This paper follows in Pavel Tichý’s concept of distinguishing between trivial (i.e. constant) and non-trivial properties. This classification has been extended by Pavel Cmorej who distinguished two kinds of non-trivial properties, namely purely empirical and partly essential (which are partly empirical) properties (partly essential property is essential for certain individual(s), but that it is not for other(s)). The present study provides rigorous formal definitions of trivial / non-trivial, essential / non-essential, and purely empirical / partly essential / purely essential properties (...) with respect to the possible partiality of these properties. In addition, a definition of trivially void properties completing the classification of the kinds of properties to form a quadruplet is proposed. Furthermore, the introduction of the concept of accidental properties gives rise to another (yet not equivalent) quadruplet: purely accidental / partly essential (i.e. partly accidental) / purely essential / void properties. (shrink)