Skip to main content
SpringerLink
Log in

A survey on temporal logics for specifying and verifying real-time systems

  • Review Article
  • Published:
Frontiers of Computer Science Aims and scope Submit manuscript

Abstract

Over the last two decades, there has been an extensive study of logical formalisms on specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have been introduced for formal specification of real-time and complex systems, an up to date survey of these logics does not exist in the literature. In this paper we analyse various temporal formalisms introduced for specification, including propositional/first-order linear temporal logics, branching temporal logics, interval temporal logics, real-time temporal logics and probabilistic temporal logics. We give decidability, axiomatizability, expressiveness, model checking results for each logic analysed. We also provide a comparison of features of the temporal logics discussed.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bellini P, Mattolini R, Nesi P. Temporal logics for real-time system specification. ACM Computing Surveys, 2000, 32(1): 12–42

    Article  Google Scholar 

  2. Alur R, Henzinger T A. Real-time logics: complexity and expressiveness. In: Proceedings of the 5th Annual IEEE Symposium on Logic in Computer Science. 1990, 390-401

  3. Ostroff J S. Formal methods for the specification and design of realtime safety critical systems. Journal of Systems and Software, 1992, 18(1): 33–60

    Article  Google Scholar 

  4. Øhrstrøm P, Hasle P F. Temporal logic: from ancient ideas to artificial intellgience. Dordrecht, The Netherlands: Kluwer Academic Publishers, 1995

    Google Scholar 

  5. Hirshfeld Y, Rabinovich A. Logics for real time: decidability and complexity. Fundamenta Informaticae, 2004, 62(1): 1–28

    MathSciNet  MATH  Google Scholar 

  6. Chaochen Z, Hansen M. Duration calculus: a formal approach to realtime systems. EATCS Series of Monographs in Theoretical Computer Science. Springer, 2004

    Google Scholar 

  7. Goranko V, Montanari A, Sciavicco G. A road map of interval temporal logics and duration calculi. Journal of Applied Non-Classical Logics, 2004, 14(1–2): 9–54

    Article  MATH  Google Scholar 

  8. Guelev D, Van Hung D. On the completeness and decidability of duration calculus with iteration. Theoretical Computer Science, 2005, 337(1): 278–304

    Article  MathSciNet  MATH  Google Scholar 

  9. Venema Y. Temporal logic. Blackwell Guide to Philosophical Logic, Blacwell Publishers, 1998

    Google Scholar 

  10. Fiaderio J L, Maibaum T. Action refinement in a temporal logic of objects. In: Gabbay D, Ohlbach H, eds, Temporal Logic. Springer LNAI 927, 1994

    Google Scholar 

  11. Schwartz R, Melliar-Smith P. From state machines to temporal logic: specification methods for protocol standards. IEEE Transactions on Communications, 1982, 30(12): 2486–2496

    Article  Google Scholar 

  12. Schwartz R L, Melliar-Smith P M, Voght F H. An interval logic for higher-level temporal reasoning. In: Proceedings of the 2nd ACM Symposium on Principles of Distributed Computing. 1983, 173–186

    Chapter  Google Scholar 

  13. Moszkowski B. Reasoning about digital circuits. PhD thesis, Computer Science Department, Stanford University, 1983

    Google Scholar 

  14. Ladkin P. Logical time pieces. AI Expert, 1987, 2(8): 58–67

    Google Scholar 

  15. Melliar-Smith P M. Extending interval logic to real time systems. In: Melliar-Smith P M, ed, Temporal Logic in Specification. Springer, 1989, 224–242

    Chapter  Google Scholar 

  16. Razouk R, Gorlick M. Real-time interval logic for reasoning about executions of real-time programs. ACM SIGSOFT Software Engineering Notes, 1989, 14(8): 10–19

    Article  Google Scholar 

  17. Halpern J Y, Shoham Y. A propositional modal logic of time intervals. Journal of the ACM, 1991, 38(4): 935–962

    Article  MathSciNet  MATH  Google Scholar 

  18. Allen J. Maintaining knowledge about temporal intervals. Communications of the ACM, 1983, 26(11): 832–843

    Article  MATH  Google Scholar 

  19. Venema Y. A modal logic for chopping intervals. Journal of Logic and Computation, 1991, 1(4): 453–476

    Article  MathSciNet  MATH  Google Scholar 

  20. Benthem V J F. The logic of time: a model-theoretic investigation into the varieties of temporal ontology and temporal discourse. 2nd ed. Kluwer, 1991

    MATH  Google Scholar 

  21. Montanari A, Sciavicco G, Vitacolonna N. Decidability of interval temporal logics over split-frames via granularity. In: Proceedings of the 8th Europian Conference on Logics in AI. 2002, 259–270

    Google Scholar 

  22. Vitacolonna N. Intervals: logics, algorithms and games. PhD thesis, Department of Mathematics and Computer Science, University of Udine, 2005

    Google Scholar 

  23. Walker A. Durées et instants. Revue Scientifique, 1947, 85: 131–134

    MATH  Google Scholar 

  24. Hamblin C. Instants and intervals. The Study of Time, 1972, 1: 324–331

    Article  Google Scholar 

  25. Humberstone I. Interval semantics for tense logic: some remarks. Journal of philosophical logic, 1979, 8(1): 171–196

    Article  MathSciNet  MATH  Google Scholar 

  26. Dowty D. Word meaning and montague grammar. Dordrecht: D. Reidel, 1979

    Book  Google Scholar 

  27. Kamp H. Events, instants and temporal reference. Semantics from Different Points of View, 1979, 376: 417

    Google Scholar 

  28. Röper P. Intervals and tenses. Journal of Philosophical Logic, 1980, 9(4): 451–469

    Article  MathSciNet  MATH  Google Scholar 

  29. Burgess J P. Axioms for tense logic 2: time periods. Notre Dame Journal of Formal Logic, 1982, 23(2): 375–383

    Article  MathSciNet  MATH  Google Scholar 

  30. Benthem V J F. The logic of time. Kluwer Academic Publishers, Dor-drecht, 1983

    MATH  Google Scholar 

  31. Galton A. The logic of aspect. Claredon Press, Oxford, 1984

    Google Scholar 

  32. Simons P. Parts, a study in ontology. Oxford: Claredon Press, 1987

    Google Scholar 

  33. Allen J. Towards a general theory of action and time. Artificial intelligence, 1984, 23(2): 123–154

    Article  MATH  Google Scholar 

  34. Allen J F, Hayes J P. Moments and points in an interval-based temporal logic. In: Poole D, Mackworth A, Goebel R, eds, Computational Intelligence Blackwell Publishers. 1989, 225–238

