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International Workshop on Logic, Rationality and Interaction

LORI 2017: Logic, Rationality, and Interaction pp 151–165Cite as

Contradictory Information as a Basis for Rational Belief

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

Abstract

As agents faced with fallible information, we frequently find ourselves in situations where we are forced to base our beliefs on evidence which is in some way or another contradictory. We nevertheless want these beliefs to be rational. This paper presents a simple probabilistic model of what it means for a belief based on a contradictory body of evidence to be rational. In this approach, we model contradictions in the evidence available to us as resulting from random noise, and we model our task as rational agents as reconstructing the most likely states of affairs given the evidence available to us. Our main result consists in providing several equivalent descriptions of the non-reflexive and non-monotonic consequence relation which formalizes the notion that it is reasonable to accept that a proposition is true given good evidence supporting some set of propositions.

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Notes

  1. 1.

    At least if we disregard issues relating to logical non-omniscience and dialetheism. Our logic is intended to model reasoning with ordinary empirical propositions where such issues are not prominent.

  2. 2.

    We have no particular story to tell about how one comes into possession of good evidence, or what precisely constitutes good evidence. It is entirely up to the user of the logic to supply such a story. We simply imagine that the user of the logic collects some information about the world and at the end of this process he ends up with a certain probability with information supporting or contradicting p (given that p is true, or given that p is false).

  3. 3.

    The following proposition was suggested to the author by one of the referees.

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Acknowledgments

This research was supported by the project 16-07954J SEGA “From shared attitudes to group agency” of the Czech Science Foundation and DFG. The author would also like to thank the two anonymous referees for their helpful comments, in particular for suggesting that Proposition 2 might hold.

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Authors and Affiliations

  1. Department of Logic, Faculty of Arts, Charles University, Prague, Czech Republic

    Adam Přenosil

  2. Institute of Computer Science, Czech Academy of Sciences, Prague, Czech Republic

    Adam Přenosil

Authors
  1. Adam Přenosil
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Correspondence to Adam Přenosil .

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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

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Přenosil, A. (2017). Contradictory Information as a Basis for Rational Belief. 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_11

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  • DOI: https://doi.org/10.1007/978-3-662-55665-8_11

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  • 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)

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