DEFINING RELEVANT IMPLICATION IN A PROPOSITIONALLY QUANTIFIED S4

R. K. Meyer once gave precise form to the question of whether relevant implication can be defined in any modal system, and his answer was 'n o'. In the present paper, we extend S4, first with propositional quant ifiers, to the system S4 pi+; and then with definite propositional des criptions, to the system S4 pi+(ip). We show that relevant implication can in some sense be defined in the modal system S4 pi+(ip), although it cannot be defined in S4 pi+.