  In this work, we propose a novel method to find temporal properties that lead
to the unexpected behaviors from labeled dataset. We express these properties
in past time Signal Temporal Logic (ptSTL). First, we present a novel approach
for finding parameters of a template ptSTL formula, which extends the results
on monotonicity based parameter synthesis. The proposed method optimizes a
given monotone criteria while bounding an error. Then, we employ the parameter
synthesis method in an iterative unguided formula synthesis framework. In
particular, we combine optimized formulas iteratively to describe the causes of
the labeled events while bounding the error. We illustrate the proposed
framework on two examples.
