Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Handling Heterogeneous Disagreements Through Abstract Argumentation (Extended Abstract) Read chapter Read first chapter

2017 | OriginalPaper | Chapter

Reasoning About Belief, Evidence and Trust in a Multi-agent Setting

Authors : Fenrong Liu, Emiliano Lorini

Published in: PRIMA 2017: Principles and Practice of Multi-Agent Systems

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We present a logic for reasoning about the interplay between belief, evidence and trust in a multi-agent setting. We call this logic DL-BET which stands for “Dynamic Logic of Belief, Evidence and Trust”. According to DL-BET, if the amount of evidence in support a given fact \(\varphi \) and the ratio of evidence in support of \(\varphi \) to the total amount of evidence in support of either \(\varphi \) or its negation are sufficient then, as a consequence, one should be willing to believe \(\varphi \). We provide a sound and complete axiomatization for the logic and illustrate its expressive power with the aid of a concrete example.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Revision and Updates in Possibly Action-Occurrence-Incomplete Narratives
next chapter Reachability and Expectation in Gossiping
Footnotes
1
As we will show in Sect. 3, formula \(\lnot \mathsf { T}_{i {, } j } \bot \) is valid in the logic DL-BET. Thus, if \(\mathsf { T}_{i {, } j }\) was a normal modal operator, \( \lnot (\mathsf { T}_{i {, } j } \varphi \wedge \mathsf { T}_{i {, } j } \lnot \varphi )\) would have been valid, which is highly counter-intuitive.
 
2
Note that this ratio can be conceived as the probability that \(\varphi \) is true, computed of the basis of the number of evidence supporting \(\varphi \).
 
3
Here we take the term “envisaged” to be synonymous of the term “imagined”. Clearly, there are situations that one can imagine that she considers impossible. For example, a person can imagine a situation in which she is the president of French republic and, at the same time, considers this situation impossible.
 
4
The proof can be found in the extended version of this paper [28].
 
Literature
1.
Alchourrón, C.E., Gärdenfors, P., Makinson, D.: On the logic of theory change: partial meet contraction and revision functions. J. Symbo. Logic 50, 510–530 (1985)MathSciNetCrossRefMATH
2.
3.
Ayer, A.J.: Probability and Evidence. Columbia University Press, New York City (1972)CrossRef
4.
Baltag, A., Liu, F., Smets, S.: Reason-based belief revision in social networks. In: Slides, KNAW-Workshp on the Logical Dynamics of Information, Agency and Interaction, Amsterdam (2014)
5.
Baltag, A., Moss, L.S., Solecki, S.: The logic of common knowledge, public announcements, and private suspicions. In: Gilboa, I. (ed.) Proceedings of the 7th Conference on Theoretical Aspects of Rationality and Knowledge (TARK 1998), pp. 43–56 (1998)
6.
Baltag, A., Renne, B., Smets, S.: The logic of justified belief, explicit knowledge, and conclusive evidence. Ann. Pure Appl. Logic 165(1), 49–81 (2014)MathSciNetCrossRefMATH
7.
Baltag, A., Smets, S.: A qualitative theory of dynamic interactive belief revision. In: Wooldridge, M., Bonanno, G., van der Hoek, W. (eds.) Logic and the Foundations of Game and Decision Theory. Texts in Logic and Games, vol. 3. Amsterdam University Press, Amsterdam (2008)
8.
9.
van Benthem, J.: Logical Dynamics of Information and Interaction. Cambridge University Press, Cambridge (2011)CrossRefMATH
10.
van Benthem, J., Fernández-Duque, D., Pacuit, E.: Evidence logic: a new look at neighborhood structures. In: Bolander, T., Braüner, T., Ghilardi, S., Moss, L. (eds.) Proceedings of Advances in Modal Logic, vol. 9, pp. 97–118. King’s College Press, London (2012)
11.
12.
13.
Christoff, Z.: Dynamic logics of networks. Information Flow and the Spread of Opinion. Ph.D. thesis, ILLC, University of Amsterdam (2016)
14.
Dastani, M., Herzig, A., Hulstijn, J., van der Torre, L.: Inferring trust. In: Leite, J., Torroni, P. (eds.) CLIMA 2004. LNCS, vol. 3487, pp. 144–160. Springer, Heidelberg (2005). doi:10.​1007/​11533092_​9 CrossRef
15.
Dietrich, F., List, C.: Judgment aggregation by quota rules: majority voting generalized. J. Theor. Polit. 19(4), 391–424 (2007)CrossRef
16.
Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Springer, Berlin (2007)CrossRefMATH
17.
Dubois, D., Liu, W., Ma, J., Prade, H.: The basic principles of uncertain information fusion. An organised review of merging rules in different representation frameworks. Inf. Fusion 32, 12–39 (2016)CrossRef
18.
Dubois, D., Prade, H.: Representation and combination of uncertainty with belief functions and possibility measures. Comput. Intell. 4(3), 244264 (1988)CrossRef
19.
Falcone, R., Castelfranchi, C.: Social trust: a cognitive approach. In: Tan, Y.-H., Castelfranchi, C. (eds.) Trust and Deception in Virtual Societies, pp. 55–90. Springer, Netherlands (2001). doi:10.​1007/​978-94-017-3614-5_​3. Chap. 1CrossRef
20.
21.
Grandi, U., Lorini, E., Perrussel, L.: Propositional opinion diffusion. In: Proceedings of the 14th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2015), pp. 989–997. ACM Press (2015)
22.
Hunter, A., Booth, R.: Trust-sensitive belief revision. In: Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence (IJCAI 2015), pp. 3062–3068. AAAI Press (2015)
23.
24.
Jøsang, A.: Interpretation of fusion and hyper opinions in subjective logic. In: 15th International Conference on Information Fusion, Singapore, pp. 1225–1232 (2017)
25.
Keynes, J.M.: A Treatise on Probability. The Collected Writings, vol. 8. Macmillan, Hampshire (1973)CrossRefMATH
26.
27.
Liau, C.-J.: Belief, information acquisition, and trust in multi-agent systems: a modal logic formulation. Artif. Intell. 149(1), 31–60 (2003)MathSciNetCrossRefMATH
28.
Liu, F., Lorini, E.: Reasoning about belief, evidence and trust in a multi-agent setting (extended version). Technical report, Institut de Recherche en Informatique de Toulouse (IRIT) (2017)
29.
30.
31.
Lorini, E., Jiang, G., Perrussel, L.: Trust-based belief change. In: Proceedings of the 21st European Conference on Artificial Intelligence (ECAI 2014), pp. 549–554. IOS Press (2014)
32.
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)MATH
33.
Singh, M.: Trust as dependence: a logical approach. In: Proceedings of the 10th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2011), pp. 863–870. ACM (2011)
34.
Xue, Y., Parikh, R.: Strategic belief updates through influence in a community. Stud. Logic 8, 124–143 (2015)
Metadata
Title
Reasoning About Belief, Evidence and Trust in a Multi-agent Setting
Authors
Fenrong Liu
Emiliano Lorini
Copyright Year
2017
Book
PRIMA 2017: Principles and Practice of Multi-Agent Systems

Print ISBN: 978-3-319-69130-5

Electronic ISBN: 978-3-319-69131-2

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-69131-2_5

Premium Partner

    Image Credits