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Square of Opposition Under Coherence

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

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.

Keywords

  • Generalize Quantifier
  • Conditional Event
  • Logical Relation
  • Probability Assessment
  • Probabilistic Version

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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

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Fig. 1

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).

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Correspondence to Giuseppe Sanfilippo .

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Pfeifer, N., Sanfilippo, G. (2017). Square of Opposition Under Coherence. In: , 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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