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International Conference on Scalable Uncertainty Management

SUM 2018: Scalable Uncertainty Management pp 196–211Cite as

Probabilistic Semantics for Categorical Syllogisms of Figure II

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11142))

Abstract

A coherence-based probability semantics for categorical syllogisms of Figure I, which have transitive structures, has been proposed recently (Gilio, Pfeifer, & Sanfilippo [15]). We extend this work by studying Figure II under coherence. Camestres is an example of a Figure II syllogism: from Every P is M and No S is M infer No S is P. We interpret these sentences by suitable conditional probability assessments. Since the probabilistic inference of \(\bar{P}|S\) from the premise set \(\{M|P,\bar{M}|S\}\) is not informative, we add \(p(S|(S \vee P))>0\) as a probabilistic constraint (i.e., an “existential import assumption”) to obtain probabilistic informativeness. We show how to propagate the assigned (precise or interval-valued) probabilities to the sequence of conditional events \((M|P,\bar{M}|S, S|(S \vee P))\) to the conclusion \(\bar{P}|S\). Thereby, we give a probabilistic meaning to the other syllogisms of Figure II. Moreover, our semantics also allows for generalizing the traditional syllogisms to new ones involving generalized quantifiers (like Most S are P) and syllogisms in terms of defaults and negated defaults.

N. Pfeifer and G. Sanfilippo—Shared first authorship (both authors contributed equally to this work).

N. Pfeifer—Supported by his DFG grant PF 740/2-2 (within the SPP1516).

G. Sanfilippo—Partially supported by the “National Group for Mathematical Analysis, Probability and their Applications” (GNAMPA – INdAM).

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Acknowledgments

We thank three anonymous reviewers for their useful comments and suggestions.

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Authors and Affiliations

  1. Munich Center for Mathematical Philosophy, LMU Munich, Geschwister-Scholl-Platz 1, 80539, Munich, Germany

    Niki Pfeifer

  2. Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy

    Giuseppe Sanfilippo

Authors
  1. Niki Pfeifer
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  2. Giuseppe Sanfilippo
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Correspondence to Niki Pfeifer or Giuseppe Sanfilippo .

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Editors and Affiliations

  1. University of Milano-Bicocca, Milan, Italy

    Davide Ciucci

  2. University of Milano-Bicocca, Milan, Italy

    Gabriella Pasi

  3. Sapienza University of Rome, Rome, Italy

    Barbara Vantaggi

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Pfeifer, N., Sanfilippo, G. (2018). Probabilistic Semantics for Categorical Syllogisms of Figure II. In: Ciucci, D., Pasi, G., Vantaggi, B. (eds) Scalable Uncertainty Management. SUM 2018. Lecture Notes in Computer Science(), vol 11142. Springer, Cham. https://doi.org/10.1007/978-3-030-00461-3_14

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  • DOI: https://doi.org/10.1007/978-3-030-00461-3_14

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  • Online ISBN: 978-3-030-00461-3

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