Journal of Logic, Language and Information

, Volume 25, Issue 2, pp 191–213 | Cite as

Some Properties of Iterated Languages

  • Shane Steinert-Threlkeld


A special kind of substitution on languages called iteration is presented and studied. These languages arise in the application of semantic automata to iterations of generalized quantifiers. We show that each of the star-free, regular, and deterministic context-free languages are closed under iteration and that it is decidable whether a given regular or determinstic context-free language is an iteration of two such languages. This result can be read as saying that the van Benthem/Keenan ‘Frege Boundary’ is decidable for large subclasses of natural language quantifiers. We also determine the state complexity of iteration of regular languages.


Semantic automata Generalized quantifiers Iteration Frege boundary Decidability 


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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of PhilosophyStanford UniversityStanfordUSA

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