Linguistics and Philosophy

, Volume 29, Issue 1, pp 91–134 | Cite as

Explaining Crossover and Superiority as Left-to-right Evaluation

Article

Abstract

We present a general theory of scope and binding in which both crossover and superiority violations are ruled out by one key assumption: that natural language expressions are normally evaluated (processed) from left to right. Our theory is an extension of Shan’s (2002) account of multiple-wh questions, combining continuations (Barker, 2002) and dynamic type-shifting. Like other continuation-based analyses, but unlike most other treatments of crossover or superiority, our analysis is directly compositional (in the sense of, e.g., Jacobson, 1999). In particular, it does not postulate a level of Logical Form or any other representation distinct from surface syntax. One advantage of using continuations is that they are the standard tool for modeling order-of-evaluation in programming languages. This provides us with a natural and independently motivated characterization of what it means to evaluate expressions from left to right. We give a combinatory categorial grammar that models the syntax and the semantics of quantifier scope and wh-question formation. It allows quantificational binding but not crossover, in-situ wh but not superiority violations. In addition, the analysis automatically accounts for a variety of sentence types involving binding in the presence of pied piping, including reconstruction cases such as Whose criticism of hisi mother did each personi resent?

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barker, C. 2002‘Continuations and the Nature of Quantification’Natural Language Semantics10211242CrossRefGoogle Scholar
  2. Barker, C. 2004, ‘Continuations in Natural Language’, in Hayo Thielecke (ed.), CW’04: Proceedings of the 4th ACM SIGPLAN Continuations Workshop, pp. 1–11. Tech. Rep. CSR-04-1, School of Computer Science, University of Birmingham.Google Scholar
  3. Barker, C. 2005‘Remark on Jacobson 1999: Crossover as a Local Constraint’Linguistics and Philosophy4447472CrossRefGoogle Scholar
  4. Barker, C. and C.-C. Shan in press, ‘Types as Graphs: Continuations in Type Logical Grammar’, Journal of Logic, Language and Information.Google Scholar
  5. Bresnan, J. 1994, ‘Linear Order vs. Syntactic Rank: Evidence from Weak Crossover’, in CLS 30-1: The Main Session. Chicago Linguistic Society.Google Scholar
  6. Bresnan, J. 1998

    ‘Morphology Competes with Syntax: Explaining Typological Variation in Weak Crossover Effects’

    Barbosa, P.Fox, D.Hagstrom, P.McGinnis, M.Pesetsky, D. eds. Is the Best Good Enough? Optimality and Competition in SyntaxMIT PressCambridge5992
    Google Scholar
  7. Büring, D. 2001

    ‘A Situation Semantics for Binding out of DP

    Hastings, R.Jackson, B.Zvolensky, Z. eds. SALT XI: Semantics and Linguistic TheoryCornell University PressIthaca5675
    Google Scholar
  8. Büring, D. 2004‘Crossover Situations’Natural Language Semantics122362CrossRefGoogle Scholar
  9. Chierchia G. (1991), ‘Functional WH and Weak crossover’. In: Bates, D. (eds). Proceedings of the 10th West Coast Conference on Formal Linguistics, pp. 75–90. Center for the Study of Language and Information, Stanford, CA.Google Scholar
  10. Chierchia, G. 1993‘Questions with Quantifiers’Natural Language Semantics1181234CrossRefGoogle Scholar
  11. Chierchia, G. 1995The Dynamics of Meaning: Anaphora, Presupposition, and the Theory of GrammarUniversity of Chicago PressChicagoGoogle Scholar
  12. Chomsky, N. 1973

    ‘Conditions on Transformations’

    Anderson, S.Kiparsky, P. eds. A Festschrift for Morris HalleHolt, Rinehart and WinstronNew York232286
    Google Scholar
  13. Danvy, O. and A. Filinski: 1989, ‘A Functional Abstraction of Typed Contexts’. Tech. Rep. 89/12, DIKU, University of Copenhagen, Denmark. http://www.daimi.au.dk/~danvy/Papers/fatc.ps.gz.
  14. Danvy, O. 1990, ‘Abstracting Control’, in Proceedings of the 1990 ACM Conference on Lisp and Functional Programming, pp. 151–160. ACM Press, New York.Google Scholar
  15. Danvy, O. 1992‘Representing Control: A Study of the CPS Transformation’Mathematical Structures in Computer Science2361391CrossRefGoogle Scholar
  16. Dayal, V. 1996Locality in WH Quantification: Questions and Relative Clauses in HindiKluwerDordrechtGoogle Scholar
  17. Dayal, V. 2003

