 It follows from (O1–2) that \(P(n)F(n)p \equiv p\) and \(F(n)P(n)p \equiv p\) are valid theses in the semantics. Furthermore, it is easily verified that (T3′), (T4), and (T5) are valid as well in the system. It is also obvious that \(P(n)F(n+m)p \supset \Box P(n)F(n+m)p\) is not valid in general according to this semantics. In consequence, the crucial principle (P3) should be rejected on this view. It seems that the semantics sketched here will have all the properties, which one would expect in Ockhamistic (and Molinistic) semantics (see Øhrstrøm 2014; Øhrstrøm and Jakobsen 2018; De Florio and Frigerio 2019).