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On Some Extensions of Syntactic Concept Lattices: Completeness and Finiteness Results

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Book cover Formal Grammar (FG 2015, FG 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9804))

Abstract

We provide some additional completeness results for the full Lambek calculus and syntactic concept lattices, where the underlying structure is extended to tuples of arbitrary finite and infinite size. Whereas this answers an open question for finite tuples, infinite tuples have not been considered yet. Nonetheless, they have a number of interesting properties which we establish in this paper, such as a particular class of languages which results in a finite lattice.

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Notes

  1. 1.

    Or words, respectively, depending on whether we think of our language as a set of words or a set of strings of words; we will choose the former option.

  2. 2.

    Whereas L and L1 are equally powerful in the sense of languages which are recognizable, [11] shows that \(\mathbf{FL }\) is considerably more powerful than L: whereas L only recognizes context-free languages by the classical result of [17], \(\mathbf{FL }\) can recognize any finite intersection of context-free languages. We only briefly mention this, because we have no space to make precise what it means for a calculus to recognize a class of languages.

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Authors and Affiliations

  1. Universität Düsseldorf, Düsseldorf, Germany

    Christian Wurm

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  1. Christian Wurm
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Correspondence to Christian Wurm .

Editor information

Editors and Affiliations

  1. IRISA, University of Rennes 1 , Rennes, France

    Annie Foret

  2. Department of Computer Science, Universitat Politècnica de Catalunya , Barcelona, Spain

    Glyn Morrill

  3. Tilburg University , Tilburg, The Netherlands

    Reinhard Muskens

  4. Department of General Linguistics, Heinrich-Heine-University Düsseldorf , Düsseldorf, Germany

    Rainer Osswald

  5. INRIA Nancy, Villers-lès-Nancy, France

    Sylvain Pogodalla

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Wurm, C. (2016). On Some Extensions of Syntactic Concept Lattices: Completeness and Finiteness Results. In: Foret, A., Morrill, G., Muskens, R., Osswald, R., Pogodalla, S. (eds) Formal Grammar. FG FG 2015 2016. Lecture Notes in Computer Science(), vol 9804. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53042-9_10

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  • DOI: https://doi.org/10.1007/978-3-662-53042-9_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53041-2

  • Online ISBN: 978-3-662-53042-9

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