Semantics of the Barwise sentence: insights from expressiveness, complexity and inference

Abstract

In this paper, we study natural language constructions which were first examined by Barwise: The richer the country, the more powerful some of its officials. Guided by Barwise’s observations, we suggest that conceivable interpretations of such constructions express the existence of various similarities between partial orders such as homomorphism or embedding (strong readings). Semantically, we interpret the constructions as polyadic generalized quantifiers restricted to finite models (similarity quantifiers). We extend the results obtained by Barwise by showing that similarity quantifiers are not expressible in elementary logic over finite models. We also investigate whether the proposed readings are sound from the cognitive perspective. We prove that almost all similarity quantifiers are intractable. This leads us to first-order variants (weak readings), which only approximate the strong readings, but are cognitively more plausible. Driven by the question of ambiguity, we recall Barwise’s argumentation in favour of strong readings, enriching it with some arguments of our own. Given that Barwise-like sentences are indeed ambiguous, we use a generalized Strong Meaning Hypothesis to derive predictions for their verification. Finally, we propose a hypothesis according to which conflicting pressures of communication and cognition might give rise to an ambiguous construction, provided that different semantic variants of the construction withstand different pressures involved in its usage.

References

  1. Arora, S., & Barak, B. (2009). Computational complexity: A modern approach (1st ed.). New York, NY: Cambridge University Press.

    Google Scholar 

  2. Barwise, J. (1979). On branching quantifiers in English. Journal of Philosophical Logic, 8(1), 47–80.

    Article  Google Scholar 

  3. Barwise, J., & Cooper, R. (1981). Generalized quantifiers and natural language. Linguistics and Philosophy, 4(2), 159–219.

    Article  Google Scholar 

  4. Christiansen, M. H., & Chater, N. (2016). Creating language: Integrating evolution, acquisition, and processing. Cambridge: MIT Press.

    Google Scholar 

  5. Culicover, P. W., & Jackendoff, R. (1999). The view from the periphery: The English comparative correlative. Linguistic Inquiry, 30(4), 543–571.

    Article  Google Scholar 

  6. Dalrymple, M., Kanazawa, M., Kim, Y., McHombo, S., & Peters, S. (1998). Reciprocal expressions and the concept of reciprocity. Linguistics and Philosophy, 21(2), 159–210.

    Article  Google Scholar 

  7. de Haan, R., & Szymanik, J. (2015). A dichotomy result for ramsey quantifiers. In V. de Paiva, R. de Queiroz, L. S. Moss, D. Leivant, & A. G. de Oliveira (Eds.), Logic, language, information, and computation: 22nd International workshop, WoLLIC 2015, Bloomington, IN, USA, July 20–23, 2015, Proceedings (pp. 69–80). Berlin: Springer. https://doi.org/10.1007/978-3-662-47709-0_6.

    Google Scholar 

  8. de Haan, R., & Szymanik, J. (to appear). Characterizing polynomial Ramsey quantifiers. Mathematical Structures in Computer Science. arxiv:1601.02258

  9. Dummett, M. A. E. (1975). What is a theory of meaning? In S. Guttenplan (Ed.), Mind and language. Oxford: Oxford University Press.

    Google Scholar 

  10. Edmonds, J. (1965). Paths, trees, and flowers. Canadian Journal of mathematics, 17(3), 449–467.

    Article  Google Scholar 

  11. Fagin, R. (1974). Generalized first-order spectra and polynomial-time recognizable sets. In Karp, R. (Ed.), Complexity of computation, volume 7 of SIAM-AMS Proceedings (pp. 43–73).

  12. Frixione, M. (2001). Tractable competence. Minds and Machines, 11(3), 379–397.

    Article  Google Scholar 

  13. Gierasimczuk, N., & Szymanik, J. (2009). Branching quantification v. two-way quantification. Journal of Semantics, 26(4), 367–392.

    Article  Google Scholar 

  14. Grice, H. P. (1975). Logic and conversation. In P. Cole & J. Morgan (Eds.), Syntax and semantics (Vol. 3). New York: Academic Press.

