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Workshop on Proof Theory, Modal Logic and Reflection Principles
October 20, 2017 10:35, Moscow, Steklov Mathematical Institute

Lambek calculus extended with subexponential and bracket modalities

A. Scedrov
 Video records: MP4 828.7 Mb MP4 226.9 Mb

For instance, an extension with so-called bracket modalities introduced by Morrill (1992) and Moortgat (1995) is capable of representing controlled non-associativity and is suitable for the modeling of islands. The syntax is more involved than the syntax of a standard sequent calculus. Derivable objects are sequents of the form Gamma $\to$ A , where the antecedent Gamma is a structure called meta-formula and the succedent A is a formula. Meta-formulae are built from formulae (types) using two metasyntactic operators: comma and brackets.