The core idea of vector logic is to represent the classical truth values \(W\), \(F\) as two linearly independent vectors \(a_ 1\), \(a_ 2\) of some real vector space, and to represent truth functions by matrices. This idea is first extended to the many-valued case in taking the convex hull of \(\{a_ 1, a_ 2\}\) as set of truth degrees. On this basis, secondly, the old idea of Łukasiewicz and Tarski, to define \(\lozenge p=_{\text{def}}\neg p\to p\) in a 3-valued logic, is adapted in such a way that \(\lozenge p\) is defined truth-functionally as the limit of a suitable sequence of vectors. There is no discussion concerning the existence of these limits. But there is proven a sequence of formulas which also hold true in the standard systems of modal logic. Nevertheless, the meaning of this reformulation remains unclear.