Journal of Logic, Language and Information

, Volume 12, Issue 1, pp 13–45 | Cite as

A Two-Variable Fragment of English

  • Ian Pratt-Hartmann


Controlled languages are regimented fragments of natural languagedesigned to make the processing of natural language more efficient andreliable. This paper defines a controlled language, E2V, whose principalgrammatical resources include determiners, relative clauses, reflexivesand pronouns. We provide a formal syntax and semantics for E2V, in whichanaphoric ambiguities are resolved in a linguistically natural way. Weshow that the expressive power of E2V is equal to that of thetwo-variable fragment of first-order logic. It follows that the problemof determining the satisfiability of a set of E2V sentences is NEXPTIMEcomplete. We show that E2V can be extended in various ways withoutcompromising these complexity results; however, relaxing our policy onanaphora resolution renders the satisfiability problem for E2Vundecidable. Finally, we argue that our results have a bearing on thebroader philosophical issue of the relationship between natural andformal languages.

controlled languages logic natural language specification two-variable fragment 


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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Ian Pratt-Hartmann
    • 1
  1. 1.Department of Computer ScienceUniversity of ManchesterManchesterU.K.

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