  35. Allen J F, Ferguson G. Actions and events in interval temporal logic. Journal of Logic and Computation, 1994, 4(5): 531–579

    Article  MathSciNet  MATH  Google Scholar 

  36. Galton A. A critical examination of allen’s theory of action and time. Artificial Intelligence, 1990, 42(2): 159–188

    Article  MathSciNet  MATH  Google Scholar 

  37. Roşu G, Bensalem S. Allen linear (interval) temporal logic- translation to ltl andmonitor synthesis. In: Proceedings of the 18th International Conference on Computer Aided Verification. 2006, 263–277

    Chapter  Google Scholar 

  38. Parikh R. A decidability result for a second order process logic. In: Proceedings of the 19th Annual Symposium on Foundations of Computer Science. 1978, 177-183

  39. Pratt V. Process logic: preliminary report. In: Proceedings of the 6th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages. 1979, 93–100

    Google Scholar 

  40. Harel D, Kozen D, Parikh R. Process logic: expressiveness, decidability, completeness. Journal of Computer and System Sciences, 1982, 25(2): 144–170

    Article  MathSciNet  MATH  Google Scholar 

  41. Halpern J, Manna Z, Moszkowski B. A high-level semantics based on interval logic. In: Proceedings of the 10th International Conference on Automata, Languages and Programming (ICALP). 1983, 278–291

    Chapter  Google Scholar 

  42. Gabbay D, Hodkinson I, Reynolds M. Temporal logic: mathematical foundations and computational aspects. Volume 1. Clarendon Press, Oxford, 1994

    Google Scholar 

  43. Prior A N. Time and modality. Oxford: Clarendon Press, 1957

    MATH  Google Scholar 

  44. Prior A N. Past, present and future. Oxford University Press, 1967

    Book  MATH  Google Scholar 

  45. Prior A N. Papers on time and tense. Oxford University Press, 1968

    Google Scholar 

  46. Kamp J A. Tense logic and the theory of linear order. PhD thesis, University of California, Los Angeles, 1968

    Google Scholar 

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

    Google Scholar 

  48. Szalas A. Temporal logic of programs: a standard approach. In: Bolc L, Szalas A, eds, Time and Logic: A Computational Approach UCL Press, 1995, 1–50.

    Google Scholar 

  49. Gabbay D M, Pnueli A, Shelah S, Stavi J. On the temporal analysis of fairness. In: Proceedings of the 7th Annual ACM Symposium on Principles of Programming Languages. 1980, 163–173

    Google Scholar 

  50. Sistla A, Clarke E. The complexity of propositional linear temporal logics. Journal of the ACM, 1985, 32(3): 733–749

    Article  MathSciNet  MATH  Google Scholar 

  51. Fisher M. A resolution method for temporal logic. In: Proceedings of 12th International Joint Conference on Artificial Intelligence. 1991, 99–104

    Google Scholar 

  52. Fisher M, Dixon C, Peim M. Clausal temporal resolution. ACM Transactions on Computational Logic, 2001, 2(1): 12–56

    Article  MathSciNet  Google Scholar 

  53. Lichtenstein O, Pnueli A, Zuck L. The glory of the past. In: Parikh R, ed, Logics of Programs. Springer Berlin Heidelberg, 1985, 196–218

    Chapter  Google Scholar 

  54. Lichtenstein O, Pnueli A. Propositional temporal logics: decidability and completeness. Logic Journal of the IGPL, 2000, 8(1): 55–85

    Article  MathSciNet  MATH  Google Scholar 

  55. Reynolds M. The complexity of the temporal logic with “until” over general linear time. Journal of Computer and System Sciences, 2003, 66(2): 393–426

    Article  MathSciNet  MATH  Google Scholar 

  56. Lutz C, Walther D, Wolter F. Quantitative temporal logics over the reals: PSPACE and below. Information and Computation, 2007, 205(1): 99–123

    Article  MathSciNet  MATH  Google Scholar 

  57. Reynolds M. The complexity of temporal logic over the reals. Annals of Pure and Applied Logic, 2010, 161(8): 1063–1096

    Article  MathSciNet  MATH  Google Scholar 

  58. McDermott D. A temporal logic for reasoning about processes and plans. Cognitive science, 1982, 6(2): 101–155

    Article  Google Scholar 

  59. Rao A, Georgeff M. A model-theoretic approach to the verification of situated reasoning systems. In: Proceedings of the 13th International Joint Conference on Artificial Intelligence. 1993

    Google Scholar 

  60. Abrahamson K. Decidability and expressiveness of logics of programs. PhD thesis, University of Washington, 1980

    Google Scholar 

  61. Ben-Ari M, Manna Z, Pnueli A. The temporal logic of branching time. In: Proceedings of the 8th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. 1981, 164–176

    Google Scholar 

  62. Clarke E M, Emerson E A. Design and synthesis of synchronization skeletons using branching-time temporal logic. In: Workshop on Logic of Programs. 1982, 52–71

