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Proof-Theoretic Semantics for Natural Language

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Abstract

The paper has two parts: 1. A brief exposition of proof-theoretic semantics (PTS), not necessarily in connection to natural language (NL). 2. A review, with a contrastive flavour, of some of the applications of PTS to NL with an indication of advantages of PTS as a theory of meaning for NL.

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Notes

  1. Note that PTS is an umbrella term, having several versions. I present here my own view of PTS.

  2. This is known as Gentzen’s ‘logistic’ presentation of ND.

  3. Because there are no I-rules for atoms.

  4. More colloquially, a is used instead of some. In this context, I take both as synonyms.

  5. For readability, I use proper names and definite description instead of determiners, in spite of the former not present in the NL fragment under discussion.

  6. Except on a marginal level, with expressions like everything or something. For the difficulties raised by the notion of quantifying over everything see, for example, Rayo and Uzquiano (2006).

  7. For example, decomposing seek as try to find.

  8. For technical reasons, I avoid the use of proper names like John, Mary.

  9. Thus, the proof language is a slight extension of the natural language.

  10. Again, for the same reason as in logic, that no I-rules are involved in deriving them.

  11. As is common in ND-presentation, in actual examples we suppress the \(\Gamma \), using only the succedent, to save space; note that \(\Gamma \) is easily recoverable in such small examples.

  12. Similar rules govern something in a subject position, but they do not matter here and are omitted.

  13. Note that neither Blom et al. (2012) nor Giorgolo and Asudeh (2012) relate to this issue, discussing only sentences with proper names as subjects.

  14. As noted in Glanzberg (2006), it suffices to conduct this study in an extensional fragment of NL, as intentionality seems orthogonal to QDR-problem.

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  1. Computer Science Department, The Technion, Haifa, 32000, Israel

    Nissim Francez

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Francez, N. Proof-Theoretic Semantics for Natural Language. Topoi 40, 55–69 (2021). https://doi.org/10.1007/s11245-019-09662-5

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