Context-Passing and Underspecification in Dependent Type Semantics

  • Daisuke BekkiEmail author
  • Koji Mineshima
Part of the Studies in Linguistics and Philosophy book series (SLAP, volume 98)


Dependent type semantics (DTS) is a framework of discourse semantics based on dependent type theory, following the line of Sundholm (Handbook of Philosophical Logic, 1986) and Ranta (Type-Theoretical Grammar, 1994). DTS attains compositionality as required to serve as a semantic component of modern formal grammars including variations of categorial grammars, which is achieved by adopting mechanisms for local contexts, context-passing, and underspecified terms. In DTS, the calculation of presupposition projection reduces to type checking, and the calculation of anaphora resolution and presupposition binding both reduce to proof search in dependent type theory, inheriting the paradigm of anaphora resolution as proof construction.


Common Noun Natural Language Semantic Categorial Grammar Anaphora Resolution Proof Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Ahn, R., & Kolb, H.-P. (1990). Discourse representation meets constructive mathematics. In L. Kalman & L. Polos (Eds.), Papers from the Second Symposium on Logic and Language. Akademiai Kiado.Google Scholar
  2. Asher, N. (2011). Lexical Meaning in Context: A Web of Words. Cambridge: Cambridge University Press.Google Scholar
  3. Atlas, J., & Levinson, S. (1981). It-clefts, informativeness and logical form: Radical pragmatics. In P. Cole (Ed.), Radical Pragmatics (pp. 1–61). Cambridge: Academic Press.Google Scholar
  4. Barendregt, H. P. (1992). Lambda calculi with types. In S. Abramsky, D. M. Gabbay, & T. Maibaum (Eds.), Handbook of Logic in Computer Science (Vol. 2, pp. 117–309). Oxford: Oxford Science Publications.Google Scholar
  5. Beaver, D. I. (2001). Presupposition and Assertion in Dynamic Semantics. Studies in Logic, Language and Information. Stanford: CSLI Publications & FoLLI.Google Scholar
  6. Bekki, D. (2013). Dependent type semantics: an introduction. In the 2012 Edition of the LIRa Yearbook: A Selection of Papers. Amsterdam: University of Amsterdam.Google Scholar
  7. Bekki, D. (2014). Representing anaphora with dependent types. In N. Asher & S. V. Soloviev (Eds.), Proceedings of the Logical Aspects of Computational Linguistics (8th International Conference, LACL2014, Toulouse, France, June 2014), LNCS (Vol. 8535, pp. 14–29). Springer, Heiderburg.Google Scholar
  8. Bekki, D., & McCready, E. (2014). CI via DTS. In Proceedings of LENLS11 (pp. 110–123). Tokyo.Google Scholar
  9. Bekki, D., & Sato, M. (2015). Calculating projections via type checking. In The Proceedings of TYpe Theory and LExical Semantics (TYTLES), ESSLLI2015 Workshop. Barcelona, Spain.Google Scholar
  10. Bos, J. (2003). Implementing the binding and accommodation theory for anaphora resolution and presupposition projection. Computational Linguistics, 29(2), 179–210.CrossRefGoogle Scholar
  11. Chatzikyriakidis, S., & Luo, Z. (2014). Natural language inference in Coq. Journal of Logic, Language and Information, 23(4), 441–480.CrossRefGoogle Scholar
  12. Chatzikyriakidis, S., & Luo, Z. (2016). On the Interpretation of Common Nouns: Types v.s. Predicates. In Modern Perspectives in Type Theoretical Semantics, Studies of Linguistics and Philosophy. Heidelberg: Springer.Google Scholar
  13. Clark, H. H. (1975). Bridging. In S. Roger, & B. L. Nash-Webber (Eds.), In the Proceedings of TINLAP’75: Proceedings of the 1975 Workshop on Theoretical Issues in Natural Language Processing (pp. 169–174). Cambridge, Massachusetts. (Association for Computational Linguistics, Stroudsburg, PA, USA).Google Scholar
  14. Cooper, R. (1983). Quantification and Syntactic Theory. Dordrecht: Reidel.CrossRefGoogle Scholar
  15. Cooper, R. (2005). Austinian truth, attitudes and type theory. Research on Language and Computation, 3, 333–362.CrossRefGoogle Scholar
  16. Coquand, T. (1986). An analysis of Girard’s paradox. In The Proceedings of the First Symposium on Logic in Computer Science (pp. 227–236). IEEE Computer Society: Washington, D.C.Google Scholar
  17. Coquand, T., & Huet, G. (1988). The calculus of constructions. Information and Computation, 76(2–3), 95–120.CrossRefGoogle Scholar
  18. Dávila-Pérez, R. (1994). Translating English into Martin-Löf’s Theory of Types: A Compositional Approach, Technical report, University of Essex.Google Scholar