    Chapter  Google Scholar 

  63. Emerson E A, Halpern J. “Sometimes” and “not never” revisited: on branching versus linear time temporal logic. Journal of the ACM, 1986, 33(1): 151–178

    Article  MathSciNet  MATH  Google Scholar 

  64. Laroussinie F, Schnoebelen P. A hierarchy of temporal logics with past. Theoretical Computer Science, 1995, 148(2): 303–324

    Article  MathSciNet  MATH  Google Scholar 

  65. Clarke E M, Grumberg O, Peled D A. Model Checking. MIT Press, 2000

    Google Scholar 

  66. Emerson E A, Halpern J Y. Decision procedures and expressiveness in the temporal logic of branching time. In: Proceedings of the 14th Annual ACM Symposium on Theory of Computing. 1982, 169–180

    Google Scholar 

  67. Emerson E, Srinivasan J. Branching time temporal logic. In: Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency. Springer, 1989, 123–172

    Chapter  Google Scholar 

  68. Emerson E A, Clarke E M. Using branching time temporal logic to synthesize synchronization skeletons. Science of Computer programming, 1982, 2(3): 241–266

    Article  MATH  Google Scholar 

  69. Clarke E M, Emerson E A, Sistla A P. Automatic verification of finite state concurrent systems using temporal logic. ACM Transactions on Programming Languages and Systems, 1986, 2(8): 244–263

    Article  Google Scholar 

  70. Penczek W. Branching time and partial order in temporal logics. In: Bolc L, Szalas A, eds, Time and Logic: A Computational Approach. UCL Press, 1995, 179–228

    Google Scholar 

  71. Emerson E A, Jutla C S. The complexity of tree automata and logics of programs. SIAM Journal of Compututation, 2000, 29(1): 132–158

    Article  MathSciNet  Google Scholar 

  72. Reynolds M. An axiomatization of full computation tree logic. Journal of Symbolic Logic, 2001, 66: 1011–1057

    Article  MathSciNet  MATH  Google Scholar 

  73. Reynolds M. An axiomatization of PCTL. Information and Computation, 2005, 201(1): 72–119

    Article  MathSciNet  MATH  Google Scholar 

  74. Laroussinie F, Schnoebelen P. Specification in CTL+past, verification in CTL. Information and Computation, 2000, 156(1): 236–263

    Article  MathSciNet  MATH  Google Scholar 

  75. Bozzelli L. The complexity of CTL* + linear past. In: Amadio R, ed, Foundations of Software Science and Computational Structures. Springer, 2008, 186–200

    Chapter  Google Scholar 

  76. Pratt V R. On the composition of processes. In: Proceedings of the 9th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL’ 82. 1982, 213–223

    Chapter  Google Scholar 

  77. Pinter S S, Wolper P. A temporal logic for reasoning about partially ordered computations (extended abstract). In: Proceedings of the 3rd Annual ACM Symposium on Principles of Distributed Computing. 1984, 28–37

    Chapter  Google Scholar 

  78. Kornatzky Y, Pinter S. An extension to partial order temporal logic (POTL). Research Report 596, Department of Electrical Engineering, Technion-Israel Institute of Technology, 1986

    Google Scholar 

  79. Bhat G, Peled D. Adding partial orders to linear temporal logic. Fundamenta Informaticae, 1998, 36(1): 1–21

    MathSciNet  MATH  Google Scholar 

  80. Gerth R, Kuiper R, Peled D, Penczek W. A partial order approach to branching time logic model checking. Information and Computation, 1999, 150(2): 132–152

    Article  MathSciNet  MATH  Google Scholar 

  81. Alexander A, Reisig W. Compositional temporal logic based on partial order. In: Proceedings of the 11th International Symposium on Temporal Representation and Reasoning, TIME’ 04. 2004, 125–132

    Google Scholar 

  82. Lomuscio A, Penczek W, Qu H. Partial order reductions for model checking temporal epistemic logics over interleaved multi-agent systems. In: Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems, AAMAS’ 10. 2010, 659–666

    Google Scholar 

  83. Fagin R, Halpern J, Moses Y, Vardi M. Reasoning about knowledge. MIT Press, 1996

    Google Scholar 

  84. Chomicki J, Toman D. Temporal logic in information systems. Logics for Databases and Information Systems, 1998, 31–70

    Chapter  Google Scholar 

  85. Abadi M. The power of temporal proofs. Theoretical Computer Science, 1989, 65(1): 35–83

    Article  MathSciNet  MATH  Google Scholar 

  86. Andréka H, Németi I, Sain I. Mathematical foundations of computer science. Lecture Notes in Computer Science, 1979, 208–218

    Google Scholar 

  87. Reynolds M. Axiomatising first-order temporal logic: until and since over linear time. Studia Logica, 1996, 57(2): 279–302

    Article  MathSciNet  MATH  Google Scholar 

  88. Merz S. Decidability and incompleteness results for first-order temporal logics of linear time. Journal of Applied Non-Classical Logics, 1992, 2(2): 139–156

    Article  MathSciNet  MATH  Google Scholar 

  89. Chomicki J. Efficient checking of temporal integrity constraints using bounded history encoding. ACM Transactions on Database Systems, 1995, 20(2): 149–186

    Article  Google Scholar 

  90. Pliuskevicius R. On the completeness and decidability of a restricted first order linear temporal logic. In: Proceedings of the 5th Kurt Gödel Colloquium on Computational Logic and Proof Theory. 1997, 241–254

    Chapter  Google Scholar 

  91. Wolter F, Zakharyaschev M. Axiomatizing the monodic fragment of first-order temporal logic. Annals of Pure and Applied logic, 2002, 118(1): 133–145

    Article  MathSciNet  MATH  Google Scholar 

  92. Andréka H, Németi I, Benthem V J. Modal languages and bounded fragments of predicate logic. Journal of Philosophical Logic, 1998, 27(3): 217–274

