Article

Dynamic logic with trace semantics

Authors:

Bernhard Beckert and

Daniel BrunsAuthors Info & Claims

CADE'13: Proceedings of the 24th international conference on Automated Deduction

June 2013

Pages 315 - 329

https://doi.org/10.1007/978-3-642-38574-2_22

Published: 09 June 2013 Publication History

Abstract

Dynamic logic is an established instrument for program verification and for reasoning about the semantics of programs and programming languages. In this paper, we define an extension of dynamic logic, called Dynamic Trace Logic (DTL), which combines the expressiveness of program logics such as dynamic logic with that of temporal logic. And we present a sound and relatively complete sequent calculus for proving validity of DTL formulae.

Due to its expressiveness, DTL can serve as a basis for proving functional and information-flow properties in concurrent programs, among other applications.

References

[1]

Abadi, M., Manna, Z.: Nonclausal deduction in first-order temporal logic. Journal of the ACM 37(2), 279-317 (1990).

Digital Library

[2]

Bauer, A., Leucker, M., Schallhart, C.: Comparing LTL semantics for runtime verification. J. Log. Comput. 20(3), 651-674 (2010).

Digital Library

[3]

Beckert, B.: A dynamic logic for Java Card. In: Proceedings, 2nd ECOOP Workshop on Formal Techniques for Java Programs, Cannes, France, pp. 111-119 (2000).

[4]

Beckert, B., Bruns, D.: Dynamic trace logic: Definition and proofs. Tech. Rep. 2012- 10, Karlsruhe Institute of Technology, Department of Computer Science (2012), revised version available at http://formal.iti.kit.edu/~bruns/papers/trace-tr.pdf

[5]

Beckert, B., Hähnle, R., Schmitt, P.H. (eds.): Verification of Object-Oriented Software. LNCS (LNAI), vol. 4334. Springer, Heidelberg (2007).

Digital Library

[6]

Beckert, B., Schlager, S.: A sequent calculus for first-order dynamic logic with trace modalities. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 626-641. Springer, Heidelberg (2001).

Digital Library

[7]

Goré, R.: Tableau methods for modal and temporal logics. In: D'Agostino, M., Gabbay, D., Hähnle, R., Posegga, J. (eds.) Handbook of Tableau Methods, pp. 297-396. Kluwer Academic Publishers, Dordrecht (1999).

[8]

Harel, D.: Dynamic logic. In: Gabbay, D., Guenther, F. (eds.) Handbook of Philosophical Logic, Volume II: Extensions of Classical Logic, pp. 497-604. D. Reidel Publishing Co., Dordrecht (1984).

[9]

Moszkowski, B.: A temporal logic for multilevel reasoning about hardware. IEEE Computer 18(2) (February 1985).

Digital Library

[10]

Platzer, A.: A temporal dynamic logic for verifying hybrid system invariants. In: Artemov, S., Nerode, A. (eds.) LFCS 2007. LNCS, vol. 4514, pp. 457-471. Springer, Heidelberg (2007).

Digital Library

[11]

Reynolds, M., Dixon, C.: Theorem-proving for discrete temporal logic. In: Fisher, D.M., Gabbay, Vila, L. (eds.) Handbook of Temporal Reasoning in Artificial Intelligence. Elsevier Science (2005).

[12]

Scheben, C., Schmitt, P.H.: Verification of information flow properties of java programs without approximations. In: Beckert, B., Damiani, F., Gurov, D. (eds.) FoVeOOS 2011. LNCS, vol. 7421, pp. 232-249. Springer, Heidelberg (2012).

Digital Library

[13]

Schellhorn, G., Tofan, B., Ernst, G., Reif, W.: Interleaved programs and rely-guarantee reasoning with ITL. In: Combi, C., Leucker, M., Wolter, F. (eds.) Eighteenth International Symposium on Temporal Representation and Reasoning, TIME 2011, pp. 99-106. IEEE (2011).

Digital Library

[14]

Thums, A., Schellhorn, G., Ortmeier, F., Reif, W.: Interactive verification of state-charts. In: Ehrig, H., Damm, W., Desel, J., Große-Rhode, M., Reif, W., Schnieder, E., Westkämper, E. (eds.) INT 2004. LNCS, vol. 3147, pp. 355-373. Springer, Heidelberg (2004).