  19. Dávila-Pérez, R. (1995). Semantics and Parsing in Intuitionistic Categorial Grammar”, Ph.d. thesis, University of Essex.Google Scholar
  20. Dummett, M. (1975). What is a theory of meaning? In S. Guttenplan (Ed.), Mind and Language (pp. 97–138). Oxford: Oxford University Press.Google Scholar
  21. Dummett, M. (1976). What is a theory of meaning? (II). In Evans & McDowell (Eds.), Truth and Meaning (pp. 67–137). Oxford: Oxford University Press.Google Scholar
  22. Evans, G. (1980). Pronouns. Linguistic Inquiry, 11, 337–362.Google Scholar
  23. Fox, C. (1994a). Discourse representation, type theory and property theory. In H. Bunt, R. Muskens & G. Rentier (Eds.), The Proceedings of the International Workshop on Computational Semantics (pp. 71–80). Tilburg: Institute for Language Technology and Artificial Intelligence (ITK).Google Scholar
  24. Fox, C. (1994b). Existence presuppositions and category mistakes. Acta Linguistica Hungarica, 42(3/4), 325–339. (Published 1996).Google Scholar
  25. Francez, N., & Dyckhoff, R. (2010). Proof-theoretic semantics for a natural language fragment. Linguistics and Philosophy, 33(6), 447–477.CrossRefGoogle Scholar
  26. Francez, N., Dyckhoff, R., & Ben-Avi, G. (2010). Proof-theoretic semantics for subsentential phrases. Studia Logica, 94(3), 381–401.CrossRefGoogle Scholar
  27. Geach, P. (1962). Reference and Generality: An Examination of Some Medieval and Modern Theories. Ithaca, New York: Cornell University Press.Google Scholar
  28. Gentzen, G. (1935). Untersuchungen über das logische Schliessen I,II. Mathematische Zeitschrift 39, pp. 176–210, 405–431. (Translated as ‘Investigations into Logical Deduction’, and printed in M.E. Szabo, The Collected Works of Gerhard Gentzen, Amsterdam: North-Holland, 1969, pp. 68–131).Google Scholar
  29. Geurts, B. (1999). Presuppositions and Pronouns. Oxford: Elsevier.Google Scholar
  30. Girard, J.-Y. (1972). Interprétation fonctionnelle et élimination des coupures de l’arithmétique d’ordre supérieur. Thése de doctorat d’état: Université Paris VII.Google Scholar
  31. Groenendijk, J., & Stokhof, M. (1991). Dynamic predicate logic. Linguistics and Philosophy, 14, 39–100.CrossRefGoogle Scholar
  32. Heim, I. (1982). The Semantics of Definite and Indefinite Noun Phrases, Ph.d dissertation, University of Massachusetts. Published 1989 by Garland Press, New York.Google Scholar
  33. Heim, I., & Kratzer, A. (1998). Semantics in Generative Grammar. Malden: Blackwell Publishers.Google Scholar
  34. Hook, J. G., & Howe, D. J. (1986). Impredicative Strong Existential Equivalent to Type:Type, Technical Report TR 86–760. Department of Computer Science, Cornell University.Google Scholar
  35. Kamp, H. (1981). A theory of truth and semantic representation. In J. Groenendijk, T. M. Janssen & M. Stokhof (eds.), Formal Methods in the Study of Language. Amsterdam: Mathematical Centre Tract 135.Google Scholar
  36. Kamp, H., J. van Genabith, & U. Reyle. (2011). Discourse representation theory. In D. M. Gabbay & F. Gunthner (Eds.), Handbook of Philosophical Logic (Vol. 15, pp.125–394). Doredrecht, Springer.Google Scholar
  37. Karttunen, L. (1976). Discourse referents. In J. D. McCawley (Ed.), Syntax and Semantics 7: Notes from the Linguistic Underground (Vol. 7, pp. 363–385). New York: Academic Press.Google Scholar
  38. Krahmer, E., & Piwek, P. (1999). Presupposition projection as proof construction. In H. Bunt & R. Muskens (Eds.), Computing Meanings: Current Issues in Computational Semantics, Studies in Linguistics Philosophy Series. Dordrecht: Kluwer Academic Publishers.Google Scholar
  39. Kripke, S. (2009). Presupposition and anaphora: remarks on the formulation of the projection problem. Linguistic Inquiry, 40(3), 367–386.CrossRefGoogle Scholar
  40. Levesque, H. J. (2011). The winograd schema challenge. In The Proceedings of AAAI Spring Symposium: Logical Formalization of Commonsense Reasoning.Google Scholar
  41. Luo, Z. (2012a). Common nouns as types. In D. Béchet & A. Dikovsky (Eds.), Proceedings of the Logical Aspects of Computational Linguistics, 7th International Conference, LACL2012, Nantes, France, July 2012 (pp. 173–185). Heidelberg: Springer.Google Scholar
  42. Luo, Z. (2012b). Formal semantics in modern type theories with coercive subtyping. Linguistics and Philosophy, 35(6), 491–513.Google Scholar