    Article  MathSciNet  MATH  Google Scholar 

  93. Grädel E. On the restraining power of guards. Journal of Symbolic Logic, 1999, 64: 1719–1742

    Article  MathSciNet  MATH  Google Scholar 

  94. Hodkinson I, Wolter F, Zakharyaschev M. Decidable fragments of first-order temporal logics. Annals of Pure and Applied logic, 2000, 106(1): 85–134

    Article  MathSciNet  MATH  Google Scholar 

  95. Börger E, Grädel E, Gurevich Y. The classical decision problem. Springer, 1997

    Book  MATH  Google Scholar 

  96. Hodkinson I M, Wolter F, Zakharyaschev M. Monodic fragments of first-order temporal logics: 2000–2001 A.D. In: Proceedings of the 2001 Artificial Intelligence on Logic for Programming, LPAR’ 01. 2001, 1–23

    Chapter  Google Scholar 

  97. Gabbay D, Kurucz A, Wolter F, Zakharyaschev M. Many-dimensional modal logics: theory and applications. Elsevier, 2002

    Google Scholar 

  98. Degtyarev A, Fisher M, Lisitsa A. Equality and monodic first-order temporal logic. Studia Logica, 2002, 72(2): 147–156

    Article  MathSciNet  MATH  Google Scholar 

  99. Woltert P, Zakharyaschev M. Modal description logics: modalizing roles. Fundamenta Informaticae, 1999, 39(4): 411–438

    MathSciNet  Google Scholar 

  100. Lutz C, Sturm H, Wolter F, Zakharyaschev M. A tableau decision algorithm for modalized ALC with constant domains. Studia Logica, 2002, 72(2): 199–232

    Article  MathSciNet  MATH  Google Scholar 

  101. Dixon C, Fisher M, Konev B, Lisitsa A. Practical first-order temporal reasoning. In: Proceedings of the 15th International Symposium on Temporal Representation and Reasoning, TIME’ 08. 2008, 156–163

    Google Scholar 

  102. Emerson E, Mok A, Sistla A, Srinivasan J. Quantitative temporal reasoning. Real-Time Systems, 1992, 4(4): 331–352

    Article  Google Scholar 

  103. Koymans R. Specifying real-time properties with metric temporal logic. Real-Time Systems, 1990, 2(4): 255–299

    Article  Google Scholar 

  104. Alur R, Henzinger T A. A really temporal logic. Journal of the ACM, 1994, 41(1): 181–203

    Article  MathSciNet  MATH  Google Scholar 

  105. Henzinger T A. The temporal specification and verification of realtime systems. PhD thesis, Department of Computer Science, Stanford University, 1991

    Google Scholar 

  106. Emerson E A, Trefler R J. Generalized quantitative temporal reasoning: an automata theoretic-approach. In: Proceedings of the 7th International Joint Conference Theory and Practice of Software Development. 1996, 189–200

    Google Scholar 

  107. Laroussinie F, Meyer A, Petonnet E. Counting LTL. In: Proceedings of the 17th International Symposium on Temporal Representation and Reasoning. 2010, 51–58

    Google Scholar 

  108. Ouaknine J, Worrell J. Some recent results in metric temporal logic. In: Proceedings of the 6th international conference on Formal Modeling and Analysis of Timed Systems, FORMATS’ 08. 2008, 1–13

    Chapter  Google Scholar 

  109. Ouaknine J, Worrell J. On the decidability of metric temporal logic. In: Proceedings 20th Annual IEEE Symposium on Logic in Computer Science. 2005, 188–197

    Google Scholar 

  110. Alur R, Feder T, Henzinger T A. The benefits of relaxing punctuality. Journal of the ACM, 1996, 43(1): 116–146

    Article  MathSciNet  MATH  Google Scholar 

  111. Henzinger T A, Raskin J F, Schobbens P Y. The regular real-time languages. In: Proceedings of the 25th International Colloquium on Automata, Languages and Programming. 1998, 580–591

    Chapter  Google Scholar 

  112. Henzinger T A. It’s about time: real-time logics reviewed. In: Proceedings of the 9th International Conference on Concurrency Theory. 1998, 439–454

    Google Scholar 

  113. Lasota S, Walukiewicz I. Alternating timed automata. ACM Transactions on Computational Logic, 2008, 9(2): 1–27

    Article  MathSciNet  Google Scholar 

  114. Maler O, Nickovic D, Pnueli A. Real time temporal logic: past, present, future. In: Pettersson P, Yi W, eds, Formal Modeling and Analysis of Timed Systems. Springer-Verlag, 2005, 2–16

    Chapter  Google Scholar 

  115. Bouyer P, Markey N, Ouaknine J, Worrell J. On expressiveness and complexity in real-time model checking. In: Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II, ICALP’ 08. 2008, 124–135

    Chapter  Google Scholar 

  116. Bouyer P, Chevalier F, Markey N. On the expressiveness of TPTL and MTL. In: Proceedings of the 25th International Conference on Foundations of Software Technology and Theoretical Computer Science. 2005, 432–443

    Google Scholar 

  117. Alur R, Henzinger T A. Logics and models of real time: a survey. In: Proceedings of the Real-Time: Theory in Practice, REX Workshop. 1992, 74–106

    Chapter  Google Scholar 

  118. Alur R, Courcoubetis C, Dill D L. Model checking for real-time systems. In: Proceedings of the 5th Conference on Logic in Computer Science. 1990, 12–21

    Google Scholar 

  119. Laroussinie F, Markey N, Schnoebelen P. Model checking timed automata with one or two clocks. In: Proceedings of the 15th International Conference on Concurrency Theory. 2004, 387

    Google Scholar 

  120. Hansson H A. Time and probability in formal design and distributed systems. PhD thesis, Department of Computer Science, Uppsala University, Sweden, 1991

