Proof-theoretic aspects of NL$λ$
This work addresses foundational aspects of formal logic for computational linguistics, offering incremental improvements in proof theory and complexity bounds.
The paper tackles the proof-theoretic analysis of the logic NLλ by introducing a novel calculus of proof nets, proving it is sound and complete, and studies decidability and complexity, showing the logic is in NP and extends linguistic coverage.
We present a proof-theoretic analysis of the logic NL$λ$ (Barker \& Shan 2014, Barker 2019). We notably introduce a novel calculus of proof nets and prove it is sound and complete with respect to the sequent calculus for the logic. We study decidability and complexity of the logic using this new calculus, proving a new upper bound for complexity of the logic (showing it is in NP) and a new lower bound for the class of formal language generated by the formalism (mildly context-sensitive languages extended with a permutation closure operation). Finally, thanks to this new calculus, we present a novel comparison between NL$λ$ and the hybrid type-logical grammars of Kubota \& Levine (2020). We show there is an unexpected convergence of the natural language analyses proposed in the two formalism. In addition to studying the proof-theoretic properties of NL$λ$, we greatly extends its linguistic coverage.