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A public announcement separation logic

Published online by Cambridge University Press:  15 April 2019

J.R. Courtault ,
H. van Ditmarsch  and
D. Galmiche
J.R. Courtault
Affiliation:
Université de Lorraine, CNRS, LORIA, UMR 7503, Vandoeuvre-lès-Nancy, F-54506, France
H. van Ditmarsch
Affiliation:
Université de Lorraine, CNRS, LORIA, UMR 7503, Vandoeuvre-lès-Nancy, F-54506, France
D. Galmiche*
Affiliation:
Université de Lorraine, CNRS, LORIA, UMR 7503, Vandoeuvre-lès-Nancy, F-54506, France
*
*Corresponding author. Email: Didier.Galmiche@loria.fr
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Abstract

We define a Public Announcement Separation Logic (PASL) that allows us to consider epistemic possible worlds as resources that can be shared or separated, in the spirit of separation logics. After studying its semantics and illustrating its interest for modelling systems, we provide a sound and complete tableau calculus that deals with resource, agent and announcement constraints and give also a countermodel extraction method.

Keywords

Separation logicepistemic logicpublic announcementtableau calculus
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 29 , Issue 6 , June 2019 , pp. 828 - 871
Copyright
© Cambridge University Press 2019 

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References

Alechina, N., Logan, B., Nguyen, H. N. and Raimondi, F. (2017). Model-checking for resource-bounded ATL with production and consumption of resources. Journal of Computer and System Science 88 126–144.CrossRefGoogle Scholar
Alur, R., Henzinger, T. A. and Kupferman, O. (2002). Alternating-time temporal logic. Journal of the ACM 49 672–713.CrossRefGoogle Scholar
Balbiani, P., van Ditmarsch, H., Herzig, A. and de Lima, T. (2010). Tableaux for public announcement logic. Journal of Logic and Computation 20(1) 55–76.CrossRefGoogle Scholar
Baltag, A., Coecke, B. and Sadrzadeh, M. (2006). Epistemic actions as resources. Journal of Logic and Computation 17(3) 555–585.CrossRefGoogle Scholar
Biri, N. and Galmiche, D. (2003). A separation logic for resource distribution. In Proceedings of 23rd FSTTCS LNCS 2914, 23–37.Google Scholar
Collinson, M. and Pym, D. (2009). Algebra and logic for resource-based systems modelling. Mathematical Structures in Computer Science 19(5) 959–1027.CrossRefGoogle Scholar
Courtault, J.-R. andGalmiche, D. (2013). A modal BI logic for dynamic resource properties. In: International Symposium on Logical Foundations of Computer Science, LFCS, LNCS 7734, 134–148.CrossRefGoogle Scholar
Courtault, J.-R. andGalmiche, D. (2015). A modal separation logic for resource dynamics. Journal of Logic and Computation. doi.org/10.1093/logcom/exv031.Google Scholar
Courtault, J.-R., van Ditmarsch, H. and Galmiche, D. (2015). An epistemic separation logic. In: Proceedings of 22ndWoLLIC LNCS 9160, 156–173.Google Scholar
French, T., van der Hoek, W., Iliev, P. and Kooi, B. P. (2013). On the succinctness of some modal logics. Artificial Intelligence 197 56–85.CrossRefGoogle Scholar
Galmiche, D., Méry, D. and Pym, D. (2005). The semantics of BI and resource tableaux. Mathematical Structures in Computer Science 15(6) 1033–1088.CrossRefGoogle Scholar
Gerbrandy, J. D. (1999). Bisimulations on Planet Kripke. PhD thesis, University of Amsterdam.Google Scholar
Girard, J. Y. (1987). Linear logic. Theoretical Computer Science 50(1) 1–102.CrossRefGoogle Scholar
Herzig, A. (2013). A simple separation logic. In: Logic, Language, Information, and Computation – 20th International Workshop, WoLLIC 2013, LNCS 8071, Darmstadt, Germany, 168–178.CrossRefGoogle Scholar
Hintikka, J. (1962). Knowledge and Belief, Ithaca, NY, Cornell University Press.Google Scholar
Ishtiaq, S. and O’Hearn, P. (2001). BI as an assertion language for mutable data structures. In: 28th ACM Symposium on Principles of Programming Languages (POPL), London, 14–26.CrossRefGoogle Scholar
Larchey-Wendling, D. (2016). The formal strong completeness of partial monoidal Boolean BI. Journal of Logic and Computation 26(2) 605–640.CrossRefGoogle Scholar
Lenzen, W. (1978). Recent work in epistemic logic. Acta Philosophia Fennica 30:1–219.Google Scholar
Lutz, C. (2006). Complexity and succinctness of public announcement logic. In: Proceedings of 5th AAMAS, 137–144.CrossRefGoogle Scholar
Marion, M. and Sadrzadeh, M. (2003). Reasoning about knowledge in linear logic: Modalities and complexity. In: Logic, Epistemology, and the Unity of Science, Kluwer Academic Publishers, 327–350.Google Scholar
Meyer, J.-J. andvan der Hoek, W. (1995). Epistemic logic for AI and computer science. In: Tracts in Theoretical Computer Science, vol. 41, New York, NY, Cambridge University Press.Google Scholar
Plaza, J. A. (1989). Logics of public communications. In: Proceedings of the 4th ISMIS, Oak Ridge National Laboratory, 201–216.Google Scholar
Pym, D. J. (2002). The semantics and proof theory of the logic of bunched implications, vol. 26 of Applied Logic Series, Kluwer Academic Publishers.CrossRefGoogle Scholar
Moses, Y., Fagin, R., Halpern, J. and Vardi, M. (1995). Reasoning About Knowledge, Cambridge, MA, MIT Press.Google Scholar
Reynolds, J. (July 2002). Separation logic: A logic for shared mutable data structures. In: IEEE Symposium on Logic in Computer Science, Copenhagen, Denmark, 55–74.Google Scholar
van Benthem, J. and Liu, F. (2007). Dynamic logic of preference upgrade. Journal of Applied Non-Classical Logics 17(2) 157–182.CrossRefGoogle Scholar
van der Hoek, W. and Wooldridge, M. (2005). On the logic of cooperation and propositional control. Artificial Intelligence 164(1) 81–119.CrossRefGoogle Scholar
van Ditmarsch, H. (2003). The Russian cards problem. Studia Logica 75 31–62.CrossRefGoogle Scholar
van Ditmarsch, H., van der Hoek, W. and Kooi, B. (2007). Dynamic Epistemic Logic, Springer Publishing Company.CrossRefGoogle Scholar
van Ditmarsch, H., Halpern, J., van der Hoek, W. and Kooi, B. (2015). An introduction to logics of knowledge and belief. In: Handbook of Epistemic Logic, College Publications, 1–51.Google Scholar