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Completness of relevant modal logics with disjunctive rules

Seki T.

Reports on Mathematical Logic

2009

Vol. 44

3-18

Disjunctive rules are known to validate material implication principles, which may not hold in weaker relevant logics. On the other hand, they prevent the oddity of not preserving truth at the base world, from which many weaker relevant logics suffer. The same holds for relevant modal logics. This paper proves completeness of relevant modal logics with disjunctive rules.