    Google Scholar 

  121. Beauquier D, Slissenko A. Polytime model checking for timed probabilistic computation tree logic. Acta Informatica, 1998, 35: 645–664

    Article  MathSciNet  Google Scholar 

  122. Laroussinie F, Meyer A, Petonnet E. Counting CTL. Foundations of Software Science and Computational Structures, 2010, 206–220

    Chapter  Google Scholar 

  123. Jahanian F, Mok A. Safety analysis of timing properties in real-time systems. IEEE Transactions on Software Engineering, 1986, 12(9): 890–904

    Article  Google Scholar 

  124. Jahanian F, Mok A. Modechart: a specification language for real-time systems. IEEE Transactions on Software Engineering, 1994, 20(12): 933–947

    Article  Google Scholar 

  125. Jahanian F, Stuart D. A method for verifying properties of modechart specifications. In: Proceedings of the 9th Real-time Systems Symposium. 1988, 12–21

    Google Scholar 

  126. Andrei S, Cheng A M K. Faster verification of RTL-specified systems via decomposition and constraint extension. In: Proceedings of the 27th IEEE International Real-Time Systems Symposium. 2006, 67–76

    Google Scholar 

  127. Andrei S, Cheng A M K. Verifying linear real-time logic specifications. In: Proceedings of the 28th IEEE International Real-Time Systems Symposium. 2007, 333–342

    Google Scholar 

  128. Ostroff J S, Wonham W. Modeling and verifying real-time embedded computer systems. In: Proceedings of the 8th IEEE Real-Time Systems Symposium. 1987, 124–132

    Google Scholar 

  129. Ostroff J S. Temporal logic for real-time systems. Advanced Software Development Series. Research Studies Press Limited, 1989

    Google Scholar 

  130. Harel E, Lichtenstein O, Pnueli A. Explicit clock temporal logic. In: Proceedings of the 5th Annual Symposium on Logic in Computer Science. 1990, 402–413

    Chapter  Google Scholar 

  131. Harel D, Lachover H, Naamad A, Pnueli A, Politi M, Sherman R, et al. Statemate: a working environment for the development of complex reactive systems. IEEE Transactions on Software Engineering, 1990, 16(4): 403–414

    Article  Google Scholar 

  132. Ghezzi C, Mandrioli D, Morzenti A. TRIO: a logic language for executable specifications of real-time systems. Journal of Systems and Software, 1990, 12(2): 107–123

    Article  Google Scholar 

  133. Mattolini R. TILCO: a temporal logic for the specification of real-time systems. PhD thesis, University of Florence, 1996

    Google Scholar 

  134. Mattolini R, Nesi P. Using TILCO for specifying real-time systems. In: Proceedings of the 2nd IEEE International Conference on Engineering of Complex Computer Systems. 1996, 18–25

    Google Scholar 

  135. Mattolini R, Nesi P. An interval logic for real-time system specification. IEEE Transactions on Software Engineering, 2001, 27(3): 208–227

    Article  Google Scholar 

  136. Paulson L C. Isabelle: a generic theorem prover. Springer LNCS 828, 1994

    MATH  Google Scholar 

  137. Bellini P, Giotti A, Nesi P, Rogai D. TILCO temporal logic for realtime systems implementation in C++. In: Proceedings of the 15th International Conference on Software Engineering and Knowledge Engineering. 2003, 166–173

    Google Scholar 

  138. Bellini P, Giotti A, Nesi P. Execution of TILCO temporal logic speci- fications. In: Proceedings of the 8th International Conference on Engineering of Complex Computer Systems, ICECCS’ 02. 2002, 78–87

    Google Scholar 

  139. Bellini P, Nesi P, Rogai D. Reply to comments on “an interval logic for real-time system specification”. IEEE Transactions on Software Engineering, 2006, 32(6): 428–431

    Article  Google Scholar 

  140. Bellini P, Nesi P, Rogai D. Validating component integration with C-TILCO. Electronic Notes in Theoretical Computer Science, 2005, 116: 241–252

    Article  Google Scholar 

  141. Marx M, Reynolds M. Undecidability of compass logic. Journal of Logic and Computation, 1999, 9(6): 897–914

    Article  MathSciNet  MATH  Google Scholar 

  142. Marx D, Venema Y. Multi-dimensional modal logics. Kluwer Academic Press, 1997

    Book  Google Scholar 

  143. Lodaya K. Sharpening the undecidability of interval temporal logic. In: Proceedings of the 6th Asian Computing Science Conference. 2000, 290–298

    Google Scholar 

  144. Bresolin D, Monica D, Goranko V, Montanari A, Sciavicco G. Decidable and undecidable fragments of halpern and shoham’s interval temporal logic: towards a complete classification. In: Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR’ 08. 2008, 590–604

    Chapter  Google Scholar 

  145. Bresolin D. Proof methods for interval temporal logics. PhD thesis, University of Udine, 2007

    Google Scholar 

  146. Goranko V, Montanari A, Sciavicco G. A general tableau method for propositional interval temporal logics. In: Proceedings of the 2003 International Conference Tableaux. 2003, 102–116

    Google Scholar 

  147. Hodkinson I, Montanari A, Sciavicco G. Non-finite axiomatizability and undecidability of interval temporal logics with C, D, and T. In: Proceedings of the 22nd International Workshop on Computer Science Logic. 2008, 308–322

    Chapter  Google Scholar 

  148. Chaochen Z, Hansen M. An adequate first order interval logic. In: Revised Lectures from the International Symposium on Compositionality: The Significant Difference. 1997, 584–608

    Google Scholar 

  149. Goranko V, Montanari A, Sciavicco G. Propositional interval neighbourhood temporal logics. Journal of Universal Computer Science, 2003, 9(9): 1137–1167

    MathSciNet  Google Scholar 

  150. Bresolin D, Montanari A, Sala P. An optimal tableau-based decision algorithm for propositional neighborhood logic. In: Proceedings of the 24th Annual Conference on Theoretical Aspects of Computer Science. 2007, 549–560

