Axiomatisations of the modal calculus $Q$.
Arthur N. Prior · Notre Dame Journal of Formal Logic · 1964
R. A. Bull has shown in [l] that the modal calculus Q of [2] may be axiomatised by taking as primitives a strong and a weak necessity L and L, and by adding to PC the axioms Al.CLpp A2.CLpp A3.CKLpLqLKpq and the rules (beside substitution and detachment)RQLa: h Cβγ -^VCβLy, for β fully modalised and with all its variables occurring in γ.RQLb: VClaCβY -^VCLaCβLγ, for β fully modalised and with all its variables occurring in a or γ.RQL: VCLaCβry -> VCLaCβLγ, for β fully modalised and with all variables of β and γ occurring in a.