[15]

Wolper, P.: The tableau method for temporal logic: An overview. Logique et Analyse 28(110-111), 119-136 (1985).

Cited By

Gordon CBergenti FCastegren EDe Koster JFranco J(2019)Modal assertions for actor correctnessProceedings of the 9th ACM SIGPLAN International Workshop on Programming Based on Actors, Agents, and Decentralized Control10.1145/3358499.3361221(11-20)Online publication date: 22-Oct-2019
https://dl.acm.org/doi/10.1145/3358499.3361221
Steinhöfel DHähnle R(2019)The Trace ModalityDynamic Logic. New Trends and Applications10.1007/978-3-030-38808-9_8(124-140)Online publication date: 7-Oct-2019
https://dl.acm.org/doi/10.1007/978-3-030-38808-9_8
Kamburjan E(2019)Behavioral Program LogicAutomated Reasoning with Analytic Tableaux and Related Methods10.1007/978-3-030-29026-9_22(391-408)Online publication date: 3-Sep-2019
https://dl.acm.org/doi/10.1007/978-3-030-29026-9_22
Show More Cited By

Index Terms

Dynamic logic with trace semantics
1. Theory of computation
  1. Logic
    1. Modal and temporal logics
    2. Proof theory
  2. Semantics and reasoning
    1. Program semantics

Index terms have been assigned to the content through auto-classification.

Recommendations

Semantics for disjunctive logic programs
Read More
A hoare logic for the coinductive trace-based big-step semantics of while
ESOP'10: Proceedings of the 19th European conference on Programming Languages and Systems

In search for a foundational framework for reasoning about observable behavior of programs that may not terminate, we have previously devised a trace-based big-step semantics for While. In this semantics, both traces and evaluation (relating initial ...
Read More
Neighborhood Semantics for Modal Logic
Read More

Comments

Information & Contributors

Information

Published In

cover image Guide Proceedings

CADE'13: Proceedings of the 24th international conference on Automated Deduction

June 2013

466 pages

ISBN:9783642385735

Editor:
Maria Paola Bonacina
Dipartimento di Informatica, Università degli Studi di Verona, Strada Le Grazie 15, Verona, Italy

Sponsors

CADE: CADE Inc.

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 09 June 2013

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

5
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Other Metrics

View Author Metrics

Citations

Cited By

Gordon CBergenti FCastegren EDe Koster JFranco J(2019)Modal assertions for actor correctnessProceedings of the 9th ACM SIGPLAN International Workshop on Programming Based on Actors, Agents, and Decentralized Control10.1145/3358499.3361221(11-20)Online publication date: 22-Oct-2019
https://dl.acm.org/doi/10.1145/3358499.3361221
Steinhöfel DHähnle R(2019)The Trace ModalityDynamic Logic. New Trends and Applications10.1007/978-3-030-38808-9_8(124-140)Online publication date: 7-Oct-2019
https://dl.acm.org/doi/10.1007/978-3-030-38808-9_8
Kamburjan E(2019)Behavioral Program LogicAutomated Reasoning with Analytic Tableaux and Related Methods10.1007/978-3-030-29026-9_22(391-408)Online publication date: 3-Sep-2019
https://dl.acm.org/doi/10.1007/978-3-030-29026-9_22
Adelsberger SSetzer AWalkingshaw ESabel DThiemann P(2018)Declarative GUIsProceedings of the 20th International Symposium on Principles and Practice of Declarative Programming10.1145/3236950.3236962(1-15)Online publication date: 3-Sep-2018
https://dl.acm.org/doi/10.1145/3236950.3236962
Bubel RDin CHähnle RNakata K(2015)A Dynamic Logic with Traces and CoinductionProceedings of the 24th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods - Volume 932310.1007/978-3-319-24312-2_21(307-322)Online publication date: 21-Sep-2015
https://dl.acm.org/doi/10.1007/978-3-319-24312-2_21

View Options

View options

Media

Figures

Other

Tables

View Table of Contents