TY - JOUR
T1 - Relevance and paraconsistency—A new approach. Part III
T2 - Cut-free gentzen-type systems
AU - Avron, Arnon
PY - 1991
Y1 - 1991
N2 - 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 hyperse-quents (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.
AB - 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 hyperse-quents (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.
UR - http://www.scopus.com/inward/record.url?scp=84972526024&partnerID=8YFLogxK
U2 - 10.1305/ndjfl/1093635673
DO - 10.1305/ndjfl/1093635673
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AN - SCOPUS:84972526024
SN - 0029-4527
VL - 32
SP - 129
EP - 160
JO - Notre Dame Journal of Formal Logic
JF - Notre Dame Journal of Formal Logic
IS - 1
ER -