Relevance and paraconsistency---a new approach. III. Cut-free Gentzen-type systems.
Arnon Avron · Notre Dame Journal of Formal Logic · 1990
The system RMI is a purely relevance logic based on the intuitive ideas of relevance domains and degrees of significance.In this paper, we show that unlike the systems of Anderson and Belnap, RMI has a corresponding cut-free, Gentzen-type version.This version manipulates hypersequents (i.e.finite sequences of ordinary sequents), and no translation of those hypersequents into the language of RMI is possible.This shows that RMI is multiple-conclusioned in nature and hints on possible applications of it to the study of parallelism.