Abstract categorial grammars with island constraints and effective decidability
This work addresses syntactic island constraints in formal grammar theory, offering an incremental extension to existing methods for linguists and computational linguists.
The authors tackled the problem of modeling syntactic island constraints in abstract categorial grammars by adapting bracket modalities from Lambek grammars, resulting in a framework that allows modeling simple island constraints like relativization and ensures effective decidability for specific safely bracketed ACG.
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 $λ$-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.