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Probability Propagation in Selected Aristotelian Syllogisms

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Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11726))

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Abstract

This paper continues our work on a coherence-based probability semantics for Aristotelian syllogisms (Gilio, Pfeifer, and Sanfilippo, 2016; Pfeifer and Sanfilippo, 2018) by studying Figure III under coherence. We interpret the syllogistic sentence types by suitable conditional probability assessments. Since the probabilistic inference of P|S from the premise set \(\{P|M, S|M\}\) is not informative, we add as a probabilistic constraint (i.e., an “existential import assumption”) to obtain probabilistic informativeness. We show how to propagate the assigned premise probabilities to the conclusion. Thereby, we give a probabilistic meaning to all syllogisms of Figure III. We discuss applications like generalised quantifiers (like Most S are P) and (negated) defaults.

N. Pfeifer and G. Sanfilippo—contributed equally to the article and are listed alphabetically.

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Acknowledgments

We thank three anonymous referees.

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Authors and Affiliations

  1. Department of Philosophy, University of Regensburg, Regensburg, Germany

    Niki Pfeifer

  2. Department of Mathematics and Computer Science, University of Palermo, 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. Technische Universität Dortmund, Dortmund, Germany

    Gabriele Kern-Isberner

  2. Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Zoran Ognjanović

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Pfeifer, N., Sanfilippo, G. (2019). Probability Propagation in Selected Aristotelian Syllogisms. In: Kern-Isberner, G., Ognjanović, Z. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2019. Lecture Notes in Computer Science(), vol 11726. Springer, Cham. https://doi.org/10.1007/978-3-030-29765-7_35

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