    Google Scholar 

  151. Bresolin D, Goranko V, Montanari A, Sciavicco G. On decidability and expressiveness of propositional interval neighbourhood logics. In: Proceedings of the International Symposium on Logical Foundations of Computer Science. 2007, 84–99

    Chapter  Google Scholar 

  152. Bresolin D, Montanari A. A tableau-based decision procedure for right propositional neighborhood logic. In: Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods. 2005, 63–77

    Chapter  Google Scholar 

  153. Bresolin D, Montanari A, Sciavicco G. An optimal tableau-based decision procedure for right propositional neighbourhood logic. Journal of Automated Reasoning, 2007, 38: 173–199

    Article  MathSciNet  MATH  Google Scholar 

  154. Bresolin D, Della Monica D, Goranko V, Montanari A, Sciavicco G. Metric propositional neighborhood logics: expressiveness, decidability, and undecidability. In: Proceedings of the 19th European Conference on Artificial Intelligence. 2010, 695–700

    Google Scholar 

  155. Bresolin D, Goranko V, Montanari A, Sciavicco G. Propositional interval neighborhood logics: expressiveness, decidability, and undecidable extensions. Annals of Pure and Applied Logic, 2009, 161(3): 289–304

    Article  MathSciNet  MATH  Google Scholar 

  156. Chagrov A V, Rybakov M N. How many variables does one need to prove PSPACE-hardness of modal logics? In: Advances in Modal Logic. 2003, 71–82

    Google Scholar 

  157. Demri S, Gore R. An O((n. log n)3)− time transformation from Grz into decidable fragments of classical first-order logic. In: Selected Papers from Automated Deduction in Classical and Non-Classical Logics. 2000, 153–167

    Google Scholar 

  158. Bresolin D, Goranko V, Montanari A, Sala P. Tableaux for logics of subinterval structures over dense orderings. Journal of Logic and Computation, 2010, 20(1): 133–166

    Article  MathSciNet  MATH  Google Scholar 

  159. Montanari A, Pratt-Hartmann I, Sala P. Decidability of the logics of the reflexive sub-interval and super-interval relations over finite linear orders. In: Proceedings of the 17th International Symposium on Temporal Representation and Reasoning. 2010, 27–34

    Google Scholar 

  160. Marcinkowski J, Michaliszyn J. The ultimate undecidability result for the Halpern-shoham logic. In: Proceedings of the 26th Annual IEEE Symposium on Logic in Computer Science. 2011, 377–386

    Google Scholar 

  161. Pratt-Hartmann I. Temporal prepositions and their logic. Artificial Intelligence, 2005, 166(1–2): 1–36

    Article  MathSciNet  MATH  Google Scholar 

  162. Konur S. A decidable temporal logic for events and states. In: Proceedings of the 13th International Symposium on Temporal Representation and Reasoning. 2006, 36–41

    Chapter  Google Scholar 

  163. Chaochen Z, Hoare C, Ravn A. A calculus of durations. Information Processing Letters, 1991, 40(5): 269–276

    Article  MathSciNet  MATH  Google Scholar 

  164. Dutertre B. On first-order interval temporal logic. Technical Report CSD-TR-94-3, Department of Computer Science, Royal Holloway College, University of London, 1995

    Google Scholar 

  165. Moszkowski B. A complete axiomatization of interval temporal logic with infinite time. In: Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science. 2000, 242–251

    Google Scholar 

  166. Guelev D P. A complete proof system for first order interval temporal logic with projection. Technical Report 202, UNU/IIST, 2000

    Google Scholar 

  167. Moszkowski B. Some very compositional temporal properties. In: Proceedings of the IFIP TC2/WG2. 1/WG2. 2/WG2. 3 Working Conference on Programming Concepts, Methods and Calculi. 1994, 307–326

    Google Scholar 

  168. Chaochen Z, Hansen M, Sestoft P. Decidability and undecidability results for duration calculus. In: Proceedings of the 10th Symposium on Theoretical Aspects of Computer Science. 1993, 58–68

    Google Scholar 

  169. Rabinovich A. Non-elementary lower bound for propositional duration calculus. Information Processing Letters, 1998, 66(1): 7–11

    Article  MathSciNet  MATH  Google Scholar 

  170. Fränzle M. Synthesizing controllers from duration calculus. In: Proceedings of the 4th International Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems. 1996, 168–187

    Chapter  Google Scholar 

  171. Guelev D, Dang V H. On the completeness and decidability duration calculus with iteration. In: Thiagarajan P S, Yap R, eds, Advances in Computer Science. Springer, 1999, 139–150

    Google Scholar 

  172. Chetcuti-Serandio N, Cerro L D. A mixed decision method for duration calculus. Journal of Logic and Computation, 2000, 10(6): 877–895

    Article  MathSciNet  MATH  Google Scholar 

  173. Pandya P K. Specifying and deciding quantified discrete-time duration calculus formulas using DCVALID. In: Proceedings of the 2001 Workshop on Real-Time Tools. 2001

    Google Scholar 

  174. Zhou C. Linear duration invariants. In: Proceedings of the 3rd International Symposium Organized Jointly with the Working Group Provably Correct Systems on Formal Techniques in Real-Time and Fault-Tolerant Systems. 1994, 86–109

    Google Scholar 

  175. Xuandong L, Hung D. Checking linear duration invariants by linear programming. In: Proceedings of the 2nd Asian Computing Science Conference on Concurrency and Parallelism, Programming, Networking, and Security. 1996, 321–332

    Chapter  Google Scholar 

  176. Thai P H, Hung D V. Checking a regular class of duration calculus models for linear duration invariants. In: Proceedings of the International Symposium on Software Engineering for Parallel and Distributed Systems. 1998, 61–71

