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The Logic of Ambiguity: The Propositional Case

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Formal Grammar (FG 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10686))

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Abstract

We present a logical calculus extending the classical propositional calculus with an additional connective which has some features of substructural logic. This results in a logic which seems to be suitable for reasoning with ambiguity. We use a Gentzen style proof theory based on multi-contexts, which allow us to have two ways to combine formulas to sequences. These multi-contexts in turn allow to embed both features of classical logic as well as substructural logic, depending on connectives, which would be impossible with simple sequents. Finally, we present an algebraic semantics and a completeness theorem.

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Notes

  1. 1.

    This roughly distinguishes ambiguity from cases of vagueness [10].

  2. 2.

    Technically, this translation presupposes the existence of a boy, this however is irrelevant to our argument.

  3. 3.

    Thanks to an anonymous reviewer for this example!.

  4. 4.

    Actually, this would be a meta-metalanguage, because logical representations are already a form of representation of real meanings.

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Author information

Authors and Affiliations

  1. University of Düsseldorf, Düsseldorf, Germany

    Christian Wurm

Authors
  1. Christian Wurm
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Correspondence to Christian Wurm .

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Editors and Affiliations

  1. IRISA, University of Rennes 1, Rennes, France

    Annie Foret

  2. Department of Philosophy, Tilburg University, Tilburg, The Netherlands

    Reinhard Muskens

  3. LORIA/Inria Nancy, Villers-les-Nancy, France

    Sylvain Pogodalla

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Wurm, C. (2018). The Logic of Ambiguity: The Propositional Case. In: Foret, A., Muskens, R., Pogodalla, S. (eds) Formal Grammar . FG 2017. Lecture Notes in Computer Science(), vol 10686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-56343-4_6

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  • DOI: https://doi.org/10.1007/978-3-662-56343-4_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-56342-7

  • Online ISBN: 978-3-662-56343-4

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