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Complexity in Linguistics

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Quantifiers and Cognition: Logical and Computational Perspectives

Part of the book series: Studies in Linguistics and Philosophy ((SLAP,volume 96))

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Abstract

The topic of language complexity has surfaced in many different contexts and can be measured in many different ways. In this chapter, I discuss notions relevant to the computational and descriptive complexity of language. I introduce the notion of ‘complexity class’ (e.g. P and NP), the corresponding logical distinctions (e.g. definability), and the Cobham-Edmonds thesis identifying the class of practically computable problems with P. Then, I survey how the complexity notions have been applied in the study of syntax and semantics of natural language. This discussion culminates in putting forward Ristad’s Thesis, claiming that our everyday language is semantically bounded by the properties expressible in the existential fragment of second-order logic (belongs to NP). Finally, I discuss, very common in formal semantics, restriction to finite interpretations. This chapter gives, therefore, an additional argument for studying the computational complexity of natural language expressions.

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Notes

  1. 1.

    The book focuses on computational and descriptive complexity of language, but there are many other aspects of complexity, like lexical, information-theoretic (Kolmogorov complexity), structural, or functional complexity.

  2. 2.

    See Appendix A.2 for more details.

  3. 3.

    We discuss these, mainly technical, issues in Appendix A.2.3.

  4. 4.

    See, e.g., Pullum and Gazdar (1982); Shieber (1985); Culy (1985), and Manaster-Ramer (1987).

  5. 5.

    Chomsky uses the term ‘strong generative capacity’ to refer to the set of structures (trees) that can be generated by a grammar.

  6. 6.

    The early results achieved are summarized in a book by Barton et al. (1987). A more recent survey is found in Pratt-Hartmann (2008).

  7. 7.

    The other one, which is more domain specific, will be formulated in Sect. 9.3.4.

  8. 8.

    For a discussion on the computational complexity of sentences like this, see Sect. 7.3 and Chap. 9.

  9. 9.

    One interesting question is how Ristad’s Thesis fits within cognitive science, where complexity bounds are considered as methodological guidelines for computational models (see, e.g., Rooij 2008; Isaac et al. 2014 and Sect. 8.5).

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  1. Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, The Netherlands

    Jakub Szymanik

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Szymanik, J. (2016). Complexity in Linguistics. In: Quantifiers and Cognition: Logical and Computational Perspectives. Studies in Linguistics and Philosophy, vol 96. Springer, Cham. https://doi.org/10.1007/978-3-319-28749-2_2

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  • DOI: https://doi.org/10.1007/978-3-319-28749-2_2

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