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Proof-Theoretic Semantics for a Natural Language Fragment

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The Mathematics of Language (MOL 2009, MOL 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6149))

Introduction

We propose a Proof − Theoretic Semantics (PTS) for a (positive) fragment \(E^{+}_{0}\) of Natural Language (NL) (English in this case). The semantics is intended [7] to be incorporated into actual grammars, within the framework of Type − Logical Grammar (TLG) [12]. Thereby, this semantics constitutes an alternative to the traditional model − theoretic semantics (MTS), originating in Montague’s seminal work [11], used in TLG.

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References

  1. Ben-Avi, G., Francez, N.: A proof-theoretic reconstruction of generalized quantifiers (2009) (submitted for publication)

    Google Scholar 

  2. Brandom, R.B.: Articulating Reasons. Harvard University Press, Cambridge (2000)

    Google Scholar 

  3. Dummett, M.: The Logical Basis of Metaphysics. Harvard University Press, Cambridge (1991)

    Google Scholar 

  4. Francez, N., Ben-Avi, G.: Proof-theoretic semantic values for logical operator. Synthese (2009) (under refereeing)

    Google Scholar 

  5. Francez, N., Dyckhoff, R.: A note on proof-theoretic validity (2007) (in preparation)

    Google Scholar 

  6. Francez, N., Dyckhoff, R.: A note on harmony. Journal of Philosophical Logic (2007) (submitted)

    Google Scholar 

  7. Francez, N., Dyckhoff, R., Ben-Avi, G.: Proof-theoretic semantics for subsentential phrases. Studia Logica 94, 381–401 (2010), doi:10.1007/s11225-010-9241-y

    Article  MATH  MathSciNet  Google Scholar 

  8. Gentzen, G.: Investigations into logical deduction. In: Szabo, M. (ed.) The collected papers of Gerhard Gentzen, pp. 68–131. North-Holland, Amsterdam (1935) (english translation of the 1935 paper in German)

    Google Scholar 

  9. de Groote, P., Retore, C.: On the semantic readings of proof-nets. In: Kruijf, G.J., Oehrle, D. (eds.) Formal Grammar, pp. 57–70. FOLLI (1996)

    Google Scholar 

  10. Kremer, M.: Read on identity and harmony – a friendly correction and simplification. Analysis 67(2), 157–159 (2007)

    Article  MathSciNet  Google Scholar 

  11. Montague, R.: The proper treatment of quantification in ordinary english. In: Hintikka, J., Moravcsik, J., Suppes, P. (eds.) Approaches to natural language, Reidl, Dordrecht (1973); proceedings of the 1970 Stanford workshop on grammar and semantics

    Google Scholar 

  12. Moortgat, M.: Categorial type logics. In: van Benthem, J., ter Meulen, A. (eds.) Handbook of Logic and Language, pp. 93–178. North-Holland, Amsterdam (1997)

    Chapter  Google Scholar 

  13. Moss, L.: Syllogistic logics with verbs. Journal of Logic and Information (to appear 2010)

    Google Scholar 

  14. Pfenning, F., Davies, R.: A judgmental reconstruction of modal logic. Mathematical Structures in Computer Science 11, 511–540 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  15. Plato, J.V.: Natural deduction with general elimination rules. Archive Mathematical Logic 40, 541–567 (2001)

    Article  MATH  Google Scholar 

  16. Prawitz, D.: Natural Deduction: Proof-Theoretical Study. Almqvist and Wicksell, Stockholm (1965)

    MATH  Google Scholar 

  17. Prior, A.N.: The roundabout inference-ticket. Analysis 21, 38–39 (1960)

    Article  Google Scholar 

  18. Read, S.: Harmony and autonomy in classical logic. Journal of Philosophical Logic 29, 123–154 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  19. Read, S.: Identity and harmony. Analysis 64(2), 113–119 (2004); see correction in [10]

    Article  MATH  Google Scholar 

  20. Read, S.: Harmony and modality. In: Dégremont, C., Kieff, L., Rückert, H. (eds.) Dialogues, Logics and Other Strong Things: Essays in Honour of Shahid Rahman, pp. 285–303. College Publications (2008)

    Google Scholar 

  21. Restall, G.: Proof theory and meaning: on the context of deducibility. In: Proceedings of Logica 2007, Hejnice, Czech Republic (2007)

    Google Scholar 

  22. Schroeder-Heister, P.: Validity concepts in proof-theoretic semantics. In: Kale, R., Schroeder-Heister, P. (eds.) Proof-Theoretic Semantics, vol. 148, pp. 525–571 (February 2006), special issue of Synthese

    Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Science dept., Technion-IIT, Haifa, Israel

    Nissim Francez

  2. School of Computer Science, University of St Andrews, Scotland, UK

    Roy Dyckhoff

Authors
  1. Nissim Francez
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  2. Roy Dyckhoff
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Editor information

Editors and Affiliations

  1. Department of Linguistics, University of Tuebingen, Wilhelmstrasse 19, 72074, Tuebingen, Germany

    Christian Ebert  & Gerhard Jäger  & 

  2. Faculty of Linguistics and Literary Studies, University of Bielefeld, Postfach 100131, 33501, Bielefeld, Germany

    Jens Michaelis

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Francez, N., Dyckhoff, R. (2010). Proof-Theoretic Semantics for a Natural Language Fragment. In: Ebert, C., Jäger, G., Michaelis, J. (eds) The Mathematics of Language. MOL MOL 2009 2007. Lecture Notes in Computer Science(), vol 6149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14322-9_6

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  • DOI: https://doi.org/10.1007/978-3-642-14322-9_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14321-2

  • Online ISBN: 978-3-642-14322-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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