# Predict set elements based on other elements

Sorry if this has been answered before but could someone help me with solving the following problem:

Each symbol in a dataset has a set of labels. Given a set of labels how can we predict more labels for that set?

Or to attempt a more formal wording: let a set of sets $S = \{ s_1, s_2, s_3, ... \}$ where $s_i \subseteq L$ and $L = \{ l_1, l_2, l_3,...,l_m\}$ where $L$ is the finite set of labels. Given a set of labels $Y = \{ y_1 ,..., y_n \}$ where $Y \subseteq X$ what is the probability $P(r = l_i) \forall l_i \in L$ so that $Y \cup \{r\} \in S$.