On Constraint-Based Lambek Calculi
<|reference_start|>On Constraint-Based Lambek Calculi: We explore the consequences of layering a Lambek proof system over an arbitrary (constraint) logic. A simple model-theoretic semantics for our hybrid language is provided for which a particularly simple combination of Lambek's and the proof system of the base logic is complete. Furthermore the proof system for the underlying base logic can be assumed to be a black box. The essential reasoning needed to be performed by the black box is that of {\em entailment checking}. Assuming feature logic as the base logic entailment checking amounts to a {\em subsumption} test which is a well-known quasi-linear time decidable problem.<|reference_end|>
@article{doerre1995on,
    title={On Constraint-Based Lambek Calculi},
    author={Jochen Doerre and Suresh Manandhar},
    journal={arXiv preprint arXiv:cmp-lg/9508008},
    year={1995},
    number={Tech. Report HCRC/TR-69, University of Edinburgh},
    archivePrefix={arXiv},
    eprint={cmp-lg/9508008},
    primaryClass={cmp-lg cs.CL}
}