The semantics ofR4

The LogicR4 is obtained by adding the axiom (A vB(AvB) to the modal relevant logicNR. We produce a model theory for this logic and show completeness. We also show that there is a natural embedding of a Kripke model forS4 in eachR4 model structure.We are indebted to several people for discussions relating to the topic of this paper, in particular, Kit Fine, John Slaney, J. M. Dunn, Jacques Riche, M. A. McRobbie, and Jill LeBlanc. We would also like to thank the Automated Reasoning Project for material assistance. Mares would like to thank The Social Sciences and Humanities Research Council of Canada for fellowships 456-89-0128 and 457-90-0081, which supported him while writing this paper.