Sequent and hypersequent calculi for abelian and łukasiewicz logics

@article{Metcalfe2005SequentAH,
  title={Sequent and hypersequent calculi for abelian and łukasiewicz logics},
  author={George Metcalfe and Nicola Olivetti and Dov M. Gabbay},
  journal={ArXiv},
  year={2005},
  volume={cs.LO/0211021}
}
We present two embeddings of Łukasiewicz logic <b>Ł</b> into Meyer and Slaney's Abelian logic <b>A</b>, the logic of lattice-ordered Abelian groups. We give new analytic proof systems for <b>A</b> and use the embeddings to derive corresponding systems for <b>Ł</b>. These include hypersequent calculi, terminating hypersequent calculi, co-NP labeled sequent calculi, and unlabeled sequent calculi. 

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