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Big Brother Logic: visual-epistemic reasoning in stationary multi-agent systems

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Abstract

We consider multi-agent scenarios where each agent controls a surveillance camera in the plane, with fixed position and angle of vision, but rotating freely. The agents can thus observe the surroundings and each other. They can also reason about each other’s observation abilities and knowledge derived from these observations. We introduce suitable logical languages for reasoning about such scenarios which involve atomic formulae stating what agents can see, multi-agent epistemic operators for individual, distributed and common knowledge, as well as dynamic operators reflecting the ability of cameras to turn around in order to reach positions satisfying formulae in the language. We also consider effects of public announcements. We introduce several different but equivalent versions of the semantics for these languages, discuss their expressiveness and provide translations in PDL style. Using these translations we develop algorithms and obtain complexity results for model checking and satisfiability testing for the basic logic BBL that we introduce here and for some of its extensions. Notably, we show that even for the extension with common knowledge, model checking and satisfiability testing remain in PSPACE. We also discuss the sensitivity of the set of validities to the admissible angles of vision of the agents’ cameras. Finally, we discuss some further extensions: adding obstacles, positioning the cameras in 3D or enabling them to change positions. Our work has potential applications to automated reasoning, formal specification and verification of observational abilities and knowledge of multi-robot systems.

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References

  1. Balbiani, P., Gasquet, O., & Schwarzentruber, F. (2013). Agents that look at one another. Logic Journal of IGPL, 21(3), 438–467.

    Article  MathSciNet  MATH  Google Scholar 

  2. Balbiani, P., Goranko, V., Kellerman, R., & Vakarelov, D. (2007). Logical theories of fragments of elementary geometry. In M. Aiello, J. van Benthem, & I. Pratt-Hartmann (Eds.), Handbook of spatial logics (pp. 343–428). Heidelberg: Springer.

    Chapter  Google Scholar 

  3. Balbiani, P., Van Ditmarsch, H., Herzig, A., & De Lima, T. (2010). Tableaux for public announcement logic. Journal of Logic and Computation, 20(1), 55–76.

    Article  MathSciNet  MATH  Google Scholar 

  4. Ben-Or, M., Kozen, D., & Reif, J. (1986). The complexity of elementary algebra and geometry. Journal of Computer and System Sciences, 32(2), 251–264.

    Article  MathSciNet  MATH  Google Scholar 

  5. Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal logic. Cambridge: Cambridge University Press.

    Book  MATH  Google Scholar 

  6. Bustamante, A. L., Molina, J. M., & Patricio, M. A. (2010). Multi-camera and multi-modal sensor fusion, an architecture overview. In Proceedings of the DCAI’2010 (pp. 301–308).

  7. Canny, J. (1988). Some algebraic and geometric computations in PSPACE. In Proceedings of STOC’88 (pp. 460–467). New York: ACM.

  8. Fagin, R., Halpern, J., Moses, Y., & Vardi, M. (1995). Reasoning about knowledge. Cambridge: MIT Press.

    MATH  Google Scholar 

  9. García, J., Carbó, J., & Molina, J. M. (2005). Agent-based coordination of cameras. International Journal of Computer Science & Applications, 2(1), 33–37.

    Google Scholar 

  10. Gasquet, O., Goranko, V., & Schwarzentruber, F. (2014). Big brother logic: Logical modeling and reasoning about agents equipped with surveillance cameras in the plane. In Proceedings of the AAMAS’2014 (pp. 325–332)

  11. Goranko, V., Merker, M., & Thomassen, C. (2014). Directed graphs with restricted angles of vision. Manuscript.

  12. Harel, D., Kozen, D., & Tiuryn, J. (2000). Dynamic logic. Cambridge: MIT Press.

    MATH  Google Scholar 

  13. Plaza, J. (2007). Logics of public communications. Synthese, 158(2), 165–179.

    Article  MathSciNet  MATH  Google Scholar 

  14. Schwarzentruber, F. (2011). Seeing, knowledge and common knowledge. In Logic, rationality, and interaction (pp. 258–271). Berlin: Springer.

  15. Sipser, M. (2006). Introduction to the theory of computation (Vol. 2). Boston: Thomson Course Technology.

    MATH  Google Scholar 

  16. Tarski, A. (1951). A decision method for elementary algebra and geometry. Berlin: Springer.

    MATH  Google Scholar 

  17. van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2008). Dynamic epistemic logic. Dordecht: Springer.

    MATH  Google Scholar 

Download references

Acknowledgments

This work has been partially supported by ANR-11-LABX-0040-CIMI within the program ANR-11-IDEX-0002-02. The work of Valentin Goranko was partially supported by the CIMI (Centre International de Mathematiques et d’Informatique) Excellence Program during his visit to Toulouse as a scientific expert. We thank the anonymous reviewers for the careful reading and valuable comments and criticism which contributed to the improvement of the paper.

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Correspondence to François Schwarzentruber.

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This is a revised and substantially extended version of [10].

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Gasquet, O., Goranko, V. & Schwarzentruber, F. Big Brother Logic: visual-epistemic reasoning in stationary multi-agent systems. Auton Agent Multi-Agent Syst 30, 793–825 (2016). https://doi.org/10.1007/s10458-015-9306-4

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  • DOI: https://doi.org/10.1007/s10458-015-9306-4

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