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Abstrakty
We introduce the notion of derived tree corresponding with a derivation in the nonassociative Lambek calculus with product, and examine languages of derived trees determined by categorial grammars employing the calculus as a type reduction system. We prove that the class of derived tree languages of nonassociative Lambek grammars with product contains only regular tree languages.
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Czasopismo
Rocznik
Tom
Strony
349--362
Opis fizyczny
bibliogr. 12 poz.
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autor
- Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland, mkandu@amu.edu.pl
Bibliografia
- [1] Buszkowski, W.: Typed functorial languages, Bulletin of the Polish Academy of Sciences: Mathematics 34 (1986), 495-505.
- [2] Buszkowski, W.: Generative capacity of nonassociative Lambek calculus, Bulletin of the Polish Academy of Sciences: Mathematics 34 (1986), 507-516.
- [3] Buszkowski, W.: Mathematical linguistics and proof theory, in: Handbook of Logic and Language (J. van Benthem, A. ter Meulen, Eds.), Elsevier and The MIT Press, 1997.
- [4] Gécseg, F., Steinby, M.: Tree Automata, Akadémiai Kiad´o, Budapest 1984.
- [5] Gécseg, F., Steinby, M.: Tree Languages, in: Handbook of Formal Languages, vol. III (G. Rozenberg, A. Salomaa, Eds.), Springer Verlag, 1997.
- [6] Jäger, G.: Residuation, structural rules and context freeness, Ms, 2002, to appear in: Journal of Logic, Language and Information.
- [7] Kandulski, M.: Phrase structure languages generated by categorial grammars with product, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 34 (1988), 373-383.
- [8] Kandulski, M.: Categorial grammars and tree languages. Submitted.
- [9] Moortgat, M.: Categorial type logics, in: Handbook of Logic and Language (J. van Benthem, A. ter Meulen, Eds.), Elsevier and The MIT Press, 1997.
- [10] Restall, G.: An Introduction to Substructural Logics, Routledge, London, 1999.
- [11] Tiede, H.-J.: Deductive Systems and Grammars: Proofs as Grammatical Structures, Unpublished Ph.D. thesis, Indiana University, 1999.
- [12] Tiede, H.-J.: Lambek calculus proofs and tree automata. in: Logical Aspects of Computational Linguistics, (M. Moortgat, Ed.), Lecture Notes in Artificial Intelligence 2014, Springer Verlag, 2001.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS2-0004-0118