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Type Theory and Universal Grammar

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Software Engineering and Formal Methods (SEFM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12226))

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Abstract

The idea of Universal Grammar (UG) as the hypothetical linguistic structure shared by all human languages harkens back at least to the 13th century. The best known modern elaborations of the idea are due to Chomsky. Following a devastating critique from theoretical, typological and field linguistics, these elaborations, the idea of UG itself and the more general idea of language universals stand untenable and are largely abandoned. The proposal tackles the hypothetical contents of UG using dependent and polymorphic type theory in a framework very different from the Chomskyan one(s). Linguistic-typologically, the key novelty is introducing universal supercategories (categories of categories) for natural language modeling. Type-theoretically, we introduce a typed logic for a precise, universal and parsimonious representation of natural language morphosyntax and compositional semantics. The implementation of the logic in the Coq proof assistant handles grammatical ambiguity (with polymorphic types), selectional restrictions, quantifiers, adjectives and many other categories with a partly universal set of types.

I thank Erik Palmgren and the anonymous reviewers of CIFMA. This work has been supported by IUT20-56 and European Regional Development Fund through CEES.

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Notes

  1. 1.

    A relation cannot be applied to its arguments before there are some.

  2. 2.

    COP is copula.

  3. 3.

    The full formalization is at https://gitlab.com/jaam00/nlc/blob/master/cop.v.

  4. 4.

    For an implementation illustrating some of them, see https://gitlab.com/jaam00/nlc/blob/master/compound.v.

  5. 5.

    In most written languages, the comma is a good example. Also, there is an anecdote of Bertrand Russell giving a flight attendant a lesson on the inclusiveness of or by answering “Yes” to her query on whether he wants tea or coffee. Seuren comments that if the story were true, Russell must have ignored the question’s intonation that marks for an exclusive or  [39].

  6. 6.

    Frequently also referred to as NP or DP.

  7. 7.

    john is in nominative or accusative, i.e. a CAP as well as XP.

  8. 8.

    “Warlpiri and Gun-djeyhmi, for example, make use of verbal affixes to express various kinds of quantificational meaning. And Asurini quantifiers such as all, many, two do not form a syntactic constituent with the noun, because they do not belong to the category of determiners. They are instead members of other categories such as adverb, verb and noun”  [33].

  9. 9.

    In English, words like this, that, those, etc.

  10. 10.

    The universality of possessives has been posited by  [21].

  11. 11.

    E.g. quickly and in a hurry, respectively, in English. It is a moot point whether adverbial participle should be also included in the category or analyzed somehow differently.

  12. 12.

    From XP.

  13. 13.

    Examples: an infinitival relation is like in i like to run, an auxiliary verb is must in i must run and a gerund is running in running is healthy.

  14. 14.

    Supplement A: https://gitlab.com/jaam00/nlc/blob/master/cop.v.

  15. 15.

    Supplement B: https://gitlab.com/jaam00/nlc/blob/master/frag.v.

References

  1. Asher, N.: Selectional restrictions, types and categories. J. Appl. Log. 12(1), 75–87 (2014). https://doi.org/10.1016/j.jal.2013.08.002

    Article  MathSciNet  MATH  Google Scholar 

  2. Barendregt, H.: Lambda calculi with types. In: Handbook of Logic in Computer Science, pp. 117–309. Oxford University Press (1992)

    Google Scholar 

  3. Bekki, D., Asher, N.: Logical polysemy and subtyping. In: Motomura, Y., Butler, A., Bekki, D. (eds.) JSAI-isAI 2012. LNCS (LNAI), vol. 7856, pp. 17–24. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39931-2_2

    Chapter  Google Scholar 

  4. Blake, B.J.: Case: Cambridge Textbooks in Linguistics. Cambridge University Press, Cambridge (2001). [England]; New York, NY, USA

    Book  Google Scholar 

  5. Butt, M.: Theories of Case: Cambridge Textbooks in Linguistics. Cambridge University Press, Cambridge (2006). [England]; New York, NY, USA

    Book  Google Scholar 

  6. Chatzikyriakidis, S., Luo, Z.: Natural language inference in Coq. J. Log. Lang. Inf. 23(4), 441–480 (2014). https://doi.org/10.1007/s10849-014-9208-x

