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2018 | OriginalPaper | Buchkapitel

Bracket Induction for Lambek Calculus with Bracket Modalities

verfasst von : Glyn Morrill, Stepan Kuznetsov, Max Kanovich, Andre Scedrov

Erschienen in: Formal Grammar 2018

Verlag: Springer Berlin Heidelberg

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Abstract

Relativisation involves dependencies which, although unbounded, are constrained with respect to certain island domains. The Lambek calculus L can provide a very rudimentary account of relativisation limited to unbounded peripheral extraction; the Lambek calculus with bracket modalities Lb can further condition this account according to island domains. However in naïve parsing/theorem-proving by backward chaining sequent proof search for Lb the bracketed island domains, which can be indefinitely nested, have to be specified in the linguistic input. In realistic parsing word order is given but such hierarchical bracketing structure cannot be assumed to be given. In this paper we show how parsing can be realised which induces the bracketing structure in backward chaining sequent proof search with Lb.

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We use this notation because it prefigures a planned future extension to exponentials in which onsets are coded by lists of naturals representing the size of so-called stoups; the zeros in the coding of Lb essentially mean that here all stoups are empty.

In contrast to the present paper, the calculus in [5] allows empty antecedents, but imposing the Lambek’s restriction there is quite straightforward.

Andreoli, J.M.: Logic programming with focusing in linear logic. J. Log. Comput. 2(3), 297–347 (1992)MathSciNetCrossRef

van Benthem, J.: Language in Action: Categories, Lambdas, and Dynamic Logic. Studies in Logic and the Foundations of Mathematics, No. 130. North-Holland, Amsterdam (1991). Revised student edition printed in 1995 by the MIT PressMATH

Girard, J.Y.: Linear logic. Theor. Comput. Sci. 50, 1–102 (1987). https://doi.org/10.1016/0304-3975(87)90045-4MathSciNetCrossRefMATH

Kanazawa, M.: The Lambek calculus enriched with additional connectives. J. Log. Lang. Inf. 1, 141–171 (1992). https://doi.org/10.1007/BF00171695MathSciNetCrossRefMATH

Kanovich, M., Kuznetsov, S., Morrill, G., Scedrov, A.: A polynomial-time algorithm for the Lambek calculus with brackets of bounded order. In: Miller, D. (ed.) Proceedings of the 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics, LIPIcs, vol. 84, pp. 22:1–22:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Germany (2017). https://doi.org/10.4230/LIPIcs.FSCD.2017.22, http://drops.dagstuhl.de/opus/volltexte/2017/7738/

Kanovich, M., Kuznetsov, S., Nigam, V., Scedrov, A.: A logical framework with commutative and non-commutative subexponentials. In: Automated Reasoning: Proceedings of IJCAR 2018. Springer (2018, to appear)

Kanovich, M., Kuznetsov, S., Scedrov, A.: Undecidability of the Lambek calculus with subexponential and bracket modalities. In: Klasing, R., Zeitoun, M. (eds.) FCT 2017. LNCS, vol. 10472, pp. 326–340. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-55751-8_26CrossRefMATH

Kuznetsov, S., Morrill, G., Valentín, O.: Count-invariance including exponentials. In: Kanazawa, M., de Groote, P., Sadrzadeh, M. (eds.) Proceedings of the 15th Meeting on the Mathematics of Language, pp. 128–139. Association for Computational Linguistics, London (2017). https://aclweb.org/anthology/W/W17/W17-3413.pdf

Lambek, J.: The mathematics of sentence structure. Am. Math. Mon. 65, 154–170 (1958)MathSciNetCrossRef

10.

Miller, D., Saurin, A.: From proofs to focused proofs: a modular proof of focalization in linear logic. In: Duparc, J., Henzinger, T.A. (eds.) CSL 2007. LNCS, vol. 4646, pp. 405–419. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74915-8_31CrossRefMATH

11.

Moortgat, M.: Multimodal linguistic inference. J. Log. Lang. Inf. 5(3, 4), 349–385 (1996). https://doi.org/10.1007/BF00159344MathSciNetCrossRefMATH

12.

Moortgat, M.: Categorial type logics. In: van Benthem, J., ter Meulen, A. (eds.) Handbook of Logic and Language, pp. 93–177. Elsevier Science B.V. and MIT Press, Amsterdam and Cambridge (1997)CrossRef

13.

Morrill, G.: Categorial formalisation of relativisation: pied piping, islands, and extraction sites. Technical report. LSI-92-23-R, Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya (1992)

14.

Morrill, G.: Grammar logicised: relativisation. Linguist. Philos. 40(2), 119–163 (2017). https://doi.org/10.1007/s10988-016-9197-0CrossRef

15.

Morrill, G.: Parsing logical grammar: CatLog3. In: Loukanova, R., Liefke, K. (eds.) Proceedings of the Workshop on Logic and Algorithms in Computational Linguistics 2017, LACompLing 2017, pp. 107–131. DiVA, Stockholm University (2017). http://su.diva-portal.org/smash/get/diva2:1140018/FULLTEXT03.pdf

16.

Morrill, G., Valentín, O.: Displacement calculus. Linguist. Anal. 36(1–4), 167–192 (2010). arXiv:1004.4181, special issue Festschrift for J. Lambek

17.

Morrill, G., Valentín, O.: Computational coverage of TLG: nonlinearity. In: Kanazawa, M., Moss, L., de Paiva, V. (eds.) Proceedings of Third Workshop on Natural Language and Computer Science, NLCS 2015, vol. 32, pp. 51–63. EPiC, Kyoto (2015). Workshop Affiliated with Automata, Languages and Programming (ICALP) and Logic in Computer Science (LICS)

18.

Morrill, G., Valentín, O.: Multiplicative-additive focusing for parsing as deduction. In: Cervesato, I., Schürmann, C. (eds.) First International Workshop on Focusing, Workshop Affiliated with LPAR 2015, pp. 29–54. EPTCS, No. 197, Suva, Fiji (2015)

19.

Morrill, G., Valentín, O., Fadda, M.: The displacement calculus. J. Log. Lang. Inf. 20(1), 1–48 (2011). https://doi.org/10.1007/s10849-010-9129-2MathSciNetCrossRefMATH

20.

Morrill, G.V.: Categorial Grammar: Logical Syntax, Semantics, and Processing. Oxford University Press, New York and Oxford (2011)

21.

Pentus, M.: A polynomial-time algorithm for Lambek grammars of bounded order. Linguist. Anal. 36(1–4), 44–471 (2010)

22.

Pentus, M.: Lambek calculus is NP-complete. Theor. Comput. Sci. 357(1), 186–201 (2006). https://doi.org/10.1016/j.tcs.2006.03.018MathSciNetCrossRefMATH

23.

Valentín, O., Serret, D., Morrill, G.: A count invariant for Lambek calculus with additives and bracket modalities. In: Morrill, G., Nederhof, M.-J. (eds.) FG 2012-2013. LNCS, vol. 8036, pp. 263–276. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39998-5_17CrossRef

Titel: Bracket Induction for Lambek Calculus with Bracket Modalities
verfasst von: Glyn Morrill
Stepan Kuznetsov
Max Kanovich
Andre Scedrov
Verlag: Springer Berlin Heidelberg
Buch: Formal Grammar 2018
Print ISBN: 978-3-662-57783-7

Electronic ISBN: 978-3-662-57784-4

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-3-662-57784-4_5

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