    Google Scholar 

  15. Hansen, N., & Chemla, E. (2017). Color adjectives, standards, and thresholds: An experimental investigation. Linguistics and Philosophy, 40(3), 239–278.

    Article  Google Scholar 

  16. Hella, L., Väänänen, J., & Westerståhl, D. (1997). Definability of polyadic lifts of generalized quantifiers. Journal of Logic, Language and Information, 6(3), 305–335.

    Article  Google Scholar 

  17. Immerman, N. (1999). Descriptive complexity. Berlin: Springer.

    Google Scholar 

  18. Kalociński, D. (2016). Learning the semantics of natural language quantifiers. Ph.D. Thesis, University of Warsaw, Warsaw.

  19. Keenan, E. L. (1992). Beyond the Frege boundary. Linguistics and Philosophy, 15(2), 199–221.

    Article  Google Scholar 

  20. Keenan, E. L. (1996). Further beyond the Frege boundary. In J. van der Does & J. van Eijck (Eds.), Quantifiers, logic, and language (pp. 179–201). Stanford, CA: CSLI Publications.

    Google Scholar 

  21. Keenan, E. L., & Westerståhl, D. (1997). Generalized quantifiers in linguistics and logic. In J. van Benthem & A. ter Meulen (Eds.), Handbook of logic and language (pp. 837–895). Cambridge, MA: MIT Press.

    Google Scholar 

  22. Keenan, E. L., & Ralalaoherivony, B. (2014). Correlational comparatives (CCs) in Malagasy. In The 21st annual meeting of austronesian formal linguistics association (AFLA 21), University of Hawai’i at Mānoa.

  23. Kennedy, C., & McNally, L. (2005). Scale structure, degree modification, and the semantics of gradable predicates. Language, 81(2), 345–381.

    Article  Google Scholar 

  24. Kirby, S., Tamariz, M., Cornish, H., & Smith, K. (2015). Compression and communication in the cultural evolution of linguistic structure. Cognition, 141, 87–102.

    Article  Google Scholar 

  25. Libkin, L. (2004). Elements of finite model theory. Berlin: Springer.

    Google Scholar 

  26. Lidz, J., Pietroski, P., Halberda, J., & Hunter, T. (2011). Interface transparency and the psychosemantics of most. Natural Language Semantics, 19(3), 227–256.

    Article  Google Scholar 

  27. McCawley, J. D. (1988). The comparative conditional constructions in English, German and Chinese. In Proceedings of the 14th annual meeting of the Berkeley Linguistics Society (pp. 176–187).

  28. Mostowski, M. (1994). Kwantyfikatory rozgałȩzione a problem formy logicznej. In M. Omyła (Ed.), Nauka i jȩzyk (pp. 201–242). Biblioteka Myśli Semiotycznej.

  29. Mostowski, M., & Szymanik, J. (2012). Semantic bounds for everyday language. Semiotica, 188(1/4), 363–372.

    Google Scholar 

  30. Mostowski, M., & Wojtyniak, D. (2004). Computational complexity of the semantics of some natural language constructions. Annals of Pure and Applied Logic, 127(1–3), 219–227.

    Article  Google Scholar 

  31. Peters, S., & Westerståhl, D. (2006). Quantifiers in language and logic. Oxford: Oxford University Press.

    Google Scholar 

  32. Pietroski, P., Lidz, J., Hunter, T., & Halberda, J. (2009). The meaning of most: Semantics, numerosity and psychology. Mind & Language, 24(5), 554–585.

    Article  Google Scholar 

  33. Ristad, E. (1993). The language complexity game. Cambridge: The MIT Press.

    Google Scholar 

  34. Sabato, S., & Winter, Y. (2005). From semantic restrictions to reciprocal meanings. In Proceedings of FG-MoL 2005 (pp. 13–26). CSLI Publications.

  35. Schlotterbeck, F., & Bott, O. (2013). Easy solutions for a hard problem? The computational complexity of reciprocals with quantificational antecedents. Journal of Logic, Language and Information, 22(4), 363–390.

