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ST5: A 5-Valued Logic for Truth-Value Judgments Involving Vagueness and Presuppositions

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8607)

Abstract

Both presuppositional and vague expressions may yield non-classical truth-value judgments. Given that expressions of these kinds may combine together, I propose a single logical system intended to deal with them, which would account for our truth-value judgments. The system I propose is based on Cobreros&al’s [4] 3-valued system for vagueness, ST, which comes with a notion of assertoric ambiguity that I claim naturally deals with our non-classical judgments for vagueness. I show that the specificities of presuppositions with respect to truth-value judgments can be accounted for within this system if we add two logical values to it. I discuss a specific 5-valued system that I call ST5.

Keywords

  • vagueness
  • presuppositions
  • 5-valued logic
  • truth judgments

I am very grateful to my PhD supervisors, Paul Egré and Orin Percus who gave me their support and their help all through the writing of this paper.,I want to thank the participants of the LANGUAGE seminar of the Institut Jean Nicod, of the Paris-Munich Workshop and of the Language, Truth and Logic Networkshop in Princeton, as well as the anonymous reviewers of this article.,A part of this work was supported by a ‘Euryi’ grant from the European Science Foundation (“Presupposition: A Formal Pragmatic Approach” to P. Schlenker). The ESF is not responsible for any claims made here.,Acknowledgments to the ANR-10-LABX-0087 IEC and ANR-10-IDEX-0001-02 PSL grants.

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Zehr, J. (2014). ST5: A 5-Valued Logic for Truth-Value Judgments Involving Vagueness and Presuppositions. In: Colinet, M., Katrenko, S., Rendsvig, R.K. (eds) Pristine Perspectives on Logic, Language, and Computation. ESSLLI ESSLLI 2013 2012. Lecture Notes in Computer Science, vol 8607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44116-9_16

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  • DOI: https://doi.org/10.1007/978-3-662-44116-9_16

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