# 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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