    Article  Google Scholar 

  36. Sedgewick, R., & Wayne, K. (2011). Algorithms (4th ed.). Reading: Addison-Wesley.

    Google Scholar 

  37. Sevenster, M. (2006). Branches of imperfect information: Logic, games, and computation. Ph.D. thesis, University of Amsterdam.

  38. Stanosz, B. (1974). Status poznawczy semantyki [The cognitive status of semantics]. Studia Semiotyczne, 5, 101–115. Translation: http://studiaes.pts.edu.pl/volumev/sses_V_3.pdf.

  39. Suppes, P. (1980). Procedural semantics. In R. Haller & W. Grassl (Eds.), Language, logic, and philosophy: Proceedings of the 4th international Wittgenstein symposium (pp. 27–35). Vienna: Hölder-Pichler-Tempsy.

    Google Scholar 

  40. Suppes, P. (1982). Variable-free semantics with remark on procedural extensions. In S. Simon (Ed.), Language, mind and brain (pp. 21–34). Hillsdale: Erlbaum.

    Google Scholar 

  41. Szymanik, J. (2010). Computational complexity of polyadic lifts of generalized quantifiers in natural language. Linguistics and Philosophy, 33(3), 215–250.

    Article  Google Scholar 

  42. Szymanik, J. (2016). Quantifiers and cognition: Logical and computational perspectives. Number 96 in Studies in linguistics and philosophy (1st ed.). New York: Springer.

  43. Szymanik, J., & Zajenkowski, M. (2010). Comprehension of simple quantifiers. Empirical evaluation of a computational model. Cognitive Science: A Multidisciplinary Journal, 34(3), 521–532.

    Article  Google Scholar 

  44. Tichy, P. (1969). Intension in terms of Turing machines. Studia Logica, 24(1), 7–21.

    Article  Google Scholar 

  45. Tomaszewicz, B. (2013). Linguistic and visual cognition: Verifying proportional and superlative most in Bulgarian and Polish. Journal of Logic, Language and Information, 22(3), 335–356.

    Article  Google Scholar 

  46. van Benthem, J. (1986). Essays in logical semantics. Dordrecht: Reidel.

    Google Scholar 

  47. van Benthem, J. (1987). Towards a computational semantics. In Gärdenfors P. (Eds.), Generalized quantifiers. Studies in linguistics and philosophy (formerly Synthese Language Library) (Vol. 31). Dordrecht: Springer.

  48. van Benthem, J. (1989). Polyadic quantifiers. Linguistics and Philosophy, 12(4), 437–464.

    Article  Google Scholar 

  49. van Lambalgen, M., & Hamm, F. (2005). The proper treatment of events. London: Wiley.

    Google Scholar 

  50. van Rooij, I. (2008). The tractable cognition thesis. Cognitive Science, 32(6), 939–984.

    Article  Google Scholar 

  51. Westerståhl, D. (1984). Some results on quantifiers. Notre Dame Journal of Formal Logic, 25(2), 152–170.

    Article  Google Scholar 

  52. Winter, Y. (2001). Plural predication and the strongest meaning hypothesis. Journal of Semantics, 18(4), 333–365.

    Article  Google Scholar 

  53. Zajenkowski, M., Styła, R., & Szymanik, J. (2011). A computational approach to quantifiers as an explanation for some language impairments in schizophrenia. Journal of Communication Disorders, 44(6), 595–600.

    Article  Google Scholar 

  54. Zipf, G. K. (1949). Human behavior and the principle of least effort: An introduction to human ecology. Cambridge, MA: Addison-Wesley Press.

    Google Scholar 

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Correspondence to Dariusz Kalociński.

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Kalociński, D., Godziszewski, M.T. Semantics of the Barwise sentence: insights from expressiveness, complexity and inference. Linguist and Philos 41, 423–455 (2018). https://doi.org/10.1007/s10988-018-9231-5

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Keywords

  • Homomorphism
  • Embedding
  • Computational complexity
  • Partial order
  • Polyadic quantification
  • Expressiveness
  • Strong Meaning Hypothesis
  • Ambiguity
  • Tractable cognition