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Trust Evidence Logic

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Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12897))

Abstract

We investigate the application of a modal language à la Hennessy-Milner to the specific domain of evidence-based trust estimations. In particular, we refer to a context-aware notion of computational trust joining in a quantitative setting both assessment of subjective opinions and third-party recommendations. Moreover, for a comprehensive analysis of the proposed logics, we offer an axiomatization and provide soundness and completeness results.

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Notes

  1. 1.

    An alternative approach is to employ majority logics [26]. Such logics are well suited to deal with dynamic scenarios where the number of evaluations is not fixed. The advantage of employing majority logics instead of GML is given by the fact that majority logics only specify that the (strict) majority of evaluations must be positive, without specifying a given number of those. On the contrary, in GML, this number must always be specified.

  2. 2.

    In [10] it is shown that disjunction can be discarded (and in [8] that, as an alternative to disjunction, conjunction can be discarded), without changing the logical characterization result, which still holds when we move from rational numbers to real numbers.

References

  1. Aldini, A: A formal framework for modeling trust and reputation in collective adaptive systems. In: Electronic Proceedings in Theoretical Computer Science, EPTCS, vol. 217, pp. 19–30 (2016)

    Google Scholar 

  2. Aldini, A.: Design and verification of trusted collective adaptive systems. Trans. Model. Comput. Simul. (TOMACS) 28(2), 1–27 (2018)

    Article  MathSciNet  Google Scholar 

  3. Aldini, A., Tagliaferri, M.: Logics to reason formally about trust computation and manipulation. In: Saracino, A., Mori, P. (eds.) ETAA 2019. LNCS, vol. 11967, pp. 1–15. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-39749-4_1

    Chapter  Google Scholar 

  4. Baier, A.: Trust and antitrust. Ethics 96(2), 231–260 (1986)

    Article  Google Scholar 

  5. Baier, C., de Alfaro, L., Forejt, V., Kwiatkowska, M.: Model checking probabilistic systems. In: Handbook of Model Checking, pp. 963–999. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-10575-8_28

    Chapter  MATH  Google Scholar 

  6. Baier, C., Katoen, J.-P., Hermanns, H., Wolf, V.: Comparative branching-time semantics for Markov chains. Inf. Comput. 200(2), 149–214 (2005)

    Article  MathSciNet  Google Scholar 

  7. Becker, M.Y., Russo, A., Sultana, N.: Foundations of logic-based trust management. In: 2012 IEEE Symposium on Security and Privacy, pp. 161–175 (2012)

    Google Scholar 

  8. Bernardo, M., Miculan, M.: Disjunctive probabilistic modal logic is enough for bisimilarity on reactive probabilistic systems. In: Bilò, V., Caruso, A. (eds.) 17th Italian Conference on Theoretical Computer Science, vol. 1720 of CEUR Workshop Proceedings, pp. 203–220. CEUR-WS.org (2016)

    Google Scholar 

  9. De Caro, F.: Graded modalities, II (canonical models). Studia Logica 47(1), 1–10 (1988)

    Article  MathSciNet  Google Scholar 

  10. Desharnais, J., Edalat, A., Panangaden, P.: Bisimulation for labelled Markov processes. Inf. Comput. 179(2), 163–193 (2002)

    Article  MathSciNet  Google Scholar 

  11. Evans, D.: The Internet of Things: how the next evolution of the Internet is changing everything. CISCO white paper (2011)

    Google Scholar 

  12. Fattorosi-Barnaba, M., Amati, G.: Modal operators with probabilistic interpretations. I. Studia Logica 46(4), 383–393 (1987)

    Article  MathSciNet  Google Scholar 

  13. Fine, K.: In so many possible worlds. Notre Dame J. Formal Logic 13(4), 516–520 (1972)

    MathSciNet  MATH  Google Scholar 

  14. Gambetta, D.: Trust: Making and Breaking Cooperative Relations. Blackwell, Hoboken (1988)

    Google Scholar 

  15. Globe, L.S.: Grades of modality. Logique et Analyse 13(51), 323–334 (1970)

    MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  17. Hennessy, M., Milner, R.: On observing nondeterminism and concurrency. In: de Bakker, J., van Leeuwen, J. (eds.) ICALP 1980. LNCS, vol. 85, pp. 299–309. Springer, Heidelberg (1980). https://doi.org/10.1007/3-540-10003-2_79

    Chapter  Google Scholar 

  18. Jøsang, A.: Trust and reputation systems. In: Aldini, A., Gorrieri, R. (eds.) FOSAD 2006-2007. LNCS, vol. 4677, pp. 209–245. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74810-6_8