  43. Luo, Z. (2014). Formal semantics in modern type theories: is it model-theoretic, proof-theoretic, or both? In N. Asher & S. V. Soloviev (Eds.), Logical Aspects of Computational Linguistics (8th International Conference, LACL2014, Toulouse, France, June 2014 Proceedings), LNCS 8535 (pp. 177–188). Toulouse: Springer.Google Scholar
  44. Magidor, O. (2013). Category Mistakes. Oxford: Oxford University Press.Google Scholar
  45. Martin-Löf, P. (1984). Intuitionistic Type Theory, G. Sambin (Ed.). Naples, Italy: Bibliopolis.Google Scholar
  46. Mikkelsen, L. (2011). Copular clauses. In Semantics: An International Handbook of Natural Language Meaning, HSK 33.2 (pp. 1805–1829). Berlin: de Gruyter.Google Scholar
  47. Mineshima, K. (2008). A presuppositional analysis of definite descriptions in proof theory. In: K. Satoh, A. Inokuchi, K. Nagao & T. Kawamura (Eds.), New Frontiers in Artificial Intelligence: JSAI 2007 Conference and Workshops, Revised Selected Papers, Lecture Notes in Computer Science (Vol. 4914, pp. 214–227). Heidelberg: Springer.Google Scholar
  48. Mineshima, K. (2013). Aspects of Inference in Natural Language, Ph.d. thesis, Keio University.Google Scholar
  49. Montague, R. (1974). Formal Philosophy. New Haven: Yale University Press.Google Scholar
  50. Nordström, B., Petersson, K., & Smith, J. (1990). Programming in Martin-Löf’s Type Theory. Oxford: Oxford University Press.Google Scholar
  51. Piwek, P., & Krahmer, E. (2000). Presuppositions in context: constructing bridges. In P. Bonzon, M. Cavalcanti, & R. Nossum (Eds.), Formal Aspects of Context, Applied Logic Series. Dordrecht: Kluwer Academic Publishers.Google Scholar
  52. Prawitz, D. (1980). Intuitionistic Logic: A Philosophical Challenge. In G. von Wright (Ed.), Logics and Philosophy. The Hague: Martinus Nijhoff.Google Scholar
  53. Ranta, A. (1994). Type-Theoretical Grammar. Oxford: Oxford University Press.Google Scholar
  54. Russell, B. (1919). Introduction to Mathematical Philosophy. Crows Nest: George Allen & Unwin.Google Scholar
  55. Soames, S. (1989). Presupposition. In D. Gabbay & F. Guenthner (Eds.), Handbook of Philosophical Logic (Vol. 4, pp. 553–616). Dordrecht: Reidel.CrossRefGoogle Scholar
  56. Steedman, M. J. (1996). Surface Structure and Interpretation. Cambridge: The MIT Press.Google Scholar
  57. Sudo, Y. (2012). On the semantics of Phi features on pronouns, Doctoral dissertation, MIT.Google Scholar
  58. Sundholm, G. (1986). Proof theory and meaning. In D. Gabbay & F. Guenthner (Eds.), Handbook of Philosophical Logic (Vol. III, pp. 471–506). Reidel: Kluwer.Google Scholar
  59. Sundholm, G. (1989). Constructive generalized quantifiers. Synthese, 79, 1–12.CrossRefGoogle Scholar
  60. Tanaka, R. (2014). A proof-theoretic approach to generalized quantifiers in dependent type semantics. In R. de Haan (Ed.), The Proceedings of the ESSLLI 2014 Student Session, 26th European Summer School in Logic, Language and Information (pp. 140–151). Tübingen, Germany.Google Scholar
  61. Tanaka, R., Mineshima, K., & Bekki, D. (2014). Resolving modal anaphora in dependent type semantics. In The Proceedings of the Eleventh International Workshop on Logic and Engineering of Natural Language Semantics (LENLS11), JSAI International Symposia on AI 2014 (pp. 43–56). Tokyo.Google Scholar
  62. Tanaka, R., Mineshima, K., Bekki, D. (2015). Factivity and presupposition in dependent type semantics. In The Proceedings of Type Theory and Lexical Semantics (TYTLES), ESSLLI2015 Workshop.Google Scholar
  63. Tanaka, R., Nakano, Y., & Bekki, D. (2013). Constructive generalized quantifiers revisited. In The Proceedings of Logic and Engineering of Natural Language Semantics 10 (LENLS 10) (pp. 69–78). Tokyo.Google Scholar
  64. van der Sandt, R. (1992). Presupposition projection as anaphora resolution. Journal of Semantics, 9, 333–377.CrossRefGoogle Scholar
  65. van der Sandt, R., & Geurts, B. (1991). Presupposition, anaphora, and lexical content. In O. Herzog & C.-R. Rollinger (Eds.), Text Understanding in LILOG (pp. 259–296). Berlin: Springer.CrossRefGoogle Scholar
  66. Watanabe, N., McCready, E., & Bekki, D. (2014). Japanese honorification: compositionality and expressivity. In S. Kawahara & M. Igarashi (Eds.), The Proceedings of FAJL 7: Formal Approaches to Japanese Linguistics, the MIT Working Papers in Linguistics 73 (pp. 265–276). International Christian University, Japan.Google Scholar

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Ochanomizu University/CREST, Japan Science and Technology Agency (JST)TokyoJapan

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