Skip to main content
Springer Nature Link
Log in

Evidence Logics with Relational Evidence

  • Conference paper
  • First Online:
Logic, Rationality, and Interaction (LORI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10455))

Included in the following conference series:

Abstract

We introduce a family of logics for reasoning about relational evidence: evidence that involves an ordering of states in terms of their relative plausibility. We provide sound and complete axiomatizations for the logics. We also present several evidential actions and prove soundness and completeness for the associated dynamic logics.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Andréka, H., Ryan, M., Schobbens, P.: Operators and laws for combining preference relations. J. Logic Comput. 12(1), 13–53 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Baltag, A., Bezhanishvili, N., Özgün, A., Smets, S.: Justified belief and the topology of evidence. In: Väänänen, J., Hirvonen, Å., de Queiroz, R. (eds.) WoLLIC 2016. LNCS, vol. 9803, pp. 83–103. Springer, Heidelberg (2016). doi:10.1007/978-3-662-52921-8_6

    Google Scholar 

  3. Baltag, A., Fiutek, V., Smets, S.: DDL as an “Internalization” of dynamic belief revision. In: Trypuz, R. (ed.) Krister Segerberg on Logic of Actions, vol. 1, pp. 253–283. Springer, Dordrecht (2014). doi:10.1007/978-94-007-7046-1_12

    Chapter  Google Scholar 

  4. Baltag, A., Occhipinti Liberman, A.: Evidence logics with relational evidence. Preprint arxiv:1706.05905 (2017)

  5. Baltag, A., Smets, S.: Protocols for belief merge: reaching agreement via communication. Logic J. IGPL 21(3), 468–487 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. Baltag, A., Smets, S., et al.: Talking your way into agreement: belief merge by persuasive communication. In: MALLOW (2009)

    Google Scholar 

  7. Christensen, D.: Higher-order evidence. Philos. Phenomenolog. Res. 81(1), 185–215 (2010)

    Article  Google Scholar 

  8. Dietrich, F., List, C.: Probabilistic opinion pooling generalized. Part one: general agendas. Soc. Choice Welfare 48(4), 747–786 (2017)

    Article  MathSciNet  Google Scholar 

  9. Girard, P.: Modal logic for lexicographic preference aggregation. In: van Benthem, J., Gupta, A., Pacuit, E. (eds.) Games, Norms and Reasons. Synthese Library (Studies in Epistemology, Logic, Methodology, and Philosophy of Science), vol. 353, pp. 97–117. Springer, Dordrecht (2011). doi:10.1007/978-94-007-0714-6_6

    Chapter  Google Scholar 

  10. Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic (Foundations of Computing). The MIT Press, Cambridge (2000)

    MATH  Google Scholar 

  11. Kooi, B., van Benthem, J.: Reduction axioms for epistemic actions. AiML-2004: Advances in Modal Logic, UMCS-04-9-1 in Technical Report Series, pp. 197–211 (2004)

    Google Scholar 

  12. Liu, F.: Reasoning about Preference Dynamics. Springer Nature, New York (2011)

    Book  MATH  Google Scholar 

  13. Paris, J., Vencovská, A.: Pure Inductive Logic. Cambridge University Press, Cambridge (2015)

    Book  MATH  Google Scholar 

  14. van Benthem, J.: Belief update as social choice. In: Girard, P., Roy, O., Marion, M. (eds.) Dynamic Formal Epistemology. Synthese Library (Studies in Epistemology, Logic, Methodology, and Philosophy of Science), vol. 351, pp. 151–160. Springer, Dordrecht (2011). doi:10.1007/978-94-007-0074-1_8

    Chapter  Google Scholar 

  15. van Benthem, J., Fernández-Duque, D., Pacuit, E.: Evidence and plausibility in neighborhood structures. Ann. Pure Appl. Logic 165(1), 106–133 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  16. van Benthem, J., Pacuit, E.: Dynamic logics of evidence-based beliefs. Stud. Logica 99(1–3), 61–92 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Benthem, J., Pacuit, E.: Logical dynamics of evidence. In: Ditmarsch, H., Lang, J., Ju, S. (eds.) LORI 2011. LNCS (LNAI), vol. 6953, pp. 1–27. Springer, Heidelberg (2011). doi:10.1007/978-3-642-24130-7_1

    Chapter  Google Scholar 

  18. van Eijck, J.: Yet more modal logics of preference change and belief revision. In: New Perspectives on Games and Interaction. Amsterdam University Press (2009)

    Google Scholar 

Download references

Acknowledgement

We thank the two anonymous referees for their useful comments. We also thank Johan van Benthem, Benedikt Löwe, Ulle Endriss and Aybüke Özgün for their valuable feedback on a previous version of this paper.

Author information

Authors and Affiliations

  1. University of Amsterdam, Amsterdam, Netherlands

    Alexandru Baltag

  2. DTU Compute, Technical University of Denmark, Copenhagen, Denmark

    Andrés Occhipinti

Authors
  1. Alexandru Baltag
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrés Occhipinti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrés Occhipinti .

Editor information

Editors and Affiliations

  1. Institute for Logic, Language and Computation, University of Amsterdam , Amsterdam, Noord-Holland, The Netherlands

    Alexandru Baltag

  2. Department of Philosophy, The University of Auckland, Auckland, Auckland, New Zealand

    Jeremy Seligman

  3. Graduate School of Letters, Hokkaido University , Sapporo, Japan

    Tomoyuki Yamada

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer-Verlag GmbH Germany

About this paper

Cite this paper

Baltag, A., Occhipinti, A. (2017). Evidence Logics with Relational Evidence. In: Baltag, A., Seligman, J., Yamada, T. (eds) Logic, Rationality, and Interaction. LORI 2017. Lecture Notes in Computer Science(), vol 10455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55665-8_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-55665-8_2

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-55664-1

  • Online ISBN: 978-3-662-55665-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Societies and partnerships