    ‘Multiple WH Questions’

    Everaert, M.Riemsdijk, H.C. eds. The Blackwell Companion to SyntaxBlackwellOxford
    Google Scholar
  18. Dowty, D.: 1991, ‘Variable-free’ Syntax, Variable-Binding Syntax, the Natural Deduction Lambek Calculus, and the Crossover Constraint, in J. Mead. (ed.), Proceedings of the 11th West Coast Conference on Formal Linguistics, Center for the Study of Language and Information, Stanford, CA.Google Scholar
  19. Felleisen, M. 1987, ‘The Calculi of λv-CS Conversion: A Syntactic Theory of Control and State in Imperative Higher-order Programming Languages’, Ph.D. thesis, Computer Science Department, Indiana University. Also as Tech. Rep. 226.Google Scholar
  20. Felleisen, M. 1988, ‘The Theory and Practice of First-Class Prompts’, in POPL ’88: Conference Record of the Annual ACM Symposium on Principles of Programming Languages, pp. 180–190. ACM Press, New York.Google Scholar
  21. Griffin, T. G. 1990, ‘A Formulae-as-Types Notion of Control’, in POPL ’90: Conference Record of the Annual ACM Symposium on Principles of Programming Languages, pp. 47–58. ACM Press, New York.Google Scholar
  22. de Groote, P. 2001, ‘Type Raising, Continuations, and Classical Logic’, in Robert van Rooy and Martin Stokhof, (eds.), Proceedings of the 13th Amsterdam Colloquium, pp. 97–101. Institute for Logic, Language and Computation, Universiteit van Amsterdam.Google Scholar
  23. Heim, I., Kratzer, A. 1998Semantics in Generative GrammarBlackwellOxfordGoogle Scholar
  24. Hendriks, H. 1993, ‘Studied Flexibility: Categories and Types in Syntax and Semantics’, Ph.D. thesis, Institute for Logic, Language and Computation, Universiteit van Amsterdam.Google Scholar
  25. Higginbotham, J. 1980‘Pronouns and Bound Variables’Linguistic Inquiry11679708Google Scholar
  26. Hindley, J.R., Seldin, J.P. 1986Introduction to Combinators and λ-CalculusCambridge University PressCambridgeGoogle Scholar
  27. Hornstein, N. 1995Logical Form: From GB to MinimalismBlackwellOxfordGoogle Scholar
  28. Jacobson, P. 1999‘Towards a Variable-Free Semantics’Linguistics and Philosophy22117184CrossRefGoogle Scholar
  29. Jäger, G. 2001, ‘Anaphora and Type Logical Grammar’, Habilitationsschrift, Humboldt University Berlin. UIL-OTS Working Papers 01004-CL/TL, Utrecht Institute of Linguistics (OTS), Utrecht University.Google Scholar
  30. Kuno, S., Robinson, J.J. 1972‘Multiple wh Questions’Linguistic Inquiry3463487Google Scholar
  31. Lasnik, H., Stowell, T. 1991‘Weakest Crossover’Linguistic Inquiry22687720Google Scholar
  32. May, R. 1985Logical Form: Its Structure and DerivationMIT PressCambridgeGoogle Scholar
  33. Meyer, A.R., Wand, M. 1985

    ‘Continuation Semantics in Typed Lambda-Calculi (summary)

    Parikh, R. eds. Logics of programsSpringer-VerlagBerlin219224Lecture Notes in Computer Science 193
    Google Scholar
  34. Moortgat, M. 1997

    ‘Categorial Type Logics’

    Benthem, J.F.A.K.ter Meulen, A.G.B. eds. Handbook of Logic and LanguageElsevier ScienceAmsterdamchap. 2
    Google Scholar
  35. O’Neil, J. 1993

    ‘A unified Analysis of Superiority, Crossover, and Scope’

    Thráinsson, H.Epstein, S.D.Kuno, S. eds. Harvard working papers in linguisticsHarvard UniversityCambridge128136vol. III
    Google Scholar
  36. Papaspyrou, N.S. 1998

