The IO and OI Hierarchies Revisited

  • Gregory M. Kobele
  • Sylvain Salvati
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7966)


We study languages of λ-terms generated by IO and OI unsafe grammars. These languages can be used to model meaning representations in the formal semantics of natural languages following the tradition of Montague [19]. Using techniques pertaining to the denotational semantics of the simply typed λ-calculus, we show that the emptiness and membership problems for both types of grammars are decidable. In the course of the proof of the decidability results for OI, we identify a decidable variant of the λ-definability problem, and prove a stronger form of Statman’s finite completeness Theorem [28].


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Gregory M. Kobele
    • 1
  • Sylvain Salvati
    • 2
  1. 1.University of ChicagoUSA
  2. 2.INRIA, LaBRIUniversité de BordeauxFrance

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