Abstract

It is known that the implicational fragment of the relevant logic E is complete with respect to the class of Urquhart's models, where a model consists of a semilattice and a set of possible worlds. This paper shows that some implicational relevant logics, which are obtained from E by adding axioms, are complete with respect to the class of Urquhart's models with certain conditions. To show this, we introduce labelled sequent calculi