. 194, pp. 15–32. Springer, Berlin/Heidelberg (1985)Google Scholar
  67. 67.
    Pradella, M., Morzenti, A., San Pietro, P.: Refining real-time system specifications through bounded model- and satisfiability-checking. In: 23rd IEEE/ACM International Conference on Automated Software Engineering (ASE 2008), 15–19 September 2008, pp. 119–127. IEEE Computer Society, Piscataway (2008)Google Scholar
  68. 68.
    Prior, A.: Time and Modality. Oxford University Press, Oxford (1957)Google Scholar
  69. 69.
    Prior, A.: Past. Present and Future. Oxford University Press, London (1967). Reprinted 2002Google Scholar
  70. 70.
    Rescher, N., Urquhart, A.: Temporal Logic. Springer, New York (1971)Google Scholar
  71. 71.
    Rozier, K.Y., Vardi, M.Y.: LTL satisfiability checking. STTT 12(2), 123–137 (2010)Google Scholar
  72. 72.
    Rozier, K.Y., Vardi, M.Y.: A multi-encoding approach for LTL symbolic satisfiability checking. In: Butler, M., Schulte, W. (eds.) FM 2011: Formal Methods. Proceedings of the 17th International Symposium on Formal Methods, Limerick, 20–24 June 2011. Lecture Notes in Computer Science, vol. 6664, pp. 417–431. Springer, Berlin/New York/Heidelberg (2011)Google Scholar
  73. 73.
    Schwartz, R.L., Melliar-Smith, P.M., Vogt, F.H.: An interval logic for higher-level temporal reasoning. In: Proceedings of the 2nd Annual ACM Symposium on Principles of Distributed Computing (PODC’83), pp. 198–212. ACM, New York (1983)Google Scholar
  74. 74.
    Sharma, B., Pandya, P.K., Chakraborty, S.: Bounded validity checking of interval duration logic. In: Halbwachs, N., Zuck, L.D. (eds.) Tools and Algorithms for the Construction and Analysis of Systems, 11th International Conference, TACAS 2005, Held as part of the Proceedings of the Joint European Conferences on Theory and Practice of Software, ETAPS 2005, Edinburgh, 4–8 April 2005. Lecture Notes in Computer Science, vol. 3440, pp. 301–316. Springer, Berlin/New York (2005)Google Scholar
  75. 75.
    Skakkebæk, J.U., Shankar, N.: Towards a duration calculus proof assistant in PVS. In: Langmaack, H., de Roever, W.P., Vytopil, J. (eds.) FTRTFT. Lecture Notes in Computer Science, vol. 863, pp. 660–679. Springer, Berlin (1994)Google Scholar
  76. 76.
    Vardi, M.Y.: Branching vs. linear time: final showdown. In: Margaria, T., Yi, W. (eds.) Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS’01). Lecture Notes in Computer Science, vol. 2031, pp. 1–22. Springer, Berlin/Heidelberg/New York (2001)Google Scholar
  77. 77.
    Zhou, C., Hansen, M.: Chopping a point. In: Cooke, J., Jifeng, H., Wallis, P. (eds.) BCS-FACS 7th Refinement Workshop, Electronic Workshops in Computing. Springer, Berlin/Heidelberg (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Carlo A. Furia
    • 1
  • Dino Mandrioli
    • 2
  • Angelo Morzenti
    • 2
  • Matteo Rossi
    • 2
  1. 1.Department of Computer ScienceZürichSwitzerland
  2. 2.Dipartimento di Elettronica e InformazionePolitecnico di MilanoMilanItaly

Personalised recommendations