A 2-set-up Routley-Meyer Semantics for the 4-valued Relevant Logic E4
![No Thumbnail [100%x80]](data:image/svg+xml;base64,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)
Abstract
The logic BN4 can be considered as the 4-valued logic of the relevant conditional and the logic E4, as the 4-valued logic of (relevant) entailment. The aim of this paper is to endow E4 with a 2-set-up Routley-Meyer semantics. It is proved that E4 is strongly sound and complete w.r.t. this semantics.