Abstract categorial grammars with island constraints and effective decidability

TL;DR

This paper extends abstract categorial grammars with island constraints using bracketed linear logic, enabling effective decidability while modeling complex syntactic phenomena like relativization.

Contribution

It introduces bracketed ACGs with island constraints, achieving effective decidability and modeling higher-order syntactic phenomena.

Findings

Bracketed ACGs can model island constraints.

Safely bracketed ACGs generate effectively decidable languages.

The approach handles relativization and syntactic islands in simple examples.

Abstract

A well-known approach to treating syntactic island constraints in the setting of Lambek grammars consists in adding specific bracket modalities to the logic. We adapt this approach to abstract categorial grammars (ACG). Thus we define bracketed (implicational) linear logic, bracketed lambda-calculus, and, eventually, bracketed ACG based on bracketed $\lambda$-calculus. This allows us modeling at least simplest island constraints, typically, in the context of relativization. Next we identify specific safely bracketed ACG which, just like ordinary (bracket-free) second order ACG generate effectively decidable languages, but are sufficiently flexible to model some higher order phenomena like relativization and correctly deal with syntactic islands, at least in simple toy examples.