    Google Scholar 

  177. Thai P, Van Hung D. Verifying linear duration constraints of timed automata. In: Proceedings of the 1st International Conference on Theoretical Aspects of Computing. 2004, 295–309

    Google Scholar 

  178. Satpathy M, Hung D V, Pandya P K. Some decidability results for duration calculus under synchronous interpretation. In: Proceedings of the 5th International Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems. 1998, 186–197

    Chapter  Google Scholar 

  179. Fränzle M. Take it NP-easy: Bounded model construction for duration calculus. In: Proceedings of the 7th International Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems: Cosponsored by IFIP WG 2.2. 2002, 245–264

    Chapter  Google Scholar 

  180. Biere A, Cimatti A, Clarke E M, Zhu Y. Symbolic model checking without BDDs. In: Proceedings of the 5th International Conference on Tools and Algorithms for Construction and Analysis of Systems. 1999, 193–207

    Chapter  Google Scholar 

  181. Fränzle M, Hansen M. Deciding an interval logic with accumulated durations. In: Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems. 2007, 201–215

    Chapter  Google Scholar 

  182. Hansen M R, Sharp R. Using interval logics for temporal analysis of security protocols. In: Proceedings of the 2003 ACM Workshop on Formal Methods in Security Engineering. 2003

    Google Scholar 

  183. Barua R, Roy S, Chaochen Z. Completeness of neighbourhood logic. Journal of Logic and Computation, 2000, 10(2): 271–295

    Article  MathSciNet  MATH  Google Scholar 

  184. Barua R, Chaochen Z. Neighbourhood logics. Research Report 120, UNU/IIST, 1997

    Google Scholar 

  185. Alur R, Dill D. Automata-theoretic verification of real-time systems. Formal Methods for Real-Time Computing, 1996, 55–82

    Google Scholar 

  186. Alur R, Henzinger T A, Ho P H. Automatic symbolic verification of embedded systems. IEEE Transactions on Software Engineering, 1996, 22(3): 181–201

    Article  Google Scholar 

  187. Bengtsson J, Larsen K, Larsson F, Pettersson P, Yi W. UPPAAL-a tool suite for automatic verification of real-time systems. In: Proceedings of the DIMACS/SYCON Workshop on Hybrid systems III: Verification and Control. 1996, 232–243

    Chapter  Google Scholar 

  188. Bozga M, Daws C, Maler O, Olivero A, Tripakis S, Yovine S. Kronos: a model-checking tool for real-time systems. In: Proceedings of the 10th International Conference on Computer Aided Verification. 1998, 546–550

    Chapter  Google Scholar 

  189. Pandya P. Interval duration logic: expressiveness and decidability. Electronic Notes in Theoretical Computer Science, 2002, 65(6): 254–272

    Article  Google Scholar 

  190. Sharma B, Pandya P, Chakraborty S. Bounded validity checking of interval duration logic. In: Proceedings of the 11th International Conference on Tools and Algorithms for the Construction and Analysis of Systems. 2005, 301–316

    Chapter  Google Scholar 

  191. Chakravorty G, Pandya P. Digitizing interval duration logic. In: Hunt JW, Somenzi F, eds, Computer Aided Verification. Springer Berlin Heidelberg, 2003, 167–179

    Chapter  Google Scholar 

  192. Filliâtre J, Owre S, Rueß H, Shankar N. ICS: integrated canonizer and solver. In: Proceedings of the 13th International Conference on Computer Aided Verification. 2001, 246–249

    Chapter  Google Scholar 

  193. Van Hung D, Chaochen Z. Probabilistic duration calculus for continuous time. Formal Aspects of Computing, 1999, 11(1): 21–44

    Article  MATH  Google Scholar 

  194. Fagin R, Halpern J Y. Reasoning about knowledge and probability. Journal of the ACM, 1994, 41(2): 340–367

    Article  MathSciNet  MATH  Google Scholar 

  195. Marković Z, Ognjanović Z, Rašković M. A probabilistic extension of intuitionistic logic. Mathematical Logic Quarterly, 2003, 49(4): 415–424

    Article  MathSciNet  MATH  Google Scholar 

  196. Hansson H, Jonsson B. A framework for reasoning about time and reliability. In: Proceedings of the 1999 Real Time Systems Symposium. 1989, 102–111

    Chapter  Google Scholar 

  197. Hansson H, Jonsson B. A logic for reasoning about time and reliability. Formal Aspects of Computing, 1994, 6(5): 512–535

    Article  MATH  Google Scholar 

  198. Brázdil T, Forejt V, Kretinsky J, Kucera A. The satisfiability problem for probabilistic CTLw. In: Proceedings of the 23rd Annual IEEE Symposium on Logic in Computer Science. 2008, 391–402

    Google Scholar 

  199. Aziz A, Singhal V, Balarin F. It usually works: the temporal logic of stochastic systems. In: Proceedings of the 7th International Conference on Computer Aided Verification. 1995, 155–165

    Chapter  Google Scholar 

  200. Bianco A, Alfaro L. Model checking of probabalistic and nondeterministic systems. In: Proceedings of the 15th Conference on Foundations of Software Technology and Theoretical Computer Science. 1995, 499–513

    Chapter  Google Scholar 

  201. Kwiatkowska M, Norman G, Segala R, Sproston J. Automatic verification of real-time systems with discrete probability distributions. In: Katoen J P, ed, Formal Methods for Real-Time and Probabilistic Systems. Springer, 1999, 75–95

    Chapter  Google Scholar 

  202. Kwiatkowska M, Norman G, Segala R, Sproston J. Verifying quantitative properties of continuous probabilistic timed automata. In: Proceedings of the 11th International Conference on Concurrency Theory. 2000, 123–137

    Google Scholar 

  203. Jurdzinski M, Laroussinie F, Sproston J.Model checking probabilistic timed automata with one or two clocks. In: Abdulla P, Leino K, eds, Tools and Algorithms for the Construction and Analysis of Systems. Springer, 2007, 170–184