    ‘Denotational Semantics of Evaluation Order in Expressions with Side Effects’

    Mastorakis, N.E. eds. Recent Advances in Information Science and Technology: 2nd part of the Proceedings of the 2nd IMACS International Conference on Circuits, Systems and ComputersWorld ScientificSingapore8794
    Google Scholar
  37. Parigot, M. 1992

    ‘λ μ-Calculus: An Algorithmic Interpretation of Classical Natural Deduction’

    Voronkov, A. eds. Proceedings of LPAR ’92: International Conference on Logic Programming and Automated Reasoning.Springer-VerlagBerlin190201Lecture Notes in Artificial Intelligence 624
    Google Scholar
  38. Parigot, M. 1993

    ‘Classical Proofs as Programs’

    Gottlob, G.Leitsch, A.Mundici, D. eds. Proceedings of KGC’93: Computational Logic and Proof Theory, 3rd Kurt Gödel ColloquiumSpringer-VerlagBerlin263276Lecture Notes in Computer Science 713
    Google Scholar
  39. Partee, B.H. 1987

    ‘Noun Phrase Interpretation and Type-Shifting Principles’

    Groenendijk, J.Jongh, D.Stokhof, M. eds. Studies in Discourse Representation Theory and the Theory of Generalized QuantifiersGroningen-Amsterdam Studies in Semantics 8Foris, Dordrecht115143
    Google Scholar
  40. Partee, B.H., Mats Rooth,  1983

    ‘Generalized Conjunction and Type Ambiguity’

    Bäuerle, R.Schwarze, C.Stechow, A. eds. Meaning, Use and Interpretation of Languagede GruyterBerlin361383
    Google Scholar
  41. Pesetsky, D. 1987

    ‘Wh-In-situ: Movement and Unselective Binding’

    Reuland, E.J.ter Meulen, A.G.B. eds. The Representation of (In) DefinitenessMIT PressCambridge
    Google Scholar
  42. Phillips, C. 2003‘Linear Order and Constituency’Linguistic Inquiry343790CrossRefGoogle Scholar
  43. Plotkin, G.D. 1975‘Call-by-Name, Call-by-Value and the λ-Calculus’Theoretical Computer Science1125159CrossRefGoogle Scholar
  44. Postal, P.M. 1971Cross-over PhenomenaHolt, Rinehart and WinstonNew YorkGoogle Scholar
  45. Postal, P.M. 1993‘Remarks on Weak Crossover Effects’Linguistic Inquiry24539556Google Scholar
  46. Potts, C. 2001‘(Only) Some Crossover Effects Repaired’Snippets31314Google Scholar
  47. Reinhart, T. 1983Anaphora and Semantic InterpretationCroom HelmLondonGoogle Scholar
  48. Ruys, E.G. 2000‘Weak Crossover as a Scope Phenomenon’Linguistic Inquiry31513539CrossRefGoogle Scholar
  49. Shan, Chung-chieh 2002

    ‘A Continuation Semantics of Interrogatives that Accounts for Baker’s Ambiguity’

    Jackson, B. eds. SALT XII: Semantics and Linguistic TheoryCornell University PressIthaca246265
    Google Scholar
  50. Sitaram, D., Flleisen, M. 1990‘Control Delimiters and Their HierarchiesLisp and Symbolic Computation36799CrossRefGoogle Scholar
  51. Steedman, M. 2000‘The Syntactic Process’MIT PressCambridgeGoogle Scholar
  52. Sternefeld, W. 1997, ‘The Semantics of Reconstruction and Connectivity’, Arbeitspapiere des SFB 340 97, Universität Stuttgart and Tübingen.Google Scholar
  53. Tanenhaus, M.K., Garnsey, S.M., Boland, J. 1990

    ‘Combinatory Lexical Information and Language Comprehension’

    Altmann, G.T.M. eds. Cognitive Models of Speech Processing: Psycholinguistic and Computational PerspectivesMIT PressCambridge383408
    Google Scholar
  54. Wadler, P.L. 1992‘Comprehending Monads’Mathematical Structures in Computer Science2461493Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Department of Computer Science and Center for Cognitive ScienceRutgers, the State University of New JerseyPiscatawayUSA
  2. 2.0108 Department of LinguisticsUniversity of California San DiegoLa JollaUSA

Personalised recommendations