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Intuitionistic-Bayesian Semantics of First-Order Logic for Generics

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Logic and Argumentation (CLAR 2020)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12061))

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Abstract

Generics are used frequently in various natural languages. Cohen’s theory (1999) is one of the most promising theories of generics. Cohen proposes a probabilistic account of generics. Leslie (2007, 2008) points out the three shortcomings of Cohen’s theory. Asher and Pelletier (2013) point out five more shortcomings of Cohen’s theory. The aim of this paper is to propose a new version of logic for generics—First-Order Logic for Generics (\(\mathsf {FLG}\))—that can overcome all of the eight shortcomings. To accomplish this goal, we provide the language of \(\mathsf {FLG}\) with an intuitionistic-Bayesian semantics.

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Notes

  1. 1.

    For nonstandard probability theory, consult [14]. For the relation between epistemic modals and nonstandard probability theory, refer to [18].

  2. 2.

    For the strong soundness and completeness of intuitionistic first-order logic with respect to \(\mathbf {P}_I\), consult [12] and [13].

  3. 3.

    For the strong soundness and completeness of superintuitionistic first-order logics with respect to \(\mathbf {P}_{S(\varPhi _1\wedge \ldots \wedge \varPhi _n)}\), consult [13].

  4. 4.

    For the strong soundness and completeness with respect to \(\mathbf {P}_C\), consult [7] and [13].

  5. 5.

    The arguments on triviality results originate in [10] and [11].

  6. 6.

    Weatherson provides four arguments for intuitionistic Bayesianism. However, these four arguments can be reduced to the following three arguments.

  7. 7.

    For nonstandard probability theory, consult [14]. For the relation between epistemic modals and nonstandard probability theory, refer to [18].

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Acknowledgements

The author would like to thank three anonymous reviewers of CLAR 2020 for their very helpful comments.

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Authors and Affiliations

  1. Faculty of Arts and Sciences, Komazawa University, 1-23-1, Komazawa, Setagaya-ku, Tokyo, 154-8525, Japan

    Satoru Suzuki

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  1. Satoru Suzuki
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Correspondence to Satoru Suzuki .

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Editors and Affiliations

  1. Utrecht University, Utrecht, Utrecht, The Netherlands

    Mehdi Dastani

  2. Zhejiang University, Hangzhou, China

    Huimin Dong

  3. University of Luxembourg, Luxembourg, Luxembourg

    Leon van der Torre

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Suzuki, S. (2020). Intuitionistic-Bayesian Semantics of First-Order Logic for Generics. In: Dastani, M., Dong, H., van der Torre, L. (eds) Logic and Argumentation. CLAR 2020. Lecture Notes in Computer Science(), vol 12061. Springer, Cham. https://doi.org/10.1007/978-3-030-44638-3_12

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  • DOI: https://doi.org/10.1007/978-3-030-44638-3_12

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  • Print ISBN: 978-3-030-44637-6

  • Online ISBN: 978-3-030-44638-3

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