    Chapter  Google Scholar 

  204. Ognjanović Z. Discrete linear-time probabilistic logics: completeness, decidability and complexity. Journal of Logic and Computation, 2006, 16(2): 257–285

    Article  MathSciNet  MATH  Google Scholar 

  205. Liu Z, Ravn A P, Sorensen E V, Zhou C. A probabilistic duration calculus. Technical Report, University of Warwick, 1992

    Google Scholar 

  206. Hung D V, Zhang M. On verification of probabilistic timed automata against probabilistic duration properties. In: Proceedings of the 13th IEEE International Conference on Embedded and Real-Time Computing Systems and Applications. 2007, 165–172

    Google Scholar 

  207. Choe Changil D V H. Model checking durational probabilistic systems against probabilistic linear duration invariants. Research Report 337, UNU/IIST, 2006

    Google Scholar 

  208. Kwiatkowska M, Norman G, Segala R, Sproston J. Automatic verification of real-time systems with discrete probability distributions. Theoretical Computer Science, 2002, 282(1): 101–150

    Article  MathSciNet  MATH  Google Scholar 

  209. Guelev D P. Probabilistic neighbourhood logic. In: Proceedings of the 6th International Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems. 2000, 264–275

    Chapter  Google Scholar 

  210. Guelev D. Probabilistic neighbourhood logic. Research Report 196, UNU/IIST, 2000

    Google Scholar 

  211. Guelev D P. Probabilistic interval temporal logic. Technical Report 144, UNU/IIST, 1998

    Google Scholar 

  212. Segerberg K. A completeness theorem in the modal logic of programs. In: Traczyk T, ed, Universal Algebra. Banach Centre Publications, 1982, 31–46

    Google Scholar 

  213. Pippenger N, Fischer M J. Relations among complexity measures. Journal of the ACM, 1979, 26(2): 361–381

    Article  MathSciNet  MATH  Google Scholar 

  214. Harel D, Tiuryn J, Kozen D. Dynamic Logic. Cambridge, MA, USA: MIT Press, 2000

    MATH  Google Scholar 

  215. Lamport L. The temporal logic of actions. ACM Transactions on Programming Languages and Systems, 1994, 16(3): 872–923

    Article  Google Scholar 

  216. Giordano L, Martelli A, Schwind C. Reasoning about actions in dynamic linear time temporal logic. Logic Journal of IGPL, 2001, 9(2): 273–288

    Article  MathSciNet  MATH  Google Scholar 

  217. Kowalski R, Sergot M. A logic-based calculus of events. New Generation Computing, 1986, 4(1): 67–95

    Article  Google Scholar 

  218. Shoham Y. Reasoning about Action and Change. MIT Press, 1987

    Google Scholar 

  219. Reiter R. Proving properties of states in the situation calculus. Artifi- cial Intelligence, 1993, 64(2): 337–351

    Article  MathSciNet  MATH  Google Scholar 

  220. Gelfond M, Lifschitz V. Representing action and change by logic programs. The Journal of Logic Programming, 1993, 17(2): 301–321

    Article  MathSciNet  MATH  Google Scholar 

  221. Belnap N D. Facing the future: agents and choices in our indeterminist world. Oxford University Press, USA, 2001

    Google Scholar 

  222. Kozen D. Semantics of probabilistic programs. In: Proceedings of the 20th Annual Symposium on Foundations of Computer Science. 1979, 101–114

    Google Scholar 

  223. Feldman Y A, Harel D. A probabilistic dynamic logic. In: Proceedings of the 14th Annual ACM Symposium on Theory of Computing. 1982, 181–195

    Google Scholar 

  224. Pratt V R. Semantical consideratiosn on Floyd-Hoare logic. Technical Report, MIT, 1976

    Google Scholar 

  225. Feidman Y A. A decidable propositional probabilistic dynamic logic. In: Proceedings of the 15th Annual ACM Symposium on Theory of Computing. 1983, 298–309

    Google Scholar 

  226. Kozen D. A probabilistic PDL. In: Proceedings of the 15th annual ACM symposium on Theory of Computing. 1983, 291–297

    Google Scholar 

  227. Feldman Y A. A decidable propositional dynamic logic with explicit probabilities. Information Control, 1984, 63(1): 11–38

    Article  MATH  Google Scholar 

  228. Segerberg K. Qualitative probability in a modal setting. In: Proceedings of the 2nd Scandinavian Logic Symposium. 1971, 575–604

    Google Scholar 

  229. Guelev D. A propositional dynamic logic with qualitative probabilities. Journal of philosophical logic, 1999, 28(6): 575–604

    Article  MathSciNet  MATH  Google Scholar 

  230. Cleaveland R, Iyer S, Narasimha M. Probabilistic temporal logics via the modalMu-Calculus. Theoretical Computer Science, 2005, 342(2): 316–350

    Article  MathSciNet  MATH  Google Scholar 

  231. Konur S. An interval temporal logic for real-time system specification. PhD thesis, Department of Computer Science, University of Manchester, UK, 2008

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, the University of Liverpool, Liverpool, L69 3BX, UK

    Savas Konur

Authors
  1. Savas Konur
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Savas Konur.

Additional information

Savas Konur is a member of staff at the Department of Computer Science, University of Liverpool. He obtained a PhD in computer science from University of Manchester in 2008. He is currently a member of Logic and Computation research group in the Department of Computer Science, University of Liverpool. His research interests include temporal reasoning, formal specification and verification, model checking, real-time systems, multi-agent systems, and pervasive systems.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Konur, S. A survey on temporal logics for specifying and verifying real-time systems. Front. Comput. Sci. 7, 370–403 (2013). https://doi.org/10.1007/s11704-013-2195-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11704-013-2195-2

Keywords

Search

Navigation