    Article  MathSciNet  MATH  Google Scholar 

  7. Chatzikyriakidis, S., Luo, Z.: Natural language reasoning using proof-assistant technology: rich typing and beyond. In: Proceedings of the EACL 2014 Workshop on Type Theory and Natural Language Semantics (TTNLS), pp. 37–45. Association for Computational Linguistics, Gothenburg, April 2014. http://www.aclweb.org/anthology/W14-1405

  8. Chatzikyriakidis, S., Luo, Z.: Proof assistants for natural language semantics. In: Amblard, M., de Groote, P., Pogodalla, S., Retoré, C. (eds.) LACL 2016. LNCS, vol. 10054, pp. 85–98. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53826-5_6. http://www.cs.rhul.ac.uk/~zhaohui/LACL16PA.pdf

    Chapter  Google Scholar 

  9. Chomsky, N.: Remarks on nominalization. In: Jacobs, R., Rosenbaum, P. (eds.) Readings in English Transformational Grammar, pp. 184–221. Ginn, Waltham (1970)

    Google Scholar 

  10. Chomsky, N.: Lectures on Government and Binding. Foris, Dordrecht (1981)

    Google Scholar 

  11. Chomsky, N.: The Minimalist Program. Current Studies in Linguistics Series, vol. 28. MIT Press, Cambridge (1995)

    MATH  Google Scholar 

  12. Czaykowska-Higgins, E., Kinkade, M.D.: Salish languages and linguistics. In: Czaykowska-Higgins, E., Kinkade, M.D. (eds.) Salish Languages and Linguistics: Theoretical and Descriptive Perspectives, pp. 1–68. Mouton, The Hague (1998)

    Chapter  Google Scholar 

  13. Evans, N., Levinson, S.C.: The myth of language universals: language diversity and its importance for cognitive science. Behav. Brain Sci. 32, 429–492 (2009)

    Article  Google Scholar 

  14. Futrell, R., Stearns, L., Everett, D.L., Piantadosi, S.T., Gibson, E.: A corpus investigation of syntactic embedding in Pirahã. PLoS ONE 11(3), e0145289 (2016). https://doi.org/10.1371/journal.pone.0145289

    Article  Google Scholar 

  15. Gil, D.: Numeral classifiers. In: Dryer, M.S., Haspelmath, M. (eds.) The World Atlas of Language Structures Online. Max Planck Institute for Evolutionary Anthropology, Leipzig (2013). https://wals.info/chapter/55

    Google Scholar 

  16. Greenberg, J.H.: Some universals of grammar with particular reference to the order of meaningful elements. In: Greenberg, J.H. (ed.) Universals of Grammar, pp. 73–113. MIT Press, Cambridge (1966)

    Google Scholar 

  17. de Groote, P.: Towards abstract categorial grammars. In: Proceedings of 39th Annual Meeting of the Association for Computational Linguistics, pp. 252–259. Association for Computational Linguistics, Toulouse, July 2001. https://doi.org/10.3115/1073012.1073045. https://www.aclweb.org/anthology/P01-1033

  18. Gruzitis, N., Dannélls, D.: A multilingual FrameNet-based grammar and lexicon for controlled natural language. Lang. Resour. Eval. 51(1), 37–66 (2015). https://doi.org/10.1007/s10579-015-9321-8

    Article  Google Scholar 

  19. Gruzitis, N.: Abstract meaning representation (AMR) (2019). https://github.com/GrammaticalFramework/gf-contrib/tree/master/AMR

  20. Haspelmath, M.: Pre-established categories don’t exist: consequences for language description and typology. Linguist. Typology 11(1), 119–132 (2007). https://doi.org/10.1515/LINGTY.2007.011

    Article  Google Scholar 

  21. Heine, B.: Cognitive Foundations of Grammar. Oxford University Press, Oxford (1997)

    Google Scholar 

  22. Himmelmann, N.P.: Lexical categories and voice in Tagalog. In: Austin, P., Musgrave, S. (eds.) Voice and Grammatical Functions in Austronesian Languages. CSLI, Stanford (2007)

    Google Scholar 

  23. Jackendoff, R.: Foundations of Language: Brain, Meaning, Grammar, Evolution. Oxford University Press, Oxford (2002)

    Book  Google Scholar 

  24. Jacobsen, W.H.: Noun and verb in Nootkan. In: Efrat, B. (ed.) The Victorian Conference on Northwestern Languages, pp. 83–153. British Columbia Provincial Museum, Victoria (1979)

