Abstract
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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Kobele, G.M., Salvati, S. (2013). The IO and OI Hierarchies Revisited. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7966. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39212-2_31
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