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Toward the Formulation of Presupposition by Illative Combinatory Logic

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Logical Aspects of Computational Linguistics (LACL 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7351))

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Abstract

Model-theoretic semantics, which originates with Tarski, and proof-thoretic semantics, which originates with Gentzen, are two views in semantics of logic that are distinct from but closely related to each other. Each has advantages over the other in investigating a certain aspect of logic, and it is more or less commonly accepted that rather than being a matter of methodological choice, utilizing them gives us diversified standpoints on various issues. A good example of this is the two proofs of the consistency of LK: one proof is based on soundness and the other on cut-elimination, which makes use of different resources but also together reveals what the consistency of predicate calculus indeed depends on.

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References

  1. Barendregt, H., Bunder, M., Dekkers, W.: Systems of illative combinatory logic complete for first-order propositional and predicate calculus. The Journal of Symbolic Logic 58(3), 769–788 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  2. Beaver, D.I.: Presupposition and Assertion in Dynamic Semantics. Studies in Logic, Language and Information. CSLI Publications & folli. (2001)

    Google Scholar 

  3. Bekki, D.: Combinatory categorial grammar as a substrutural logic - preliminary remarks -. In: The Seventh International Workshop on Logic and Engeneering of Natural Language Semantics (LENLS 7), pp. 70–83 (2010)

    Google Scholar 

  4. Carlström, J.: Interpreting descriptions in intensional type theory. Journal of Symbolic Logic 70(2), 488–514 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Curry, H.B., Feys, R.: Combinatory logic, vol. 1. North-Holland, Amsterdam (1958)

    MATH  Google Scholar 

  6. Francez, N., Dyckhoff, R.: Proof-Theoretic Semantics for a Natural Language Fragment. In: Ebert, C., Jäger, G., Michaelis, J. (eds.) MOL 10/11. LNCS (LNAI), vol. 6149, pp. 56–71. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  7. Gazdar, G.: Pragmatics: Implicature, Presupposition, and Logical Form. Academic Press, London (1979)

    Google Scholar 

  8. Karttunen, L.: Presuppositions and liguistic contexxt. Theoretical Linguistics 1, 181–193 (1974)

    Article  Google Scholar 

  9. Mineshima, K.: A Presuppositional Analysis of Definite Descriptions in Proof Theory. In: Satoh, K., Inokuchi, A., Nagao, K., Kawamura, T. (eds.) JSAI 2007. LNCS (LNAI), vol. 4914, pp. 214–227. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  10. Montague, R.: The proper treatment of quantification in ordinary english. In: Hintikka, J., Moravcsic, J., Suppes, P. (eds.) Approaches to Natural Language, pp. 221–242. Reidel, Dordrecht (1973)

    Chapter  Google Scholar 

  11. Ozaki, H., Bekki, D.: Extractability as deduction theorem in subdirectional combinatory logic. In: The Eighth International Workshop on Logic and Engeneering of Natural Language Semantics (LENLS 8), pp. 80–93 (2011)

    Google Scholar 

  12. Ranta, A.: Type-Theoretical Grammar. Oxford University Press (1994)

    Google Scholar 

  13. van der Sandt, R.: Presupposition projection as anaphora resolution. Journal of Semantics 9, 333–377 (1992)

    Article  Google Scholar 

  14. van der Sandt, R., Geurts, B.: Presupposition, Anaphora, and Lexical Content. In: Herzog, O., Rollinger, C.-R. (eds.) LILOG 1991. LNCS, vol. 546, pp. 259–296. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  15. Soames, S.: A projection problem for speaker presuppositions. Linguistic Inquiry 10, 623–666 (1979)

    MATH  Google Scholar 

  16. Stalnaker, R.: Pragmatic presupposition. In: Munitz, M.K., Unger, D.K. (eds.) Semantics and Philosophy, pp. 197–213. New York University Press (1974)

    Google Scholar 

  17. Steedman, M.J.: The Syntactic Process (Language, Speech, and Communication). The MIT Press, Cambridge (2000)

    Google Scholar 

  18. Strawson, P.F.: On referring. Mind, New Series 59(235), 320–344 (1950)

    Article  Google Scholar 

  19. Sundholm, G.: Proof theory and meaning. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, 2nd edn., vol. 9, pp. 165–198. Kluwer Academic Publishers (2002)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Graduate School of Humanities and Sciences, Division of Advanced Sciences, Department of Computer Science, Ochanomizu University, Japan

    Yuri Ishishita & Daisuke Bekki

Authors
  1. Yuri Ishishita
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  2. Daisuke Bekki
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Editor information

Editors and Affiliations

  1. LINA UMR 6241, Université de Nantes, 2, rue de la Houssinière, BP 92208, 44322, Nantes Cedex 3, France

    Denis Béchet  & Alexander Dikovsky  & 

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Ishishita, Y., Bekki, D. (2012). Toward the Formulation of Presupposition by Illative Combinatory Logic. In: Béchet, D., Dikovsky, A. (eds) Logical Aspects of Computational Linguistics. LACL 2012. Lecture Notes in Computer Science, vol 7351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31262-5_5

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  • DOI: https://doi.org/10.1007/978-3-642-31262-5_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31261-8

  • Online ISBN: 978-3-642-31262-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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