    Chapter  Google Scholar 

  19. Jøsang, A., Ismail, R.: The beta reputation system. In: Proceedings of the 15th Bled Electronic Commerce Conference, pp. 1–14 (2002)

    Google Scholar 

  20. Keymolen, E.: Trust on the Line: A Philosophical Exploration of Trust in the Networked Era. Wolf Publishers, Nijmegen (2016)

    Google Scholar 

  21. Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: verification of probabilistic real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22110-1_47

    Chapter  Google Scholar 

  22. Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing. In: 16th Annual ACM Symposium on Principles of Programming Languages, pp. 344–352. ACM Press (1989)

    Google Scholar 

  23. Leturc, C., Bonnet, G.: A normal modal logic for trust in the sincerity. In: International Foundation for Autonomous Agents and Multiagent Systems, AAMAS’18, pp. 175–183 (2018)

    Google Scholar 

  24. Liu, F., Lorini, E.: Reasoning about belief, evidence and trust in a multi-agent setting. In: An, B., Bazzan, A., Leite, J., Villata, S., van der Torre, L. (eds.) PRIMA 2017. LNCS (LNAI), vol. 10621, pp. 71–89. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-69131-2_5

    Chapter  Google Scholar 

  25. Luhmann, N.: Trust and Power. John Wiley and Sons Inc., Hoboken (1979)

    Google Scholar 

  26. Pacuit, E., Salame, S.: Majority logic. In: Dubois, D., Welty, C.A., Williams, M.-A. (eds.) Principles of Knowledge Representation and Reasoning: 9th International Conference (KR2004), pp. 598–605. AAAI Press (2004)

    Google Scholar 

  27. Putnam, R.: Making Democracy Work. Princeton University Press, Princeton (1993)

    Google Scholar 

  28. Schröder, L., Pattinson, D.: Strong completeness of coalgebraic modal logics. In: Albers, S., Marion, J.-Y. (eds.) 26th International Symposium on Theoretical Aspects of Computer Science (STACS 2009), pp. 673–684. Leibniz International Proceedings in Informatics (2009)

    Google Scholar 

  29. Singh, M.P.: Trust as dependence: a logical approach. In: 10th International Conference on Autonomous Agents and Multiagent Systems, AAMAS ’11, vol. 2, pp. 863–870 (2011)

    Google Scholar 

  30. Sonya, G.K., Schratt-Bitter, S.: Trust in online social networks: a multifaceted perspective. Forum Social Econ. 44(1), 48–68 (2013)

    Google Scholar 

  31. Tagliaferri, M., Aldini, A.: From knowledge to trust: a logical framework for pre-trust computations. In: Gal-Oz, N., Lewis, P.R. (eds.) IFIPTM 2018. IAICT, vol. 528, pp. 107–123. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-95276-5_8

    Chapter  Google Scholar 

  32. van der Hoek, W.: Some considerations on the logic PfD. In: Voronkov, A. (ed.) First Russian Conference on Logic Programming, vol. 592 of LNCS, pp. 474–485. Springer, Heidelberg (1991)

    Google Scholar 

  33. Williamson, O.: Calculativeness, trust, and economic organization. J. Law Econ. 36(2), 453–486 (1993)

    Article  Google Scholar 

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Acknowledgements

This work was supported by a UKRI Future Leaders Fellowship, ‘Structure vs Invariants in Proofs’, project reference MR/S035540/1, and by the Italian Ministry of Education, University and Research through the PRIN 2017 project “The Manifest Image and the Scientific Image” prot. 2017ZNWW7F_004.

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Authors and Affiliations

  1. University of Urbino Carlo Bo, Urbino, Italy

    Alessandro Aldini, Pierluigi Graziani & Mirko Tagliaferri

  2. University of Birmingham, Birmingham, UK

    Gianluca Curzi

Authors
  1. Alessandro Aldini
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  2. Gianluca Curzi
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  3. Pierluigi Graziani
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  4. Mirko Tagliaferri
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Correspondence to Alessandro Aldini .

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Editors and Affiliations

  1. Institute of Information Theory and Automation, Prague, Czech Republic

    Jiřina Vejnarová

  2. Insight Centre for Data Analytics, School of Computer Science and IT University College Cork, Cork, Ireland

    Nic Wilson

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Aldini, A., Curzi, G., Graziani, P., Tagliaferri, M. (2021). Trust Evidence Logic. In: Vejnarová, J., Wilson, N. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2021. Lecture Notes in Computer Science(), vol 12897. Springer, Cham. https://doi.org/10.1007/978-3-030-86772-0_41

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  • DOI: https://doi.org/10.1007/978-3-030-86772-0_41

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