  Tennant’s core logic, however, accepts disjunctive syllogism. It also accepts conjunction elimination and disjunction introduction. In fact, Core Logic supports all the standard primitive rules that we find in the proof theory of   intuitionist logic. Thus, one could say that the meanings of the connectives in Core logic are just their meanings in intuitionist logic. What is different is its treatment of one of the structural rules of proof -- it rejects the transitivity of logical consequence in its most general form. 