21st International Symposium, Fundamentals of Computation Theory 2017, FCT 2017
This book constitutes the refereed proceedings of the 21st International Symposium on Fundamentals of Computation Theory, FCT 2017, held in Bordeaux, France, in September 2017. The 29 revised full papers and 5 invited papers presented were carefully reviewed and selected from 99 submissions. The papers cover topics of all aspects of theoretical computer science, in particular algorithms, complexity, formal and logical methods.
The Lambek calculus is a well-known logical formalism for modelling natural language syntax. The original calculus covered a substantial number of intricate natural language phenomena, but only those restricted to the context-free setting. In order to address more subtle linguistic issues, the Lambek calculus has been extended in various ways. In particular, Morrill and Valentín (2015) introduce an extension with so-called exponential and bracket modalities. Their extension is based on a non-standard contraction rule for the exponential that interacts with the bracket structure in an intricate way. The standard contraction rule is not admissible in this calculus. In this paper we prove undecidability of the derivability problem in their calculus. We also investigate restricted decidable fragments considered by Morrill and Valentín and we show that these fragments belong to the NP class.