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Square of Opposition Under Coherence

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Soft Methods for Data Science (SMPS 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 456))

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Abstract

Various semantics for studying the square of opposition have been proposed recently. So far, only [14] studied a probabilistic version of the square where the sentences were interpreted by (negated) defaults. We extend this work by interpreting sentences by imprecise (set-valued) probability assessments on a sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square in terms of acceptability and show how to construct probabilistic versions of the square of opposition by forming suitable tripartitions. Finally, as an application, we present a new square involving generalized quantifiers.

Shared first authorship (both authors contributed equally to this work).

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Notes

  1. 1.

    Some definitions of contrariety additionally require that “\(s_1\) and \(s_2\) can both be acceptable.” For reasons stated in [14], we omit this additional requirement. Similarly, mutatis mutandis, in our definition of subcontrariety.

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Acknowledgments

We thank A. Gilio and the anonymous referees for useful comments. We thank Villa Vigoni (Human Rationality: Probabilistic Points of View). N. Pfeifer is supported by his DFG project PF 740/2-2 (within the SPP1516). G. Sanfilippo is supported by the INdAM–GNAMPA Projects (2016 Grant U 2016/000391 and 2015 grant U 2015/000418).

Author information

Authors and Affiliations

  1. Ludwig-Maximilians-University Munich, Munich, Germany

    Niki Pfeifer

  2. University of Palermo, Palermo, Italy

    Giuseppe Sanfilippo

Authors
  1. Niki Pfeifer
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  2. Giuseppe Sanfilippo
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Corresponding author

Correspondence to Giuseppe Sanfilippo .

Editor information

Editors and Affiliations

  1. Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy

    Maria Brigida Ferraro

  2. Department of Statistical Sciences, Sapienza University of Rome, Roma, Italy

    Paolo Giordani

  3. Dept of Basic & Applied Sciences Engg, Sapienza University of Rome, Rome, Italy

    Barbara Vantaggi

  4. Dept of Stoc Metds,Polish Academy of Sci, Systems Research Institute, Warsaw, Poland

    Marek Gagolewski

  5. Dept of Statis&OR and MD, Univ de Oviedo, Oviedo, Spain

    María Ángeles Gil

  6. Dept of Stoc Metds,Polish Aca of Science, Systems Res Inst, Warsaw, Poland

    Przemysław Grzegorzewski

  7. Sys Res Inti, Dept of Stoch Methods, Polish Acadmy Sci in Warsaw, Warsaw, Poland

    Olgierd Hryniewicz

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Pfeifer, N., Sanfilippo, G. (2017). Square of Opposition Under Coherence. In: Ferraro, M., et al. Soft Methods for Data Science. SMPS 2016. Advances in Intelligent Systems and Computing, vol 456. Springer, Cham. https://doi.org/10.1007/978-3-319-42972-4_50

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  • DOI: https://doi.org/10.1007/978-3-319-42972-4_50

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42971-7

  • Online ISBN: 978-3-319-42972-4

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