Sequent and Hypersequent Calculi for Abelian and Lukasiewicz Logics
<|reference_start|>Sequent and Hypersequent Calculi for Abelian and Lukasiewicz Logics: We present two embeddings of infinite-valued Lukasiewicz logic L into Meyer and Slaney's abelian logic A, the logic of lattice-ordered abelian groups. We give new analytic proof systems for A and use the embeddings to derive corresponding systems for L. These include: hypersequent calculi for A and L and terminating versions of these calculi; labelled single sequent calculi for A and L of complexity co-NP; unlabelled single sequent calculi for A and L.<|reference_end|>
@article{metcalfe2002sequent,
    title={Sequent and Hypersequent Calculi for Abelian and Lukasiewicz Logics},
    author={G. Metcalfe, N. Olivetti and D. Gabbay},
    journal={arXiv preprint arXiv:cs/0211021},
    year={2002},
    archivePrefix={arXiv},
    eprint={cs/0211021},
    primaryClass={cs.LO}
}