Some relevance logics from the point of view of relational semantics

A logic can have certain desirable properties, but at the same time, it can exhibit some unattractive features too. We scrutinize some relevance logics—starting with implicational ticket entailment and continuing toward relevant implication with negation—from the point of view of the standard relational semantics for relevance logics. We define sound and complete semantics for the implicational fragments using a generalized accessibility relation and amending an earlier idea about the canonical situations. In some other cases, the semantics do not work out as expected. All the logics that we consider are decidable, which we use to prove that certain semantical constructions cannot come to fruition.