  This paper investigates the problem of inferring knowledge from data so that
the inferred knowledge is interpretable and informative to humans who have
prior knowledge. Given a dataset as a collection of system trajectories, we
infer parametric linear temporal logic (pLTL) formulas that are informative and
satisfied by the trajectories in the dataset with high probability. The
informativeness of the inferred formula is measured by the information gain
with respect to given prior knowledge represented by a prior probability
distribution. We first present two algorithms to compute the information gain
with a focus on two types of prior probability distributions: stationary
probability distributions and probability distributions expressed by discrete
time Markov chains. Then we provide a method to solve the inference problem for
a subset of pLTL formulas with polynomial time complexity with respect to the
number of Boolean connectives in the formula. We provide implementations of the
proposed approach on explaining anomalous patterns, patterns changes and
explaining the policies of Markov decision processes.
