Deducibility in the full Lambek calculus with weakening is HAckcomplete
Abstract
We prove that the problem of deciding the consequence relation of the full Lambek calculus with weakening is complete for the class HAck of hyperAckermannian problems (i.e., level F_{\omega}^{\omega} of the ordinalindexed hierarchy of fastgrowing complexity classes). Provability was already known to be PSPACEcomplete. We prove that deducibility is HAckcomplete even for the multiplicative fragment. Lower bounds are proved via a novel reduction from reachability in lossy channel systems and the upper bounds are obtained by combining structural proof theory (forward proof search over sequent calculi) and wellquasiorder theory (length theorems for Higman's Lemma).
 Publication:

arXiv eprints
 Pub Date:
 June 2024
 DOI:
 10.48550/arXiv.2406.15626
 arXiv:
 arXiv:2406.15626
 Bibcode:
 2024arXiv240615626G
 Keywords:

 Computer Science  Logic in Computer Science;
 Computer Science  Computational Complexity;
 Mathematics  Logic;
 03B47;
 F.4.1;
 F.2.2