    Google Scholar 

  25. Keenan, E.L., Westerstahl, D.: Generalized quantifiers in linguistics and logic. In: Handbook of Logic and Language, pp. 859–910. Elsevier, Burlington (2011)

    Google Scholar 

  26. Kiselyov, O.: Applicative abstract categorial grammar. In: Kanazawa, M., Moss, L.S., de Paiva, V. (eds.) NLCS 2015: Third Workshop on Natural Language and Computer Science. EPiC Series in Computing, vol. 32, pp. 29–38. EasyChair (2015). https://doi.org/10.29007/s2m4. https://easychair.org/publications/paper/RPN

  27. Luo, Z.: Type-theoretical semantics with coercive subtyping. In: Semantics and Linguistic Theory, vol. 20, pp. 38–56. Vancouver (2010)

    Google Scholar 

  28. Luo, Z.: Formal semantics in modern type theories: is it model-theoretic, proof-theoretic, or both? In: Asher, N., Soloviev, S. (eds.) LACL 2014. LNCS, vol. 8535, pp. 177–188. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-43742-1_14

    Chapter  Google Scholar 

  29. Luuk, E.: Nouns, verbs and flexibles: implications for typologies of word classes. Lang. Sci. 32(3), 349–365 (2010). https://doi.org/10.1016/j.langsci.2009.02.001

    Article  Google Scholar 

  30. Montague, R.: The proper treatment of quantification in ordinary English. In: Portner, P., Partee, B.H. (eds.) Formal Semantics: The Essential Readings, pp. 17–34. Blackwell, Oxford (2002 [1973])

    Google Scholar 

  31. Peterson, J.: There’s a grain of truth in every “myth”, or, why the discussion of lexical classes in Mundari isn’t quite over yet. Linguist. Typology 9(3), 391–405 (2005)

    Google Scholar 

  32. Pfenning, F.: Logical frameworks - a brief introduction. In: Schwichtenberg, H., Steinbrüggen, R. (eds.) Proof and System-Reliability. NAII, vol. 62, pp. 137–166. Springer, Berlin (2002). https://doi.org/10.1007/978-94-010-0413-8_5. http://www.cs.cmu.edu/~fp/papers/mdorf01.pdf

    Chapter  Google Scholar 

  33. Plank, F.: Determiner universal. In: The Universals Archive (2006). https://typo.uni-konstanz.de/archive/nav/browse.php?number=1201

  34. Pollard, C., Sag, I.A.: Head-Driven Phrase Structure Grammar. University of Chicago Press, Chicago (1994)

    Google Scholar 

  35. Ranta, A.: Type-Theoretical Grammar. Clarendon Press, Oxford (1994)

    MATH  Google Scholar 

  36. Ranta, A.: Grammatical framework: a type-theoretical grammar formalism. J. Funct. Program. 14(2), 145–189 (2004). https://doi.org/10.1017/S0956796803004738

    Article  MathSciNet  MATH  Google Scholar 

  37. Ranta, A.: Type theory and universal grammar. Philosophia Scientiæ. Travaux d’histoire et de philosophie des sciences (6), 115–131 (2006). https://journals.openedition.org/philosophiascientiae/415

  38. Ranta, A.: The status of the GF resource grammar library (2017). http://www.grammaticalframework.org/lib/doc/status.html

  39. Seuren, P.A.M.: Language from within: Vol. 2. The Logic of Language. Oxford University Press, Oxford (2010)

    Google Scholar 

  40. Westerstahl, D.: Generalized quantifiers. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University, winter 2016 edn. (2016). https://plato.stanford.edu/archives/win2016/entries/generalized-quantifiers

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  1. Tartu, Estonia

    Erkki Luuk

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  1. Department of Computer Science, University of York, York, UK

    Javier Camara

  2. Department of Informatics, University of Oslo, Oslo, Norway

    Martin Steffen

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Luuk, E. (2020). Type Theory and Universal Grammar. In: Camara, J., Steffen, M. (eds) Software Engineering and Formal Methods. SEFM 2019. Lecture Notes in Computer Science(), vol 12226. Springer, Cham. https://doi.org/10.1007/978-3-030-57506-9_14

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  • DOI: https://doi.org/10.1007/978-3-030-57506-9_14

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