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Towards Computational Non-associative Lambek Lambda-Calculi for Formal Pragmatics

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Formal Approaches to Semantics and Pragmatics

Part of the book series: Studies in Linguistics and Philosophy ((SLAP,volume 95))

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Abstract

This paper will propose a new “mathematical foundation” for formal pragmatics, based on Non-associative Lambek Lambda Calculi (Wansing 1993; Buszkowski 1987, 1997) which are enhanced by substructural modalities \(\underset{\{s\}}{!}\) for each substructurality \(s\) (Jacobs 1994; Morrill 1994), computational monads \(\mathcal {T}\) as in Computational Lambda Calculi (Moggi 1991; Benton 1995; Benton and Wadler 1996; Goubault-Larrecq et al. 2008), and new type constructor for each \(\alpha \)-position. I will show that the resulting system, called the Computational Lambek \(\alpha \lambda \)-Calculus (\(\lambda _{c\alpha \odot !}\)), is enough to treat formal pragmatics including information structures, underspecification, and communicative interactions.

This is the last paper written by Norry Ogata before his untimely death. As such, the editors have decided to leave it mostly unchanged, despite some insightful comments from reviewers (whom we would like to thank). We have only made occasional minor edits for clarity.

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Notes

  1. 1.

    This version of \((C)\) and \((W)\) are the Gentzen sequent’s ones.

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Author information

Authors and Affiliations

  1. Department of Language and Information Science, School of Language and Culture, Osaka University, Osaka, Japan

    Norihiro Ogata

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  1. Norihiro Ogata
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Editors and Affiliations

  1. Department of English, Aoyama Gakuin University, Tokyo, Japan

    Elin McCready

  2. Department of English, Naruto University of Education, Naruto, Tokushima, Japan

    Katsuhiko Yabushita

  3. Center for the Advancement of Higher Education, Tohoku University, Sendai, Miyagi, Japan

    Kei Yoshimoto

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Ogata, N. (2014). Towards Computational Non-associative Lambek Lambda-Calculi for Formal Pragmatics. In: McCready, E., Yabushita, K., Yoshimoto, K. (eds) Formal Approaches to Semantics and Pragmatics. Studies in Linguistics and Philosophy, vol 95. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8813-7_11

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